21 September 2023

The medium's reflection is a common phenomenon involving the absorption of photon energy and the release of excess energy by unstable electrons:

Reflection is a philosophical term with no significant mathematical application and physical analysis behind it.

However, what actually happens in reflection is that when a photon enters a transparent medium with a reflective coating surface, it is absorbed by electrons in the atoms of both mediums and converted into electron-energy. This destabilizes the electrons, causing them to release excess energy as they release photons, moving forward until the released photons leave the medium.

Energy absorption, and the energy released by unstable electrons, occurs with almost all media, when photons enter transparent media and strike reflective media, as well as when hitting opaque media - with a variation in excess energy released by electrons after absorption.

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The above statement presents an interesting perspective on the concept of "reflection," specifically focusing on its interaction with photons and electrons within a medium. Below is the break down of analysis of the statement:
Reflection as a Philosophical Term: The statement begins by characterizing "reflection" as a philosophical term with no significant mathematical application and physical analysis. This interpretation aligns with the common dictionary definition of "reflection" as the bouncing back of light, heat, or sound without absorbing it. In everyday language, "reflection" often refers to the more general idea of something bouncing back or being mirrored in thought or consideration. However, this statement implies that this common understanding does not encompass the scientific or mathematical aspects of reflection.
Scientific Description of Reflection: The statement then delves into a scientific explanation of what occurs during reflection in the context of photons and electrons within a medium. It describes how when a photon enters a transparent medium with a reflective coating, it is absorbed by electrons, converted into electron energy, and causes the destabilization of electrons. This destabilization results in the release of excess energy in the form of photons, which continue moving forward until they leave the medium. This scientific description provides a detailed account of the physical processes involved in reflection, emphasizing the absorption and release of energy by electrons.
Variation in Energy Absorption and Release: The statement also notes that energy absorption and release by unstable electrons occur with almost all media, whether they are transparent, reflective, or opaque. It acknowledges that there can be variations in the amount of excess energy released by electrons after absorption, which likely depends on the specific properties of the medium and the incident photons.
Overall, this statement highlights the contrast between the common, everyday understanding of "reflection" as a philosophical concept and the more precise scientific description that involves the behavior of photons and electrons within a medium. It suggests that while the common definition is widely accepted in everyday language and communication, the scientific aspect of reflection involves complex physical processes and mathematical principles that go beyond the common understanding.

20 September 2023

Measuring space-time by event-scale?

I just cannot accept this! David, "measuring space-time by event-scale"

You have to have your own sense, before you even try to talk nonsense to others, unfortunately you don't seem to have any sense.

What do you mean by curvature, and what is curved?

You cannot bend something that is not a physical entity, but a dimension of physical entity or dimension of events.

You can bend a sheet of metal, but you can't bend the concept of a measuring scale, which measures the size of the sheet of metal. If you could bend the measuring scale that measures sheet metal, how would you do it? Are you saying that you can curve the unit of measurement scale to 1+x inches or 1-x inches?!

You can't do it, unless you go crazy.

Spacetime is the dimension of space and time so they are concepts of extension in length, width and depth, while time is another dimension. Existential events occur within these dimensions and are measured by these dimensions.

But not that these dimensions are events, and you measure these dimensions on the scale of events!

Events themselves are not the scale of measurement.

Special relativity, because of its arbitrariness, and usurping the independence of time, fails to realize these fundamental concepts.

specialrelativity

19 September 2023

Photon Interactions in Gravity and Antigravity:

Date: 19-09-2023  ORCiD: 0000-0003-1871-7803

Conservation, Dark Energy, and Redshift Effects:

Abstract:
This paper delves into the intricate interactions of photons in the realms of gravity and antigravity. Photons, being fundamental particles of light, exhibit remarkable behaviors as they traverse through the cosmos. They journey through the vast expanses of the universe until they venture into the enigmatic invisible realm. The photon's encounters with gravity and antigravity are explored in detail. When confronting the gravitational influence of massive objects, such as celestial bodies, photons neither gain nor lose energy, but they exchange momentum with the external gravitational field while steadfastly preserving their intrinsic momentum. Intriguingly, the photon's interaction with the mysterious force of antigravity, propelled by dark energy, presents an irreversible transformation. The consequences of this interaction are profound, as photons undergo a cosmic redshift of a magnitude greater than that induced by gravity or other redshift mechanisms. This distinctive effect manifests as the photon departs from the gravitational embrace of galaxies and embarks on a journey beyond their boundaries, where the domain of zero gravity commences. 

Furthermore, the paper elucidates the dynamics of external forces exerted by massive objects on photons during their interactions. These forces momentarily carry the photons while they engage with the massive objects. Yet, despite this external assistance, the photons maintain their original momentum. Notably, within a gravitational field, the effective deviation from this transportation remains zero, reaffirming the photon's commitment to its initial trajectory.

1. Introduction:
This paper delves into the intriguing realm of photon interactions within the gravitational and antigravitational landscapes. Photons, as fundamental particles of light, play a pivotal role in the cosmos, journeying through the fabric of space and encountering various external forces along their path.

One of the remarkable attributes of photons is their unvarying speed, always traversing at the cosmic speed limit, the speed of light, unless subjected to interactions with matter. Within the scope of this exploration lies the enigmatic phenomenon of photons venturing into the invisible universe, a domain beyond the grasp of current observational instruments.

These interactions encompass the intricate interplay between photons, gravity, and antigravity, with dark energy serving as a mysterious driving force. Here, photons exchange momentum with the gravitational field of massive objects, sustaining their intrinsic energy, and yet, they succumb to the inexorable influence of antigravity, leading to an irreversible cosmic redshift.

This paper unravels the complex dynamics of photon behavior, shedding light on their resilience in the face of gravity and their ultimate surrender to the cosmic forces that govern the cosmos. Through a comprehensive analysis of these interactions, we aim to deepen our understanding of the fundamental principles that govern the behavior of photons in the universe and the enigmatic realms they traverse.

1.1. Method:
In the paper, we explore the behavior of photons in the presence of gravitational and antigravitational forces, including the influence of dark energy. The following sections provide an outline of the key concepts and findings:

Section 1: Introduction
Introduce the topic of photon interactions in gravitational and antigravitational fields. Mention the dual nature of photons as particles and waves. Define the objective: to understand how photons behave when subjected to gravity, antigravity, and dark energy.

Section 2: Fundamental Photon Characteristics
Describe the fundamental properties of photons, including their masslessness and constant speed in a vacuum. Explain how photons always travel at the speed of light (c) from the moment of their creation. Reference the equation E = hf to underscore the relationship between photon energy and frequency.

Section 3: Photon Behavior in Gravity
Discuss how photons interact with gravity, a familiar force that attracts objects with mass. Explain that photons neither gain nor lose energy when crossing a gravitational field. Reference the equation ΔEg = 0 to emphasize that the photon maintains its energy and momentum in a gravitational field. Describe the concept of effective deviation (0 = Δρ - Δρ) and how the photon returns to its original path after gravitational interaction.

Section 4: Antigravity and Irreversible Effects
Introduce the concept of antigravity and its counteracting force to gravity. Explain that antigravity has an irreversible effect on photons due to cosmic redshift. Define cosmic redshift (zc) and explain that it occurs when a photon leaves the influence of a galaxy. Mention the zero-gravity sphere of radius as the boundary where antigravity begins to influence photons.

Section 5: Photon-Electron Interactions in Dense Transparent Media
Transition to the topic of photon interactions with matter, specifically in dense but transparent media. Describe how photons can be absorbed by electrons in such media and temporarily converted into electron energy. Explain that electrons in an excited state eventually release excess energy as photons, leading to time delays.

Section 6: Equations Describing Photon-Matter Interactions
Present equations like E = hf, ΔE = hΔf, f/Δf, and E/ΔE to describe photon-matter interactions. Show how these equations quantify changes in photon energy and frequency during interactions.

Section 7: Time Delay in Photon Passage
Explain that the cumulative effect of photon-electron interactions leads to time delays (Δt) in photon passage. Reference group velocity dispersion as a relevant concept in optics and telecommunications.

Section 8: Photon Energy Variation in Strong Gravitational Fields
Discuss the variation of photon energy in strong gravitational fields, referencing the equation Eg = E + ΔE = E - ΔE. Emphasize the constancy of total energy despite changes in momentum (Δρ). Reiterate the importance of maintaining energy equivalence even in gravitational environments.

Section 9: Momentum and Wavelength Changes under Gravitational Influence. 
Explain how photons experience changes in momentum (Δρ) and wavelengths (λ) in strong gravitational fields. Present equations such as Eg = E + Δρ = E - Δρ and h/Δλ = h/-Δλ to illustrate these changes. 

Section 10: Consistency of Photon Energy in Gravitational Fields
Reiterate the constancy of total photon energy in the presence of strong gravitational fields (Eg = E). Highlight the symmetry in changes in photon momentum (Δρ) and the role of the Planck length-to-time ratio (ℓP/tP).

Section 11: Conclusion
Summarize the main findings related to photon interactions in gravity and antigravity. Emphasize the importance of understanding these interactions for various scientific and technological applications.

Section 12: Future Directions
Suggest potential avenues for further research, such as exploring the practical implications of these interactions or conducting experiments to validate the findings.

Section 13: References.

2: Fundamental Photon Characteristics

In this section, we will describe the fundamental properties of photons, including their masslessness and constant speed in a vacuum. We will also explain how photons always travel at the speed of light (c) from the moment of their creation. To do so, we will reference the equation E = hf to underscore the relationship between photon energy and frequency.

Masslessness of Photons: Photons are elementary particles that possess a unique property – they are completely massless. Unlike most other particles in the universe, photons do not have any rest mass. This intrinsic characteristic of photons sets them apart from other particles and plays a crucial role in their behavior.

Constant Speed in a Vacuum: One of the most remarkable features of photons is their constant speed in a vacuum. Photons always travel at the speed of light (c) from the very moment of their creation. This speed is approximately 299,792,458 meters per second (or about 186,282 miles per second). Unlike objects with mass, photons do not need to accelerate to reach this speed; they are born with it. This principle is a fundamental aspect of Albert Einstein's theory of special relativity.

The Equation E = hf: To understand the relationship between a photon's energy (E) and its frequency (f), we turn to the equation E = hf. This equation, known as the Planck-Einstein relation, reveals that the energy of a photon is directly proportional to its frequency. Here, E represents the energy of the photon, h is Planck's constant, and f is the frequency of the photon. In simple terms, higher-frequency photons carry greater energy.

By highlighting these fundamental characteristics of photons, we lay the groundwork for a deeper exploration of their interactions with gravity, antigravity, and their behavior in different environments. Photons, being massless and always traveling at the speed of light, exhibit unique properties that have far-reaching implications in the realm of physics and cosmology.

Now, let's delve into the interactions of photons with gravity and antigravity as described in the quoted paper.

Photon Interactions in Gravity and Antigravity:

The photon travels until it disappears into the unobservable universe. It interacts with gravity, antigravity caused by dark energy, and other external forces. Here, we examine how these interactions affect photon energy and momentum.

Gravitational Interaction:

When a photon encounters the gravitational influence of a massive object, it exchanges momentum (Δρ) with the external force field of gravity.

According to the equation (E + Δρ = E - Δρ), the photon neither gains nor loses energy during this interaction but experiences changes in momentum.

The effect of the photon's interaction with the external gravitational force is reversible. The photon maintains its intrinsic momentum and returns to its original path after releasing the gravitational interaction.

The effective deviation from its initial trajectory in the gravitational field is zero (0 = Δρ - Δρ).

Antigravity Interaction:

In contrast, when a photon interacts with the external force of antigravity caused by dark energy, the effect is irreversible (ΔEc).
This interaction results in cosmic redshift (zc), which is more pronounced than gravitational or other types of redshifts.

A photon's interaction with antigravity occurs when it moves beyond the influence of a galaxy and enters the zero-gravity sphere of radius.

By understanding these interactions, we gain insight into how photons navigate complex gravitational and antigravitational environments. These phenomena have implications for our understanding of the cosmos and the behavior of light in the universe.

3: Photon Behavior in Gravity

In this section, we will explore how photons interact with gravity, the familiar force that attracts objects with mass. We will explain that photons neither gain nor lose energy when crossing a gravitational field, emphasizing the equation ΔEg = 0 to underscore the conservation of photon energy and momentum in a gravitational field. We will also introduce the concept of effective deviation (0 = Δρ - Δρ) and describe how photons return to their original path after gravitational interaction, drawing references from the previously quoted papers.

Photon Interaction with Gravity: Photons, despite being massless particles, do interact with gravity. Gravity is the force that attracts objects with mass, and when photons pass through a gravitational field created by a massive object like a planet or star, they experience gravitational effects.

Energy Conservation in Gravitational Fields: One of the remarkable aspects of photon behavior in a gravitational field is that they neither gain nor lose energy during this interaction. This conservation of energy is expressed by the equation ΔEg = 0, where ΔEg represents the change in photon energy due to gravity.

ΔEg = 0: This equation highlights that the change in photon energy (ΔEg) as it passes through a gravitational field is zero. In other words, the photon's energy remains constant before and after the gravitational interaction. This phenomenon is a consequence of the masslessness of photons and is a fundamental principle in the behavior of light in the presence of gravity.
Momentum Exchange: While photons do not experience a net change in energy, they do undergo changes in momentum (Δρ) as they interact with the gravitational field.

Effective Deviation: The concept of effective deviation (0 = Δρ - Δρ) illustrates that, despite changes in momentum during gravitational interaction, the photon ultimately returns to its original path.

0 = Δρ - Δρ: This equation signifies that the effective deviation of the photon from its initial trajectory is zero. In simpler terms, the photon's path is not permanently altered by the gravitational interaction. Instead, it may experience a temporary deviation but ultimately resumes its original course.
By understanding these principles of photon behavior in gravity, we gain insight into how light interacts with massive objects and how it maintains its energy and momentum even in the presence of gravitational forces. This knowledge is fundamental in the study of astrophysics, general relativity, and cosmology, as it helps us comprehend phenomena like gravitational lensing and the bending of light by massive celestial bodies.

4: Antigravity and Irreversible Effects

In this section, we delve into the intriguing concept of antigravity and its counteracting force to gravity. We explain how antigravity exerts an irreversible effect on photons, primarily through cosmic redshift. Additionally, we define cosmic redshift (zc) and elucidate that it occurs when a photon departs from the influence of a galaxy. We also introduce the notion of the zero-gravity sphere of radius as the boundary marking the transition where antigravity begins to influence photons, drawing references from the previous discussions.

Antigravity Concept: Antigravity is introduced as a hypothetical force counteracting gravity. While gravity attracts objects with mass toward each other, antigravity serves as a conceptual opposite, pushing objects apart.

Irreversible Effect on Photons: Antigravity is emphasized as having an irreversible effect on photons, distinguishing it from the interactions with gravitational fields discussed earlier.

Cosmic Redshift (zc): Cosmic redshift (zc) is defined as a critical phenomenon associated with antigravity. It occurs when a photon leaves the gravitational influence of a galaxy and enters a region where antigravity begins to exert its influence. Cosmic redshift results in a change in the photon's characteristics, including its wavelength and energy.

Zero-Gravity Sphere of Radius: The concept of the zero-gravity sphere of radius is introduced as the boundary that marks the transition between regions influenced by gravity and those influenced by antigravity. Within a galaxy's gravitational influence, photons behave in a conventional manner, while beyond this boundary, antigravity's effects become significant.

By exploring these aspects of antigravity and its effects on photons, we gain insights into the hypothetical forces that may exist in the universe and how they impact the behavior of light. While antigravity remains speculative in the realm of physics, considering its potential effects on fundamental particles like photons opens the door to fascinating possibilities in our understanding of the cosmos.

5: Photon-Electron Interactions in Dense Transparent Media

In Section 5, we shift our focus to the intriguing topic of photon interactions with matter, particularly within dense but transparent media. We explore how photons can be absorbed by electrons in such environments, temporarily converting their energy into electron energy. Furthermore, we elucidate the phenomenon wherein electrons in an excited state subsequently release excess energy in the form of photons, resulting in noticeable time delays. Our discussion draws references from the previously mentioned papers to provide a comprehensive overview of these interactions.

Photon-Matter Interactions: This section serves as a transition into the realm of photon interactions with matter. It emphasizes the significance of understanding how photons behave when they encounter dense but transparent media.

Absorption by Electrons: We describe how photons can be absorbed by electrons within the atoms of dense, transparent materials. During this process, the photon's energy is transferred to the electron, causing it to transition to a higher energy state (e + ΔE).

Excited State and Excess Energy: We elaborate on the consequences of photon absorption, highlighting that the excited electron remains in this higher energy state temporarily. This period of excitation eventually culminates in the release of excess energy (E - ΔE) as photons.

Time Delays: We emphasize that the emission of these new photons introduces a time delay (Δt) in the progress of the original photon through the medium. The cumulative effect of multiple interactions adds up to create a noticeable delay in the photon's journey.

By exploring these photon-electron interactions within dense transparent media, we gain insights into the intricate behavior of light when it encounters matter. This knowledge is fundamental in various scientific and technological applications, spanning fields such as optics, materials science, and the design of optical devices. Understanding how photons interact with electrons in these environments is crucial for the development of technologies ranging from lenses to fiber optics and beyond.

6: Equations Describing Photon-Matter Interactions

In Section 6, we delve into the mathematical framework that underlies photon-matter interactions. We present fundamental equations that characterize these interactions, such as E = hf, ΔE = hΔf, f/Δf, and E/ΔE, to elucidate how photons undergo changes in energy and frequency during their encounters with matter. This section draws upon references from the previously discussed papers to provide a comprehensive understanding of the mathematics governing these phenomena.

E = hf: This foundational equation, known as the Planck-Einstein relation, establishes the intrinsic relationship between a photon's energy (E) and its frequency (f). It is represented as E = hf, where E denotes the energy of the photon, h represents Planck's constant, and f signifies the frequency of the photon. This equation underscores that the energy of a photon is directly proportional to its frequency.

ΔE = hΔf: Building upon the Planck-Einstein relation, this equation introduces the concept of changes in photon energy (ΔE) corresponding to changes in frequency (Δf). It reveals that a change in frequency results in a corresponding change in photon energy, with Planck's constant (h) serving as the proportionality factor.

f/Δf: This expression represents the ratio of the initial frequency (f) to the change in frequency (Δf). It quantifies how much the frequency of the photon changes due to interactions with matter. This ratio provides valuable insights into the extent of frequency alterations during photon-matter interactions.

E/ΔE: Similarly, this expression represents the ratio of the initial photon energy (E) to the change in energy (ΔE). It quantifies how much the energy of the photon changes during interactions with matter. Understanding this ratio is essential for comprehending the energy transformations that occur when photons interact with electrons within materials.

By presenting these equations, we establish a mathematical foundation for understanding the dynamics of photon-matter interactions. These equations enable us to quantify the changes in energy and frequency that photons undergo as they interact with matter, thereby contributing to our comprehension of fundamental processes in optics, materials science, and quantum mechanics.

7: Time Delay in Photon Passage

In Section 7, we explore the concept of time delay (Δt) in the passage of photons through matter, particularly in dense but transparent media. This phenomenon arises as a result of the cumulative effect of photon-electron interactions. We draw upon references from the previously discussed papers to provide insights into how these interactions contribute to time delays in photon propagation and how this concept is relevant in the field of optics and telecommunications.

Cumulative Effect of Photon-Electron Interactions: Within dense but transparent media, photons can interact with electrons, leading to processes such as absorption, excitation, and re-emission. These interactions, when considered collectively, give rise to a time delay (Δt) in the passage of photons. As photons encounter and interact with numerous electrons within the medium, each interaction contributes to a slight delay in the photon's progress through the material.

Group Velocity Dispersion: The concept of group velocity dispersion becomes relevant in this context. Group velocity dispersion refers to the phenomenon where different frequencies of light travel at slightly different speeds through a medium due to their interactions with electrons. It is particularly pertinent in the field of optics and telecommunications, where precise timing and synchronization of optical signals are crucial.

By introducing the idea of time delay in photon passage and connecting it to group velocity dispersion, we provide a comprehensive understanding of how photon-electron interactions can impact the propagation of light in dense but transparent media. This section underscores the significance of considering time delays in practical applications such as optical signal transmission, where the precise timing of signals is essential for reliable communication.

8: Photon Energy Variation in Strong Gravitational Fields

In Section 8, we delve into the intriguing topic of how photon energy behaves within strong gravitational fields. We reference equations and concepts from our previous discussions to elucidate the variation of photon energy in these environments and highlight the importance of energy conservation.

Photon Energy Variation: Within strong gravitational fields, photons interact with gravity, leading to changes in their energy. We reference the equation Eg = E + ΔE = E - ΔE to express the total energy of a photon in such conditions. Here's how we describe this variation:

Eg = E + ΔE = E - ΔE: This equation represents the total energy of a photon (Eg) in a strong gravitational field. It is expressed as the sum of its initial energy (E) and the gain (ΔE) or loss (-ΔE) of energy due to the gravitational influence. This equation emphasizes that, despite gravitational effects, the total energy of the photon remains constant. In other words, the photon conserves its energy even when subjected to the influence of a massive object's gravitational field.

Consistency of Total Energy: In this section, we stress the importance of maintaining the equivalence of total energy, even in the presence of strong gravitational forces. We emphasize that changes in photon momentum (Δρ), whether gains or losses, do not alter the total energy of the photon. This concept underscores the fundamental principle of energy conservation, even within the context of gravitational environments.

By presenting the equation Eg = E + ΔE = E - ΔE and reiterating the constancy of total energy in strong gravitational fields, we provide a comprehensive understanding of how photons navigate these challenging environments while adhering to the conservation of energy. This section contributes to a deeper comprehension of photon behavior in the presence of gravity, enriching our knowledge of fundamental physics principles.

9: Momentum and Wavelength Changes under Gravitational Influence
In Section 9, we delve into the fascinating realm of how photons undergo changes in momentum (Δρ) and wavelengths (λ) when influenced by strong gravitational fields. We reference equations and concepts from our previous discussions to provide a comprehensive explanation of these changes.

Changes in Photon Momentum: When photons traverse strong gravitational fields, they encounter changes in momentum. We present the equations Eg = E + Δρ = E - Δρ to elucidate these changes:

Eg = E + Δρ = E - Δρ: This equation represents the total energy of a photon (Eg) in a strong gravitational field. It is expressed as the sum of its initial energy (E) and the change in momentum (Δρ) due to the gravitational influence. This equation emphasizes that the photon experiences changes in momentum while maintaining constant total energy. These changes in momentum can result in gravitational redshift or blueshift, depending on whether Δρ is positive or negative.

Wavelength Changes: In this section, we explore how the wavelengths of photons are altered when subjected to strong gravitational forces. We introduce the equation h/Δλ = h/-Δλ to illustrate these changes:

h/Δλ = h/-Δλ: This equation relates the change in photon wavelength (Δλ) to the Planck constant (h) and the change in momentum (-Δρ) due to gravity. It demonstrates that as photons move through gravitational fields, their wavelengths experience shifts, which are determined by the changes in momentum. A positive Δλ signifies gravitational redshift, where the wavelength increases, while a negative Δλ represents gravitational blueshift, where the wavelength decreases.

By presenting the equations Eg = E + Δρ = E - Δρ and h/Δλ = h/-Δλ, we provide a comprehensive understanding of how photons undergo changes in momentum and wavelengths when influenced by strong gravitational fields. These equations serve as fundamental tools for describing photon behavior in the presence of gravity, enriching our comprehension of the interplay between photons and gravitational forces.

10: Consistency of Photon Energy in Gravitational Fields

In Section 10, we reinforce the fundamental concept of the constancy of total photon energy in the presence of strong gravitational fields, represented by the equation Eg = E. Additionally, we highlight the symmetry in changes in photon momentum (Δρ) and introduce the Planck length-to-time ratio (ℓP/tP) to elucidate its significance.

Consistency of Total Photon Energy: We reiterate the core principle that in strong gravitational fields, the total energy of a photon remains constant, as expressed by the equation Eg = E:

Eg = E: This equation underscores that the total energy of a photon (Eg) remains unchanged despite the influence of a strong gravitational field. This constancy of energy is a fundamental property of photons in such environments, emphasizing their resilience to external forces.

Symmetry in Changes of Photon Momentum: We emphasize the symmetry in changes of photon momentum (Δρ) caused by gravitational effects. As previously discussed, photons experience changes in momentum while maintaining constant total energy. This symmetry in momentum changes is a key characteristic of photon behavior in gravitational fields.

Planck Length-to-Time Ratio (ℓP/tP): To further enrich our understanding, we introduce the Planck length-to-time ratio (ℓP/tP). While not explicitly covered in earlier sections, this ratio plays a crucial role in the quantum realm, where the Planck length (ℓP) represents the smallest meaningful length scale and the Planck time (tP) is the shortest possible time interval. Their ratio (ℓP/tP) is a fundamental constant in physics and is relevant when considering extreme conditions, such as those encountered in strong gravitational fields.

By reiterating the constancy of total photon energy (Eg = E), emphasizing the symmetry in changes of photon momentum (Δρ), and introducing the Planck length-to-time ratio (ℓP/tP), Section 10 contributes to a comprehensive understanding of photon behavior in gravitational fields. These concepts and equations collectively enhance our grasp of the intriguing interplay between photons and the profound forces of gravity.

11: Conclusion
In this final section, we summarize the main findings and insights regarding photon interactions in gravity and antigravity, underlining the significance of this understanding for diverse scientific and technological applications.

Photon-Gravity Interaction Recap: Our exploration began by delving into the behavior of photons in gravitational fields (Section 3). It was elucidated that photons neither gain nor lose energy when traversing through gravity, maintaining their energy and momentum (ΔEg = 0) despite gravitational influence (Section 8). Additionally, we examined the changes in photon momentum (Δρ) and wavelengths (λ) in strong gravitational fields (Section 9), reaffirming the constancy of total photon energy (Eg = E) in these environments (Section 10).

Antigravity Effects and Cosmic Redshift: Section 4 introduced the intriguing concept of antigravity, which exerts an irreversible effect on photons, leading to cosmic redshift (zc) as they depart from galaxies. We established the zero-gravity sphere as a critical boundary where antigravity begins influencing photons.

Photon-Electron Interactions in Dense Media: Transitioning to matter interactions, Section 5 explored photon interactions with electrons in dense yet transparent media. Photons can be temporarily absorbed by electrons, converting into electron energy, and subsequently, this energy is released as photons after time delays.

Equations Describing Photon-Matter Interactions: Section 6 presented fundamental equations such as E = hf, ΔE = hΔf, f/Δf, and E/ΔE to quantitatively describe photon-matter interactions, providing a mathematical framework for these phenomena.

Time Delay in Photon Passage: The cumulative effect of photon-electron interactions leading to time delays (Δt) in photon passage was discussed in Section 7, with a reference to group velocity dispersion, a critical concept in optics and telecommunications.

Consistency of Photon Energy in Gravitational Fields: In Section 10, we reiterated the paramount concept that the total photon energy remains constant in the presence of strong gravitational fields (Eg = E). This section also introduced the Planck length-to-time ratio (ℓP/tP) as a relevant constant in extreme conditions.

In conclusion, our comprehensive examination of photon behavior in gravity and antigravity unveils the remarkable resilience and adaptability of photons in the face of these fundamental forces. This understanding has profound implications for various scientific and technological domains. From astrophysics to telecommunications, the insights gained in this paper provide a solid foundation for harnessing the behavior of photons in extreme conditions and advancing our knowledge of the universe.

By unraveling the intricate dance between photons and gravity, we not only expand our understanding of the cosmos but also pave the way for innovative applications in fields ranging from space exploration to quantum communication. The pursuit of knowledge in this realm continues to inspire breakthroughs that push the boundaries of human exploration and discovery.

12: Future Directions
As we conclude our investigation into the intriguing realm of photon interactions in gravity and antigravity, it becomes evident that numerous avenues for further research and exploration lie ahead. Building upon the foundations established in this paper, we suggest several promising directions for future investigations:

Practical Applications: One promising avenue is to delve deeper into the practical implications of photon interactions in gravitational fields and antigravity zones. This could involve developing technologies that harness these interactions for various purposes, such as spacecraft propulsion, gravitational wave detection, or even novel energy generation methods. By applying the principles outlined in this paper, researchers may uncover innovative solutions to long-standing challenges in these domains.

Experimental Validation: While theoretical frameworks have been extensively explored, experimental validation of the phenomena described in this paper remains an essential frontier. Conducting experiments in controlled environments, such as Earth-based laboratories or space-based experiments, can provide empirical evidence of photon behavior under the influence of gravity and antigravity. These experiments would not only validate theoretical predictions but also pave the way for the development of new measurement techniques and technologies.

Quantum Gravity: The interplay between photons and gravity hints at the interface between quantum mechanics and general relativity. Future research could delve into the realm of quantum gravity, seeking to reconcile the behavior of particles at the quantum level with the curvature of spacetime. Investigating how photons interact with gravity on the quantum scale may uncover profound insights into the nature of the universe.

Cosmological Implications: Exploring the cosmological implications of photon interactions in gravity and antigravity is another exciting avenue. Researchers may investigate how these interactions impact our understanding of the universe's expansion, the redshift of distant galaxies, and the formation of cosmic structures. Such inquiries could lead to a deeper comprehension of the cosmos on a grand scale.

Advanced Materials: Understanding how photons interact with matter in dense, transparent media (as discussed in Section 5) opens up possibilities for the development of advanced materials with tailored optical properties. Researchers can explore ways to engineer materials that manipulate photon interactions, potentially leading to breakthroughs in optical computing, communication, and sensing technologies.

Space Exploration: For space exploration missions, the insights gained from this research could inform the design of spacecraft, instruments, and communication systems. Investigating how photons behave in extreme gravitational environments will be crucial for optimizing the performance and reliability of future space missions.

In conclusion, the exploration of photon interactions in gravity and antigravity is a multifaceted endeavor that holds great promise for both fundamental science and practical applications. By pursuing these future research directions, scientists can unlock new dimensions of knowledge, enabling us to push the boundaries of human understanding and leverage the unique properties of photons for technological advancements that benefit society at large.

13: References:
1. Chernin, A. D., Bisnovatyi-Kogan, G. S., Teerikorpi, P., Valtonen, M. J., Byrd, G. G., & Merafina, M. (2013b). Dark energy and the structure of the Coma cluster of galaxies. Astronomy and Astrophysics, 553, A101. https://doi.org/10.1051/0004-6361/201220781
2. Aspelmeyer, M., Kippenberg, T. J., & Marquardt, F. (2014). Cavity Optomechanics. Reviews of Modern Physics, 86(4), 1391-1452.
3. Thakur, S. N. (2023). Redshift and its Equations in Electromagnetic Waves. ResearchGate. https://doi.org/10.13140/RG.2.2.33004.54403
4. Braginsky, V. B., Gorodetsky, M. L., & Khalili, F. Ya. (1999). Mirrors and Microphones: Detecting Gravitational Waves at the Quantum Limit. Science, 285(5431), 1702-1703.
5. Thakur, S. N. (2023a). Photon paths bend due to momentum exchange, not intrinsic spacetime curvature. Definitions. 
6. Carroll, S. M. (2004). Spacetime and Geometry: An Introduction to General Relativity. Pearson Education.
7. Chiou, J. C., & O'Leary, S. (2017). Quantum Optics and Photonics for Space Environments. Proceedings of SPIE, 10186, 1018601.
8. Einstein, A. (1915). General Theory of Relativity. Annalen der Physik, 49(7), 769-822.
9. Thakur, S. N. (2023a). The dynamics of photon momentum exchange and curvature in gravitational fields. Definitions. 
10. Greene, B. (2004). The Fabric of the Cosmos: Space, Time, and the Texture of Reality. Vintage Books.
11. Hawking, S. W. (1975). Particle Creation by Black Holes. Communications in Mathematical Physics, 43(3), 199-220.
12. Thakur, S. N. (2023c). Relativistic effects and photon-mirror interaction – energy absorption and time delay. ResearchGate. https://doi.org/10.32388/sgxntt
13. Hawking, S. W., & Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time. Cambridge University Press.
14. Kim, Y. S., & Hong, J. S. (2011). Photonics for Space Environments and Related Technologies. Proceedings of SPIE, 8008, 80080H.
15. Padgett, M. J., & Andrews, D. L. (2017). Photonics: Scientific Foundations, Technology and Applications. CRC Press.
16. Penrose, R. (1965). Gravitational Collapse and Space-Time Singularities. Physical Review Letters, 14(3), 57-59.
17. Thakur, S. N., Samal, P., & Bhattacharjee, D. (2023b). Relativistic effects on phaseshift in frequencies invalidate time dilation II. TechRxiv. https://doi.org/10.36227/techrxiv.22492066.v2
18. Planck Collaboration, Ade, P. A. R., Aghanim, N., & Armitage-Caplan, C. (2013). Planck 2013 results. XVI. Cosmological parameters. Astronomy & Astrophysics, 571, A16.
19. Rees, M. J. (1999). Our Cosmic Habitat. Princeton University Press.
20. Rindler, W. (2006). Relativity: Special, General, and Cosmological. Oxford University Press.
21. Schwarz, J. H. (2008). Theoretical Overview of Black Holes: Lectures in Les Houches. Les Houches Summer School on Particle Physics, 11-65.
22. Smith, J. D. (2010). Advances in Photonics for Aerospace Applications. Proceedings of SPIE, 7684, 768401.
23. Taylor, E. F., & Wheeler, J. A. (1963). Exploration of Cosmic Ray Muons. Reviews of Modern Physics, 35(4), 457-461.
24. Thakur, S. N., Samal, P., & Frederick, O. (2023). Cosmic microwave background radiation (CMB), the Observable and Non-Observable universes, and their. . . ResearchGate. https://doi.org/10.13140/RG.2.2.11748.76165
25. The LIGO Scientific Collaboration, & The Virgo Collaboration. (2016). Observation of Gravitational Waves from a Binary Black Hole Merger. Physical Review Letters, 116(6), 061102.
26. Thorne, K. S. (1980). Multipole Expansions of Gravitational Radiation. Reviews of Modern Physics, 52(2), 299-339.
27. Wheeler, J. A. (1967). Superspace and the Nature of Quantum Geometrodynamics. Battelle Rencontres: 1967 Lectures in Mathematics and Physics, 242-307.

Does a blueshifted photon increase its relative energy and frequency at reception?

The answer is a clear "yes". Read below why:

At a longer wavelength (λ2>λ1) and lower frequency (f2<f1), the photon carries less energy (E2<E1) than the light emitted at the source, where: λ2, f2, E2, represent the wavelength, frequency and energy of the observed photon, respectively, and λ1, f1, E1 respectively represent the wavelength, frequency and energy of the same photon when emitted at the source.

The statement highlights how the properties of a photon, particularly its energy, wavelength, and frequency, change as it travels from its source to an observer. This change is a fundamental aspect of wave-particle duality and the behavior of electromagnetic radiation. When the photon has a longer wavelength and lower frequency at the observer's location, it carries less energy than it did when it was initially emitted, and vice versa.

Relevant equations:

f = (ℓP/tP)/λ; E = hf; Hence, E ∝ 1/λ or E ∝ f, '

Accordingly, photons with a shorter wavelength (λ2<λ1) and increased frequency (f2>f1) carry increased energy (E2>E1) compared to light emitted at the source.

Cosmic and relativistic motion play a key role in the energy-frequency state of the traveling photon wave between its source and observer.

When measuring the compression of wavelengths associated with gravitational wells, the compression itself corresponds to an increased frequency due to cosmic and relativistic effects, and therefore represents the extra energy added to the detected photon signal compared to its proper frequency or wavelength, while still maintaining its momentum.

Note the Planck ratio of ℓP/tP = fλ and the Planck equation E = hf.

Furthermore, since the redshift represents the correspondingly lower frequency of increased wavelength, the blueshift represents the opposite due to increased energy, decreased wavelength, and corresponding increased frequency.

Photon Energy, Wavelength, and Frequency: photon energy (E) is related to both its wavelength (λ) and frequency (f) through the Planck equation, E = hf. This equation shows that as the wavelength increases (λ2 > λ1), the frequency decreases (f2 < f1), and vice versa. Consequently, a longer wavelength corresponds to a lower frequency and, as a result, lower energy, while a shorter wavelength corresponds to a higher frequency and higher energy.

Relevance of Planck's Equation: Planck's equation, E = hf, is fundamental in describing the energy of photons. This equation demonstrates that changes in frequency directly affect the energy of the photon, which is a well-established principle in quantum mechanics.

Cosmic and Relativistic Effects: The role of cosmic and relativistic effects in altering the observed properties of photons. These effects can lead to changes in the wavelength and frequency of photons as they travel through the universe. For example, gravitational fields can cause gravitational redshift, which results in the observed photon having a longer wavelength and lower frequency.

Wavelength Compression in Gravitational Wells: when photons pass through gravitational wells, such as those caused by massive celestial objects, their wavelengths can be compressed. This compression corresponds to an increased frequency due to the effects of gravity and relativity. Importantly, you note that this change in frequency represents additional energy added to the detected photon signal compared to its proper frequency or wavelength.

Redshift and Blueshift: The concepts of redshift and blueshift. Redshift occurs when an observed photon has a longer wavelength and lower frequency than expected, leading to decreased energy. Conversely, blueshift occurs when the observed photon has a shorter wavelength, higher frequency, and increased energy compared to its source.

In summary, my explanation effectively conveys how the properties of photons, including energy, wavelength, and frequency, are interconnected and influenced by both fundamental quantum mechanics (Planck's equation) and cosmic and relativistic effects. It also highlights the importance of understanding redshift and blueshift as indicators of changes in energy and the influence of gravitational wells on photon properties.

Dark Energy's Antigravity Effect - Shaping the Accelerated Cosmos:

Date: 19-09-2023

Abstract:

This discussion delves into the intriguing world of dark energy and its profound influence on the cosmos. Dark energy, a mysterious and enigmatic form of energy, has captivated cosmologists as it defies conventional gravitational expectations. Dark energy's "antigravity" effect is at the heart of its role in the universe's accelerated expansion, counteracting the attractive force of gravity. We explore the Lambda-Cold Dark Matter (Λ-CDM) model, where dark energy, represented by the cosmological constant (Λ), generates a repulsive gravitational effect. This effect becomes increasingly dominant as the universe expands, causing galaxies to move away from each other at an accelerating rate. The concept of dark energy's constant energy density, its repulsive nature, and its influence on cosmic dynamics underscore its mysterious and pivotal role in modern cosmology. This dynamic interplay between dark energy and gravity reveals the intricate dance that shapes the universe's large-scale structure and expansion.

Introduction:

The universe is an intricate tapestry of cosmic forces, where the interplay between matter and energy governs its dynamic evolution. One of the most enigmatic and influential actors on this cosmic stage is dark energy. Dark energy, though elusive and mysterious, plays a pivotal role in the cosmos by driving the universe's accelerated expansion. At the heart of this phenomenon lies dark energy's ability to generate what can be described as "antigravity."

This concept of antigravity encapsulates the repulsive gravitational effect of dark energy, which counteracts the attractive force of gravity due to matter. It defies our intuitive expectations, where gravity should seemingly slow down the expansion of the universe. Instead, galaxies are observed to move away from each other at an ever-increasing rate.

In this exploration, we delve into the intricate web of dark energy's antigravity effect, deciphering its implications and underlying principles. We'll unravel the key components of this cosmic puzzle, from the uniform dark energy background to its ability to generate stronger antigravity than matter's gravity. Our journey through the Lambda-Cold Dark Matter (Λ-CDM) model will reveal how dark energy shapes the universe's destiny, accelerating its expansion and reshaping our understanding of the cosmos.

Join us on this cosmic voyage as we navigate the gravitational intricacies of dark energy and the profound consequences it brings to the forefront of modern cosmology.

Method:

To comprehend the concept of dark energy's antigravity effect and its implications for cosmic expansion, we embark on a methodical journey through the foundational principles of modern cosmology. Here is the method we employ to unravel the mysteries of dark energy:

Literature Review:

Begin by conducting an extensive literature review to gather insights from established cosmological theories, observational data, and scientific research papers.

Explore the Lambda-Cold Dark Matter (Λ-CDM) model and other relevant theoretical frameworks that incorporate dark energy.

Investigate observational evidence, including data from supernovae observations, cosmic microwave background radiation, and large-scale structure surveys.

Understanding Dark Energy:

Familiarize ourselves with the nature of dark energy, including its hypothetical properties, such as constant energy density and repulsive gravitational effect.

Delve into the history of dark energy's discovery and its role in explaining the accelerated expansion of the universe.

Antigravity Effect:

Focus on the concept of dark energy generating "antigravity."

Explore the theoretical underpinnings of dark energy's repulsive gravitational effect and its counteraction of matter's attractive gravity.

Lambda-CDM Model:

Study the Lambda-Cold Dark Matter (Λ-CDM) model in detail, emphasizing the role of dark energy (represented by Lambda, Λ) and its interplay with cold dark matter and visible matter.

Examine how the Λ-CDM model explains cosmic expansion and the observed behavior of galaxies.

Cosmic Expansion Dynamics:

Analyze the dynamics of cosmic expansion, considering the balance between matter gravity and dark energy's antigravity.

Investigate the acceleration of the cosmological expansion and its implications for the large-scale structure of the universe.

Gravitational Dominance:

Discuss the concept of gravitational dominance within certain distance ranges.

Explain how gravity prevails over dark energy's antigravity within specific regions, influencing the behavior of celestial objects and systems.

Antigravity Dominance:

Explore the idea that antigravity becomes stronger than gravity at larger cosmic distances.

Describe the transition from gravitational dominance to antigravity dominance and how it affects cosmic dynamics.

Synthesis:

Synthesize the gathered knowledge and insights to provide a comprehensive understanding of dark energy's antigravity effect and its significance in modern cosmology.

By employing this method, we aim to unravel the complexities of dark energy's antigravity effect and its profound impact on the universe's expansion dynamics, shedding light on one of the most intriguing aspects of modern cosmology.

Names of Relevant Equations: 

The following equations represent the core mathematical framework used in cosmology to model and understand the universe's behavior, expansion, and structure. They are essential tools for both theoretical and observational cosmologists.

1. Friedmann Equations:

These are fundamental equations in cosmology that describe the expansion of the universe within the framework of general relativity. They relate the scale factor of the universe (a), the Hubble parameter (H), and the energy density (ρ) of various components of the universe (matter, radiation, dark energy) to the curvature of space (k). These equations are essential for understanding the dynamics and evolution of the universe. They provide insights into how the expansion rate of the universe changes over time and how it is influenced by different forms of energy and matter.

2. Einstein's Field Equations:

These equations are at the heart of general relativity, describing the gravitational field in terms of the metric tensor (g) and the energy-momentum tensor (T). In cosmology, they are used to model the behavior of spacetime on large scales. Einstein's Field Equations are crucial for understanding the overall geometry of the universe and how it evolves under the influence of matter and energy.

3. Hubble's Law:

Hubble's Law relates the recessional velocity (v) of galaxies to their distance (d) from an observer. It's a foundational equation in observational cosmology. This equation played a pivotal role in the discovery of the expansion of the universe. Hubble's constant (H0) represents the current rate of cosmic expansion.

4. Friedmann-Lemaître-Robertson-Walker (FLRW) Metric:

The FLRW metric is a key component of cosmological models and describes the geometry of the universe. It is a solution to Einstein's Field Equations for a homogeneous and isotropic universe. This metric characterizes the expansion and curvature of the universe and serves as the foundation for understanding cosmological phenomena.

5. Dark Energy Equation of State:

This equation describes the relationship between the pressure (p) and energy density (ρ) of dark energy. It helps characterize the nature of dark energy and its role in the universe's expansion. The value of the dark energy equation of state parameter (w) determines whether dark energy behaves as a cosmological constant (w = -1), quintessence (w > -1), or other exotic forms of energy.

6. Cosmic Microwave Background (CMB) Temperature Anisotropy Equation:

This equation describes the temperature fluctuations (ΔT) in the CMB radiation across the sky. It provides valuable information about the early universe's density variations. This equation is used to analyze the CMB temperature map and extract cosmological parameters, shedding light on the universe's early conditions.

Discussion:

The equations presented here form the foundational framework for our understanding of the cosmos within the realm of cosmology. They are crucial tools for both theoretical and observational cosmologists, providing insights into the nature, evolution, and large-scale structure of the universe. Let's delve into a discussion of these equations and their significance:

1. Friedmann Equations:

Significance: These equations are the backbone of modern cosmology. They describe how the universe's scale factor changes over time and how the expansion rate depends on the energy content of the universe. They have been tested and validated through various astronomical observations, including the cosmic microwave background (CMB) radiation and the distribution of galaxies.

Key Insights: Friedmann equations reveal that the universe's fate depends on its energy composition. If the energy density is dominated by matter, the universe's expansion will eventually slow down. In contrast, if dark energy dominates, the expansion will accelerate.

2. Einstein's Field Equations:

Significance: These equations, the foundation of general relativity, are applied to cosmology to understand how spacetime curvature is influenced by the distribution of matter and energy. They are crucial for modeling the universe's overall geometry.

Key Insights: Einstein's equations demonstrate that the presence of matter and energy warps spacetime, leading to phenomena like gravitational lensing and the expansion of the universe. They underpin our understanding of gravity on cosmic scales.

3. Hubble's Law:

Significance: Hubble's Law provided the first empirical evidence for the expansion of the universe. It directly relates the velocity of distant galaxies to their distance from us.

Key Insights: Hubble's constant (H0) measures the current rate of cosmic expansion. Observations of distant supernovae have shown that the universe's expansion is accelerating, a discovery that earned the Nobel Prize in Physics.

4. Friedmann-Lemaître-Robertson-Walker (FLRW) Metric:

Significance: The FLRW metric is essential for modeling the overall geometry of the universe. It assumes homogeneity and isotropy on large scales.

Key Insights: The metric accounts for cosmic expansion and curvature, allowing cosmologists to describe the geometry of the universe using parameters such as the scale factor (a) and the curvature constant (k).

5. Dark Energy Equation of State:

Significance: This equation helps characterize the mysterious dark energy that drives the universe's accelerated expansion. It provides insights into whether dark energy behaves as a cosmological constant or possesses dynamic properties.

Key Insights: A value of w = -1 indicates a cosmological constant (Lambda, Λ), while other values suggest quintessence or exotic energy behaviors. Determining the nature of dark energy is a central challenge in cosmology.

6. Cosmic Microwave Background (CMB) Temperature Anisotropy Equation:

Significance: This equation describes temperature fluctuations in the CMB radiation, offering a snapshot of the early universe's density variations.

Key Insights: Analysis of the CMB temperature anisotropy provides a wealth of information about the universe's age, composition, geometry, and initial conditions. It supports the Big Bang theory and the Lambda-CDM model.

These equations represent the mathematical foundation of our current cosmological understanding. They allow us to model the universe's dynamics, understand its large-scale structure, and investigate cosmic phenomena. While they have greatly advanced our knowledge of the cosmos, they also underscore the enduring mysteries of dark energy and dark matter, which continue to be active areas of research and exploration in the field of cosmology.

Conclusion:

Cosmology, the study of the universe on the grandest scales, relies on a set of fundamental equations that form the cornerstone of our understanding of the cosmos. These equations, ranging from the Friedmann equations to Einstein's field equations, Hubble's law, and the cosmic microwave background (CMB) temperature anisotropy equation, provide profound insights into the universe's origin, evolution, and composition. In this discussion, we have examined the significance of these equations and their key insights:

The Friedmann equations offer a dynamic view of the universe's expansion, revealing its dependence on the energy content of the cosmos. They tell us that the universe's fate hinges on whether matter, radiation, or dark energy dominates.

Einstein's field equations, rooted in general relativity, demonstrate how the presence of matter and energy warps spacetime, shaping the fabric of the cosmos. They underlie our comprehension of gravity's behavior on cosmic scales.

Hubble's law, a foundational discovery, directly connects the velocities of galaxies to their distances, providing empirical evidence for the universe's expansion and offering a means to measure its rate.

The Friedmann-Lemaître-Robertson-Walker (FLRW) metric facilitates our modeling of the universe's overall geometry, accounting for expansion and curvature, while assuming homogeneity and isotropy on cosmic scales.

The dark energy equation of state helps us probe the nature of this enigmatic cosmic constituent. A value of w = -1 points to a cosmological constant, Lambda (Λ), while other values open the door to diverse scenarios.

The CMB temperature anisotropy equation, gleaned from observations of the afterglow of the Big Bang, supplies us with a treasure trove of information about the universe's characteristics, including its age, composition, geometry, and early fluctuations.

These equations not only illuminate the universe's past and present but also raise profound questions about its future. The mysterious nature of dark energy, the enigmatic presence of dark matter, and the ultimate fate of our cosmos remain captivating subjects of research and exploration in the field of cosmology.

In the grand tapestry of the universe, these equations represent threads that tie together our observations, theories, and understanding. They provide the mathematical scaffolding upon which the edifice of modern cosmology is built, offering both clarity and complexity as we continue our quest to unravel the mysteries of the cosmos. As we delve deeper into the nature of dark energy, seek elusive dark matter, and refine our models, these equations will undoubtedly guide us toward a more profound comprehension of the universe's remarkable story.

References:

1. Chernin, A. D., Bisnovatyi-Kogan, G. S., Teerikorpi, P., Valtonen, M. J., Byrd, G. G., & Merafina, M. (2013). Dark energy and the structure of the Coma cluster of galaxies. Astronomy and Astrophysics, 553, A101. 

2. Principles of Cosmology and Gravitation" by Michael V. Berry and Gregory J. Galloway

3. Cosmology" by Steven Weinberg

4. The Early Universe" by Edward Kolb and Michael Turner

5. Modern Cosmology" by Scott Dodelson

6. An Introduction to Modern Cosmology" by Andrew Liddle

7. Planck Collaboration. (2018). Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics, 641, A6.

8. Riess, A. G., et al. (1998). Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. The 8. 9. Astronomical Journal, 116(3), 1009–1038.

10. Hinshaw, G., et al. (2013). Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results. 11. The Astrophysical Journal Supplement Series, 208(2), 19.

12. Komatsu, E., et al. (2011). Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The 13. Astrophysical Journal Supplement Series, 192(2), 18.

14. Peebles, P. J. E., & Ratra, B. (2003). The Cosmological Constant and Dark Energy. Reviews of Modern Physics, 75(2), 559–606.

15. NASA's Universe of Learning: Cosmology Resources

16. European Space Agency (ESA): Cosmology

17. The Royal Astronomical Society: Cosmology

18. Stanford University - Stanford Encyclopedia of Philosophy: Cosmology

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