The First Part
Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
07-09-2024
This study title suggests a comprehensive investigation of how various types of mass and energy, including mechanical energy as interpreted in classical mechanics, interact and shape the universe's evolution and expansion.
Energy Dynamics of the Universe: This section explores how dark energy, regarded as potential energy, was the sole energetic form in the primordial universe and later regenerated through motion and gravitational dynamics following the formation of matter mass. The study includes an analysis of the motion and gravitational dynamics of mechanical energy in the context of classical mechanics. It proposes an exploration of how potential energy, kinetic energy, and more exotic forms—such as dark energy (as a form of potential energy)—interact and contribute to the universe's evolution.
Negative Apparent Mass: This term describes a theoretical concept where generated mass appears negative under specific conditions, particularly from a mechanical perspective that involves motion and gravitational dynamics within classical mechanics. This concept is vital for understanding non-intuitive gravitational effects and how such mass influences the universe's structure and expansion.
Matter Mass: This includes both baryonic matter (ordinary matter composed of protons, neutrons, and electrons) and dark matter, which is non-luminous and interacts primarily through gravity. These two forms of matter represent the majority of mass in the universe and are essential in understanding the formation and evolution of cosmic structures such as galaxies, clusters, and filaments.
Negative Effective Mass of Dark Energy: Dark energy is observed to cause the accelerated expansion of the universe, highlighting its crucial role in cosmic evolution. The term "negative effective mass" implies a framework where dark energy possesses properties that effectively counteract gravitational attraction, resulting in a repulsive effect that accelerates the universe's expansion.
Background:
The intercontinental research study, Dark Energy and the Structure of the Coma Cluster of Galaxies by A. D. Chernin et al., introduces three types of mass that are pivotal to understanding the dynamics of the cluster:
Matter Mass (Mᴍ): This represents the total mass of both dark matter and baryonic matter within the Coma Cluster, contributing to its gravitational binding.
Dark Energy Effective Mass (Mᴅᴇ): A conceptual mass that represents the effect of dark energy, characterized by negative pressure, resulting in a negative mass (Mᴅᴇ < 0) that counteracts gravitational attraction.
Gravitating Mass (Mɢ): The net mass responsible for gravitational attraction, combining the effects of matter mass and dark energy, as expressed in the equation:
Mɢ = Mᴍ + Mᴅᴇ
The total mass per unit volume, including both dark and baryonic matter, represents the density of matter mass (ρᴍ) within the Coma Cluster, which is expressed by the formula:
ρᴍ = Mₜₒₜₐₗ/V
Our earlier research concluded that dark energy and negative apparent mass can be understood as consequences of gravitational dynamics and motion. This framework extends classical mechanics to provide a consistent and coherent explanation for gravitational interactions, accounting for phenomena associated with dark energy.
Additionally, our studies on the evolution and impact of dark energy in the universe have characterized dark energy as the potential energy of the universe, associated with a negative mass (<0). Initially, this negative mass was the driving force behind cosmic inflation and the formation of positive mass. Following this period of rapid expansion, dark energy entered a phase of hibernation as the density of gravitational mass began to exceed that of dark energy.
As the universe continued to evolve, gravitationally bound galaxies formed from regions of denser gaseous mass, leading to a reduction in the average density of this mass. The subsequent scattering of galaxies altered the motion and gravitational dynamics, allowing dark energy to regain influence in the spaces between galaxies and galactic clusters.
Currently, dark energy has reasserted its dominance in intergalactic space. The ongoing interplay between cosmic motion and gravitational dynamics enhances the effects of dark energy, resulting in the accelerated recession of gravitationally bound galaxies.
In the following sections, we will build upon our earlier conclusions that the negative effective mass of dark energy, considered as potential energy, was the sole energetic form in the primordial universe but later regenerated after a period of hibernation following the formation of matter mass. We will then link and interpret the potential energies associated with negative apparent mass and the regenerated negative effective mass of dark energy, post-hibernation, as consequences of gravitational dynamics and motion. These ideas will be discussed within the broader context of the energy dynamics of the universe, specifically focusing on Negative Apparent Mass, Matter Mass, and the Negative Effective Mass of Dark Energy.
Presentations: Analytical Description of Equations
The following equations describe the state of the universe in its primordial phase, specifically before the Big Bang event. Here is an analytical description of each equation:
Primordial Universe Before the Big Bang Event.
Potential Energy of Negative Effective Mass: Mᴅᴇ <0: Eᴅᴇ,ᴜₙᵢᵥ = ∞
• The potential energy associated with the negative effective mass of dark energy, denoted as
Eᴅᴇ,ᴜₙᵢᵥ, is infinite:
Eᴅᴇ,ᴜₙᵢᵥ = ∞
• This signifies that before the Big Bang, dark energy (characterized by a negative effective mass Mᴅᴇ, where Mᴅᴇ <0) dominated the universe with infinite potential energy.
Proportionality of Potential Energy:
• The total potential energy of the universe, (PEᴜₙᵢᵥ) ∝ Eᴅᴇ,ᴜₙᵢᵥ, is directly proportional to Eᴅᴇ,ᴜₙᵢᵥ:
PEᴜₙᵢᵥ ∝ Eᴅᴇ,ᴜₙᵢᵥ,
• Given that Eᴅᴇ,ᴜₙᵢᵥ =∞, the total potential energy PEᴜₙᵢᵥ is also infinite. This indicates a state where the universe's energy content is entirely determined by the potential energy of dark energy.
Kinetic Energy of the Universe:
• At this stage, the kinetic energy of the universe, KEᴜₙᵢᵥ, is zero:
KEᴜₙᵢᵥ =0
• This implies that there was no movement or expansion happening in the primordial universe, reflecting a static state dominated solely by potential energy.
Total Energy of the Universe:
• The total energy of the universe, Eₜₒₜₐₗ,ᴜₙᵢᵥ, is composed of both potential and kinetic energy:
Eₜₒₜₐₗ,ᴜₙᵢᵥ = PEᴜₙᵢᵥ + KEᴜₙᵢᵥ = ∞ + 0 = ∞
• This reinforces the idea that the universe, in its initial state, was completely governed by the infinite potential energy of dark energy, with no kinetic contribution.
Total Mass Equivalent of the Universe:
• The total mass of the universe, Mₜₒₜₐₗ,ᴜₙᵢᵥ, is described as the sum of effective mass and matter mass:
Mₜₒₜₐₗ,ᴜₙᵢᵥ = Mᵉᶠᶠ,ᴜₙᵢᵥ + Mᴍ,ᴜₙᵢᵥ
where Mᵉᶠᶠ,ᴜₙᵢᵥ = ∞, Mᴍ,ᴜₙᵢᵥ = 0
• This suggests that the universe's mass was entirely in the form of effective mass associated with dark energy, with no conventional matter yet formed.
Force Relationship in the Universe:
• The force within the universe is defined by the product of effective mass and its corresponding acceleration:
Fᴜₙᵢᵥ = Mᵉᶠᶠ,ᴜₙᵢᵥ·aᵉᶠᶠ,ᴜₙᵢᵥ
Given that the effective mass is infinite and the matter mass is zero, the force related to dark energy's effective mass is also infinitely large.
• This infinite force would have been a driving factor in the subsequent dynamics of the universe's expansion.
Gravitational Force Relationship:
• While the gravitational force relationship is not fully defined in the presentation, it would logically be influenced by the infinitely large effective mass, indicating a dominant repulsive or expansive force in the primordial state.
Interpretation
In the primordial universe, before the Big Bang event, the cosmos existed in a state of infinite potential energy, completely dominated by dark energy's negative effective mass. This negative effective mass carried an infinite amount of potential energy, which was the only form of energy present, as there was no kinetic energy due to the absence of movement or expansion. The total energy of the universe was thus entirely governed by this boundless potential.
During this period, the universe had no conventional matter; its total mass consisted solely of the infinite effective mass associated with dark energy. This situation created an infinitely large force within the universe, stemming from the interaction of dark energy's effective mass with gravitational dynamics. The overwhelming presence of this force and energy likely set the stage for the subsequent expansion and evolution of the universe, ultimately leading to the Big Bang and the formation of matter as we know it.
Post-Big Bang Event
Potential Energy After the Big Bang:
• The potential energy of the universe, PEᴜₙᵢᵥ →0, approaches zero after the Big Bang event:
PEᴜₙᵢᵥ →0
• This indicates that, following the Big Bang, the potential energy previously associated with dark energy's negative effective mass has diminished to negligible levels.
Kinetic Energy After the Big Bang:
• The kinetic energy of the universe, KEᴜₙᵢᵥ, becomes infinite:
KEᴜₙᵢᵥ = ∞
• This suggests that immediately after the Big Bang, the universe underwent rapid expansion, resulting in infinite kinetic energy due to the dynamic motion of matter and radiation.
Total Energy of the Universe:
• The total energy of the universe, Eₜₒₜₐₗᴜₙᵢᵥ, is the sum of potential and kinetic energy:
Eₜₒₜₐₗ,ᴜₙᵢᵥ = PEᴜₙᵢᵥ + KEᴜₙᵢᵥ = 0 + ∞ = ∞
• This reflects that, in the aftermath of the Big Bang, the universe’s total energy is dominated by the infinite kinetic energy, as the potential energy has become negligible.
Total Mass Equivalent of the Universe:
• The total mass of the universe, Mₜₒₜₐₗ,ᴜₙᵢᵥ, is now described solely by the matter mass:
Mₜₒₜₐₗ,ᴜₙᵢᵥ = Mᴍ
where Mᴍ represents the conventional mass of baryonic and dark matter formed after the Big Bang.
• This indicates that, after the Big Bang, the universe's total mass is comprised of matter mass, with the previous effective mass associated with dark energy no longer contributing to the mass.
Force Relationship in the Universe:
• The force within the universe can be related to the total mass and its acceleration:
Fᴜₙᵢᵥ = (Mᴍ,ᴜₙᵢᵥ + Mᵉᶠᶠ,ᴜₙᵢᵥ)·aᵉᶠᶠ,ᴜₙᵢᵥ
Given that the matter mass Mᴍ,ᴜₙᵢᵥ is non-zero (>0) and the kinetic energy is infinite KEᴜₙᵢᵥ = ∞, the forces involved in the universe’s expansion and structure are influenced by this mass and the accelerating expansion.
Gravitational Force Relationship:
Although not fully detailed, the gravitational forces in the universe after the Big Bang would be influenced by the distribution of matter mass and the resulting gravitational dynamics, moving away from the previously dominant repulsive forces of dark energy.
Interpretation
Following the Big Bang, the universe transitioned from a primordial state of infinite potential energy to one characterized by infinite kinetic energy. This shift marks the onset of rapid expansion, where the potential energy associated with dark energy's negative effective mass became negligible, and kinetic energy surged to dominate the universe’s energy composition.
During this phase, the total energy of the universe is described by the infinite kinetic energy resulting from the initial expansion. The mass of the universe is now composed entirely of conventional matter, reflecting the formation and distribution of baryonic and dark matter in the aftermath of the Big Bang. The forces driving the universe’s evolution are now governed by this matter mass and the dynamic motion, leading to the ongoing expansion and structuring of the cosmos.
To be continued ...
