Dark Energy as a By-Product of Negative Effective Mass: Discussion.

Soumendra Nath Thakur

31-08-2024

Effective dark energy is interpreted as a manifestation of negative effective mass, a concept rooted in extended classical mechanics and involving the dynamics of potential, kinetic, and gravitational forces. This phenomenon emerges from the apparent reduction in invariant matter mass and its resulting influence on the universe's overall dynamics. ResearchGate Discussion Link Here!

Note: Matter mass Mᴍ is understood as the combined mass of normal matter (such as baryonic matter) and dark matter.

Summary:

Effective dark energy, considered a by-product of negative effective mass, arises from the intricate interplay of potential, kinetic, and gravitational dynamics in the universe. This concept challenges traditional views by suggesting that dark energy is not a separate entity but rather a consequence of negative effective mass. The fundamental equation, PEᴛₒₜᴜₙᵢᵥ ∝ Mᵉᶠᶠᴜₙᵢᵥ, establishes a direct relationship between the universe's potential energy and its effective mass, highlighting their intrinsic connection.

In the early universe, effective mass played a critical role in determining the potential energy. The universal force was necessary to convert this potential energy into kinetic energy, facilitating the rapid expansion of the universe. As the effective mass decreased, acceleration increased, reflecting the dynamics of this early rapid expansion, as described by the equation Fᴜₙᵢᵥ = Mᵉᶠᶠᴜₙᵢᵥ · aᵉᶠᶠᴜₙᵢᵥ. This equation illustrates that the universal force is directly proportional to effective acceleration, offering key insights into the universe's expansion dynamics.

As the universe continued to evolve, its potential energy became influenced by both matter mass and effective mass, including contributions from dark energy and other effective masses. Later, the universal force was shaped by both matter and effective mass, with effective acceleration inversely related to the combined mass. The ongoing generation of dark energy and its dominance in gravitational dynamics are thus explained by the relationship between effective mass and gravitational effects, suggesting a repulsive gravitational force that significantly influences the universe's structure and evolution.

Effective dark energy can thus be seen as a by-product of negative effective mass, arising from the complex interrelations of potential, kinetic, and gravitational forces, and reflecting the apparent reduction in invariant matter mass over time.

Reference: 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. https://doi.org/10.1051/0004-6361/201220781 

UPDATE 01-09-2024: Expanded Insights on Negative Effective Mass and Dark Energy Dynamics

Negative Effective Mass: Insights from Universal Force and Acceleration Dynamics

The universal force Fᴜₙᵢᵥ is defined by the product of the effective acceleration aᵉᶠᶠᴜₙᵢᵥ and the combined inverse contributions of two types of mass: the variable effective mass Mᵉᶠᶠᴜₙᵢᵥ and the constant matter mass Mᴍᴜₙᵢᵥ. This relationship emphasizes that the universal force depends not only on acceleration but also on the dynamic interplay between these masses. The effective mass reflects the system’s response to dynamic factors such as motion and gravitational interactions, and it can differ from the constant matter mass by varying according to system conditions.

The universal force and acceleration increase or decrease proportionally with the combined reciprocal masses, where variations in the effective mass directly influence acceleration and the resulting universal force. As the effective mass decreases, acceleration increases, and vice versa. This relationship aligns with the interpretation of "negative effective mass," where changes in the dynamic state of the universe alter gravitational interactions.

The concept of "negative effective mass" arises from this interpretation of effective mass. When extended to dark energy's influence on gravitational dynamics, it captures the idea that the effective mass may exhibit properties akin to a negative effective density, leading to repulsive gravitational effects. In this context, "negative effective mass" describes how the dynamic properties of dark energy counteract gravitational attraction, contrasting with the attractive behaviour of conventional matter.

The effective mass Mᵉᶠᶠᴜₙᵢᵥ reflects the apparent mass loss or gain relative to the constant matter mass Mᴍᴜₙᵢᵥ. When there is an apparent mass loss, the effective mass increases to maintain balance within the system’s dynamics, suggesting that under certain conditions, the effective mass could be perceived as "negative." This negative value provides a framework for understanding inverse gravitational effects observed with dark energy, where repulsive dynamics challenge traditional gravitational interactions.

Additionally, when the universal force Fᴜₙᵢᵥ increases, the effective acceleration aᵉᶠᶠᴜₙᵢᵥ also increases. Initially, the effective mass Mᵉᶠᶠᴜₙᵢᵥ is equivalent to the matter mass Mᴍᴜₙᵢᵥ. However, as force or acceleration continues to increase, the effective mass can exceed the matter mass, thereby potentially dominating the gravitating mass Mɢᴜₙᵢᵥ. This implies that the effective mass plays a crucial role in determining the overall gravitational behaviour, supporting the idea of "negative effective mass" in scenarios where dark energy exerts a repulsive force.

By incorporating the concept of "negative effective mass" into the extended framework of classical mechanics, we develop a more comprehensive understanding of the gravitational dynamics, allowing us to account for the repulsive effects of dark energy on the universe's expansion. This refined interpretation bridges the abstract notion of dynamic mass variations with observable cosmological phenomena, providing insight into the complex interplay between mass, force, and acceleration in the universe.

Dark energy's influence on the universe's expansion can be understood in terms of the effective mass (Mᵉᶠᶠᴜₙᵢᵥ) exhibiting properties that suggest a negative effective density. When the effective mass exceeds the matter mass (Mᴍᴜₙᵢᵥ), it contributes to gravitational dynamics that may resemble those associated with a negative gravitating mass (Mɢᴜₙᵢᵥ), leading to the repulsive effects observed in the universe.

Mathematical Framework:

The mathematical framework establishes a relationship between potential energy, effective mass, and universal force, providing insight into the universe's expansion and the concept of "negative effective mass." The potential energy of the universe (PEᴛₒₜᴜₙᵢᵥ) is directly proportional to the effective mass (Mᵉᶠᶠᴜₙᵢᵥ), indicating that the effective mass plays a crucial role in defining the universe's dynamics.

The equation Fᴜₙᵢᵥ = Mᵉᶠᶠᴜₙᵢᵥ · aᵉᶠᶠᴜₙᵢᵥ describes the universal force as directly proportional to effective acceleration (aᵉᶠᶠᴜₙᵢᵥ) and inversely proportional to effective mass (Mᵉᶠᶠᴜₙᵢᵥ). An increase in acceleration leads to an increase in the universal force and a corresponding decrease in effective mass, which can lead to the formation of matter. Over time, potential energy becomes dependent on both the matter mass (Mᴍᴜₙᵢᵥ) and the present effective mass, shaping the gravitational dynamics.

By linking these parameters, this framework explains how variations in effective mass, particularly when perceived as negative, contribute to the repulsive effects associated with dark energy, providing a comprehensive view of the complex interplay between mass, force, and acceleration in the universe.

The Equations:

PEᴛₒₜᴜₙᵢᵥ ∝ Mᵉᶠᶠᴜₙᵢᵥ,

This expression, establishes a direct relationship between the universe's potential energy and its effective mass. In the early universe, effective mass played a critical role in determining the potential energy. The universal force was necessary to convert this potential energy into kinetic energy, facilitating the rapid expansion of the universe. As the effective mass decreased, acceleration increased, reflecting the dynamics of this early rapid expansion.

The equation Fᴜₙᵢᵥ = Mᵉᶠᶠᴜₙᵢᵥ · aᵉᶠᶠᴜₙᵢᵥ

describes that the universal force is directly proportional to effective acceleration, and effective acceleration is inversely proportional to effective mass. This relationship suggests that in the early universe, the universal force was the product of the effective mass and the effective acceleration.

Since acceleration is inversely proportional to mass, an increase in effective acceleration leads to a corresponding increase in the universal force, which, in turn, causes a decrease in the effective mass as the acceleration increases, and so corresponding increase in matter mass through formation. As acceleration increase, the effective mass decrease, forming matter mass.

Later, the potential energy became dependent on both the matter mass (Mᴍᴜₙᵢᵥ) and the present effective mass.

The force is influenced by the interaction between the matter mass and the effective mass, where the effective acceleration (aᵉᶠᶠᴜₙᵢᵥ) is inversely related to the total mass, comprising both matter and effective mass, represented by the equation:

Fᴜₙᵢᵥ = (Mᴍᴜₙᵢᵥ+Mᵉᶠᶠᴘᵣₑₛₑₙₜ) · aᵉᶠᶠᴜₙᵢᵥ

As the effective acceleration increases, the apparent matter mass decreases, corresponding increase in present effective mass, which is negative, within this combined mass. Thus, the emergence of dark energy from negative effective mass and its dominant role in gravitational dynamics can be explained by the relationship between effective mass and gravitational effects. As acceleration increased, the apparent matter mass decreased, generating effective mass.

Dark energy's influence on the universe's expansion can be understood in terms of the effective mass (Mᵉᶠᶠᴜₙᵢᵥ) exhibiting properties that suggest a negative effective density. When the effective mass exceeds the matter mass (Mᴍᴜₙᵢᵥ), it contributes to gravitational dynamics that may resemble those associated with a negative gravitating mass (Mɢᴜₙᵢᵥ), leading to the repulsive effects observed in the universe. As provided under, "Negative Effective Mass: Insights from Universal Force and Acceleration Dynamics.