1. Dark energy has been a subject of considerable debate since its discovery due to its association with the accelerated expansion of the universe. Traditionally perceived as an unknown force or substance, dark energy is better understood as a by-product of the universe’s dynamic processes, particularly the transformation of potential energy into kinetic energy during and after the Big Bang. This work explores the interconnected roles of gravitational forces, kinetic energy, and apparent negative mass, highlighting that dark energy results from the complex interplay between these elements rather than being an independent substance.
Initial State of the Universe and Energy Transformation
Immediately after the Big Bang, the universe's total energy consisted of potential and kinetic components:
Eᴛₒₜ,ᴜₙᵢᵥ = PEᴜₙᵢᵥ + KEᴜₙᵢᵥ
In the earliest moments, the universe was dominated by potential energy, which rapidly approached zero as kinetic energy surged from zero to infinity:
PEᴜₙᵢᵥ: ∞ → 0, KEᴜₙᵢᵥ: 0 → ∞
This energetic shift was driven by gravitational dynamics, where the rapid conversion of potential energy into kinetic energy fuelled the universe’s expansion.
Emergence of Dark Energy: A Dynamic Outcome
Dark energy did not pre-exist the universe but emerged from the dynamic interactions between mass, gravity, and kinetic energy. As the universe’s initial potential mass accelerated due to gravitational forces, an apparent negative mass effect arose, which we interpret as dark energy:
Fᴜₙᵢᵥ = (Mᴘᴇ,ᴜₙᵢᵥ - Mᵃᵖᵖ,ᴜₙᵢᵥ)•aᵉᶠᶠ,ᴜₙᵢᵥ
Here, the apparent mass (Mᵃᵖᵖ,ᴜₙᵢᵥ) represents the dynamic influence of dark energy, emerging from the acceleration of potential mass under universal forces.
Inverse Relationship Between Potential and Kinetic Energy
The universe’s potential energy is inversely related to its kinetic energy, illustrating the natural balance that dictates cosmic evolution:
PEᴜₙᵢᵥ ∝ 1/KEᴜₙᵢᵥ
This relationship underscores the continuous transformation and reactivation of dark energy as the kinetic energy of the universe’s matter evolves.
Dark Energy's Dormancy and Reactivation
Dark energy enters a dormant state when kinetic energy and potential energy achieve equivalence. However, as the universe’s matter mass persists in motion, dark energy reactivates, leading to the accelerated expansion observed today. This cyclical behaviour underscores the transient nature of dark energy:
When PEᴜₙᵢᵥ = KEᴜₙᵢᵥ , Mᵃᵖᵖ = 0
As the universe continues to expand, dark energy becomes dominant once again, reflecting the evolving interplay of mass-energy dynamics.
Dark energy is not a fundamental substance but a manifestation of the universe’s dynamic processes. The accelerated expansion is driven by the continuous transformation of kinetic and potential energies, highlighting that dark energy is a consequence of the cosmic gravitational and kinetic interplay. This understanding shifts the perspective from viewing dark energy as an isolated force to recognizing it as an emergent property of the universe’s mass-energy transformations.
Dear Soumendra Nath Thakur
I'm glad to meet someone who thinks like me.
Your thoughts are similar to my research.
1.The first result of Friedmann equation for accelerated expansion was negative mass density
Nobel lecture by Adam Riess : The official website of the Nobel Prize
Refer to time 11m : 35s ~
https://www.nobelprize.org/mediaplayer/?id=1729
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Negative Mass?
Actually the first indication of the discovery!
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HSS(The High-z Supernova Search) team : if Λ=0, Ω_m = - 0.38(±0.22) : negative mass density
SCP(Supernova Cosmology Project) team : if Λ=0, Ω_m = - 0.4(±0.1) : negative mass density
*This value is included in a paper awarded the Nobel Prize for the discovery of the accelerated expansion of the universe.
In the acceleration equation, (c=1)
(1/R)(d^2R/dt^2) = -(4πG/3)(ρ+3P)
In order for the universe to expand at an accelerated rate, the right side must be positive, and therefore (ρ+3P)must be negative. In other words, a negative mass density is needed for the universe to expand at an accelerated rate.
They had negative thoughts about negative mass (negative energy). So, they discarded the negative mass (density). They corrected the equation and argued that the accelerated expansion of the universe was evidence of the existence of a cosmological constant. However, the vacuum energy model has not succeeded in explaining the value of dark energy density, and the source of dark energy has not yet been determined.
They introduce negative pressure, which hides the negative mass density in the negative pressure, but this does not mean that the negative mass density has disappeared.
ρ_Λ + 3P_Λ = ρ_Λ + 3(-ρ_Λ) = - 2ρ_Λ
If we expand the dark energy term, the final result is a negative mass density of -2ρ_Λ.
2. Logical structure of the standard cosmology
We need to look at the logic behind the success of standard cosmology.
Let's look at the equation expressing (ρ+3P) as the critical density of the universe.
In the second Friedmann equation (c=1),
(1/R)(d^2R/dt^2) = -(4πG/3)(ρ+3P)
Matter + Dark Matter (approximately 31.7%) = ρ_m ~ (1/3)ρ_c
Dark energy density (approximately 68.3%) = ρ_Λ ~ (2/3)ρ_c
(Matter + Dark Matter)'s pressure = 3P_m ~ 0
Dark energy’s pressure = 3P_Λ = 3(-(2/3)ρ_c ) = -2ρ_c
ρ+3P≃ ρ_m +ρ_Λ +3(P_m +P_Λ)= (1/3)ρ_c +(2/3)ρ_c +3(−2/3)ρ_c= (+1)ρ_c + (-2)ρ_c = (−1)ρ_c
ρ+3P ≃ (+1)ρ_c + (-2)ρ_c = (−1)ρ_c
The logic behind the success of the ΛCDM model is a universe with a positive mass density of (+1)ρ_c and a negative mass density of (-2)ρ_c. So, finally, the universe has a negative mass density of “(-1)ρ_c”, so accelerated expansion is taking place.
The current universe is similar to a state where the negative mass (energy) density is twice the positive mass(energy) density. And the total mass of the observable universe is the negative mass state.
3. So, what can correspond to this negative mass density?
When mass or energy is present, the negative gravitational potential energy(gravitational self-energy or gravitational binding energy) produced by that mass or energy distribution can play a role. The gravitational potential energy model is a model in which +ρ and -ρ_gp exist, and shows that |-ρ_gp| can be larger than +ρ.
Looking at the mass deficiency effect (negative mass effect) caused by binding energy,
● ----- r ----- ●
m ------------ m
When two masses m are separated by r, the total energy of the system is
E_T=2mc^2 − Gmm/r
In the dimensional analysis of energy, E has kg(m/s)^2, so all energy can be expressed in the form of (mass) X (velocity)^2. So, E=Mc^2 holds true for all kinds of energy. Here, M is the total mass or equivalent mass. If we introduce the negative equivalent mass "-m_gp" for the negative gravitational potential energy,
−Gmm/r=(−m_gp)c^2
E_T=2mc^2−Gmm/r=(2m−m_gp)c^2=(m^∗)c^2
The gravitational force acting on a relatively distant third mass m_3 is
F=−G(m^∗)(m_3)/R^2=−G(2m−m_gp)(m_3)/R^2=−G(2m)(m_3)/R^2 + G(m_gp)(m_3)/R^2
That is, when considering the gravitational action of a bound system, not only the mass in its free state but also the binding energy term (-m_gp) should be considered.
The second term is the repulsive term and the antigravity term.
F=+ G(m_gp)(m_3)/R^2
In the general case, the value of gravitational potential energy(gravitational self-energy) is small enough to be negligible, compared to mass energy mc^2. However, as more mass is collected, the ratio of (negative) gravitational potential energy to (positive) mass energy increases.
In the case of Moon, U_{gp - Moon} = ( - 1.89 x 10^ -11)M_{Moon}(c^2)
In the case of Earth, U_{gp - Earth} = ( - 4.17 x 10^ -10)M_{Earth}(c^2)
In the case of the Sun, U_{gp - Sun} = ( - 1.27 x 10^ -4)M_{Sun}(c^2)
In case of a Black hole, U_{gp - Black - hole} = ( - 3.0 x 10^-1)M_{Black - hole}(c^2)
At R=2GM/c^2,
U_gp-Black-hole = -(3/5)(GM^2/R) = -(3/5)(GM^2/(2GM/c^2)) = -(3/10)Mc^2
In the case of a black hole, the negative gravitational potential energy is 30% of the positive mass energy (mass energy when the masses forming a black hole are free state). It can be seen that the magnitude of the gravitational potential energy is not negligible compared to the mass energy.
What would happen in a universe with more mass?
4. For the observable universe, calculating mass energy and gravitational potential energy
By Birkhoff’s theorem, only the mass or energy component within the gravitational interaction range is important. If we find the positive energy (M c^2) and negative gravitational potential energy ((−M_gp)c2) values at each radius R of gravitational interaction, positive energy is an attractive component, and the negative gravitational potential energy is a repulsive component.
[Result summary]
Use a critical density ρ_c=8.50x10^-27[kgm^-3]
At R=16.7Gly, (-M_gp)c^2 = (-0.39)Mc^2
|(-M_gp)c^2| < (Mc^2) : Decelerating expansion period
At R=26.2Gly, (-M_gp)c^2 = (-1.00)Mc^2
|(-M_gp)c^2| = (Mc^2) : Inflection point (About 5-7 billion years ago,
consistent with standard cosmology.)
At R=46.5Gly, (-M_gp)c^2 = (-3.04)Mc^2
|(-M_gp)c^2| > (Mc^2) : Accelerating expansion period
Even in the universe, gravitational potential energy (or gravitational action of the gravitational field) must be considered. And, in fact, if we calculate the value, since gravitational potential energy is larger than mass energy, so the universe has accelerated expansion. Gravitational potential energy model accounts for decelerated expansion, inflection point, and accelerated expansion.
As the universe ages, the range of gravitational interactions increases, and thus accelerated expansion appears to have occurred because the negative gravitational potential energy increased faster than the positive mass energy.
As the universe grows older, the range R of gravitational interaction increases. As a result, mass energy increases in proportion to M, but gravitational potential energy increases in proportion to -M^2/R. Therefore, gravitational potential energy increases faster.
Therefore, as the universe ages and the range of gravitational interaction expands, the phenomenon of changing from decelerated expansion to accelerated expansion occurs.
Preprint Dark Energy is Gravitational Potential Energy or Energy of t...
01-09-2024
Dear Mr. Hyoyoung Choi ,
Thank you for your insightful and detailed response. I appreciate your engagement with my work and the connections you’ve drawn with your research.
Your observations on the role of negative mass density and the Friedmann equation’s implications for accelerated expansion are fascinating. I would like to address a few points based on my study, which is grounded in extended classical mechanics and its implications for dark energy and gravitational dynamics:
1. Negative Mass Density and Gravitational Dynamics: Your reference to the HSS and SCP teams' findings about negative mass density is compelling. I agree that the Friedmann equations suggest a need for negative mass density to explain accelerated expansion. My study, however, interprets the effective mass (Mᵉᶠᶠ) in a broader context, emphasizing that dark energy manifests as a significant effective mass rather than strictly a negative mass density.
2. Effective Mass vs. Gravitating Mass: In my framework, the effective mass (Mᵉᶠᶠ) exceeds the conventional matter mass (Mᴍ) to generate dark energy. This aligns with your observation of the need for negative mass density, but from an extended classical mechanics perspective, it is essential to see how effective mass interacts with gravitating mass (Mɢ). When Mᵉᶠᶠ > Mᴍ, the resulting dynamics suggest that the effective mass contributes to the universe's overall gravitational behaviour, leading to accelerated expansion.
3. Gravitational Potential Energy Model: Your analysis of gravitational potential energy and its effects on expansion dynamics is intriguing. In my study, I propose that dark energy is closely linked with changes in gravitational potential energy, particularly in a universe where the effective mass (or its equivalent) becomes predominant. This complements your view that negative gravitational potential energy can impact expansion rates.
4. Comparison with Standard Cosmology: The comparison you provided between positive and negative mass densities highlights the nuances of standard cosmology. My study, while also considering these aspects, focuses on how extended classical mechanics can offer a complementary view. Specifically, by considering the potential energy’s role and the effective mass, my approach aims to provide a more integrated perspective on the universe’s dynamics.
In summary, while your research aligns with some aspects of my study, such as the necessity of negative mass density for explaining accelerated expansion, my work extends the classical mechanics framework to incorporate effective mass and potential energy considerations. This approach offers a nuanced view of how dark energy influences cosmic expansion beyond the standard cosmological model.
Thank you again for your engaging response. I look forward to further discussions on these intriguing topics.
Best regards,
Soumendra Nath Thakur
Dear Hyoyoung Choi
Here is a brief explanation of my view on this discussion, based on extended classical mechanics and a study on dark energy and galaxy clusters:
[ https://www.researchgate.net/post/Dark_Energy_as_a_By-Product_of_Negative_Effective_Mass_Discussion ]
Best regards, Soumendra Nath Thakur
There is another way of explaining the unexpected recession velocity of distant galaxies. This recognises that the recession velocity has two components: 1. the expansion of space 2. The movement of the distant galaxy through space due to gravitational acceleration towards the centre of the galaxy distribution.
This depends on the model of the universe in which we are 26 million light years from the centre of a finite universe. We would have to discard the cosmological principle and the Big Bang theory.
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