Dark energy! Conceptual tension for the standard cosmological model?

[Sócrates Georges Petrakis]

What are the options for the accelerated expansion of the Universe, besides Dark Energy?

 

[Gibsense]

What are the options for the accelerated expansion of the Universe, besides Dark Energy?

The shape of space and the interpretation of time. I am willing to have a go (my own explanation) but only after every sensible person has had a crack conventially because I will have to duck and weave

 

[7icarus7]

I argue that Gravitational Potential Energy (or gravitational field's energy) is the source of dark energy!
In the standard cosmology model, dark energy is described as having a positive energy density and exerting negative pressure. However, since the source of accelerated expansion is unknown, it is named dark energy, so it is also a hypothesis that it has positive energy density and acts on negative pressure. Currently, the ΛCDM model is leading the way, but there is a possibility that the answer will be wrong.

1.The ΛCDM model may be wrong

1)The Dark Energy Survey team(2024.01)
The Dark Energy Survey team, an international collaborative team of more than 400 scientists, announced the results of an analysis of 1,499 supernovae. (2024.01) This figure is approximately 30 times more than the 52 supernovae used by the team that reported the accelerated expansion of the universe in 1998.

https://noirlab.edu/public/news/noirlab2401/?lang

The standard cosmological model is known as ΛCDM, or ‘Lambda cold dark matter’. This mathematical model describes how the Universe evolves using just a few features such as the density of matter, the type of matter and the behavior of dark energy. While ΛCDM assumes the density of dark energy in the Universe is constant over cosmic time and doesn’t dilute as the Universe expands, the DES Supernova Survey results hint that this may not be true.

An intriguing outcome of this survey is that it is the first time that enough distant supernovae have been measured to make a highly detailed measurement of the decelerating phase of the Universe, and to see where the Universe transitions from decelerating to accelerating. And while the results are consistent with a constant density of dark energy in the Universe, they also hint that dark energy might possibly be varying. “There are tantalizing hints that dark energy changes with time,” said Davis, “We find that the simplest model of dark energy — ΛCDM — is not the best fit. It’s not so far off that we’ve ruled it out, but in the quest to understand what is accelerating the expansion of the Universe this is an intriguing new piece of the puzzle. A more complex explanation might be needed.”

2)Dark Energy Spectroscopic Instrument team(2024.04 / 2024.11)
https://arstechnica.com/science/2024/04/dark-energy-might-not-be-constant-after-all/#gsc.tab=0

"It's not yet a clear confirmation, but the best fit is actually with a time-varying dark energy," said Palanque-Delabrouille of the results. "What's interesting is that it's consistent over the first three points. The dashed curve [see graph above] is our best fit, and that corresponds to a model where dark energy is not a simple constant nor a simple Lambda CDM dark energy but a dark energy component that would vary with time.

1.1 ΛCDM model does not explain the origin of dark energy, or the cosmological constant Λ. In the case of vacuum energy, which was presented as a strong candidate, there is a huge difference of 10^120 times (depending on some models, it can be reduced to 10^60 times) between observed values and theoretical predictions. Cosmological Constant Problem and Cosmological Constant Coincidence Problem are unresolved.

1.2 In the case of CDM as dark matter, candidates such as MACHO (Massive Astrophysical Compact Halo Object), black hole, and neutrino failed one after another, and even WIMP, which was presented as a strong candidate, was not detected in several experiments. In addition, no suitable candidate for CDM was found in particle accelerators, which are a completely different methodological approach from WIMP detection.

1.3 Hubble tension problem: This is a discrepancy between the Hubble constant observed through cosmic background radiation (CMB) and the Hubble constant value obtained by observing actual galaxies, which implies the possibility that dark energy is not a cosmological constant.

1.4 The Dark Energy Survey team's large-scale supernova analysis results: suggest the possibility that dark energy is not a cosmological constant, but a function of time.

1.5. The Dark Energy Spectroscopic Instrument team also suggested that the dark energy density may not be constant but a function of time, meaning that the cosmological constant model may be wrong.

Therefore, we must consider whether there are other possibilities to the existing interpretation.


2.The logic behind the success of the ΛCDM model
We are faced with the possibility that the ΛCDM model is a successful model in some ways and a wrong model in others. Therefore, there is a need to analyze what makes the ΛCDM model seem like a successful model.

Let’s put the results obtained from the ΛCDM model into the acceleration equation.
matter:4.9%, dark matter:26.8%, dark energy:68.3%

In the acceleration equation,
(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(-ρ_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 standard cosmology 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 density is twice the positive mass density. And if the entire mass of the observable universe is in a negative mass state, the phenomenon of accelerated expansion can be explained.

So, is there a physical quantity that can play the role of negative energy (mass) as above? Yes!


3. Gravitational Potential Energy or Gravitational Field's Energy
*Gravitational potential energy = gravitational self-energy = - gravitational binding energy ≃ gravitational field's energy

When a binding system exerts gravitational force, the gravitational potential energy has a negative equivalent mass and exerts gravitational force.
Because the universe is a structure in which countless masses exist, the gravitational potential energy between masses must be considered.

1) Mass defect effect due to gravitational binding energy (gravitational potential energy)

● ----- r ----- ●

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 equivalent mass. If we introduce the negative equivalent mass "-m_gp" for the gravitational potential energy,

When a binding system exerts gravitational force, the gravitational potential energy has a negative equivalent mass and acts as a gravitational force (anti-gravity).

F_gp= +G(m_gp)(m_3)/R^2

In general, gravitational potential energy is small compared to mass energy, so it can be ignored. However, on a cosmic scale, the situation is different.
If we calculate the values of the gravitational potential energy of celestial bodies, we get surprising results.

In the case of spherical uniform distribution, gravitational self-energy

It can be seen that the gravitational potential energy is about 1/10000 of the (free state) mass energy in the case of the sun and 30% of the (free state) mass of the black hole at the event horizon of the black hole.

When the mass is large, it can be seen that the negative gravitational potential energy cannot be ignored.
Therefore, we need to calculate what the magnitude of gravitational potential energy is for the observable universe.


4. In the observable universe, positive mass energy and negative gravitational potential energy
The universe is almost flat, and its mass density is also very low. Thus, Newtonian mechanics approximation can be applied. And, the following reasoning should not be denied by the assertion that “it is difficult to define the total energy in general relativity.”

When it is difficult to find a complete solution, we have found numerous solutions through approximation. The success of this approximation or inference must be determined by the model’s predictions and observations of the universe.

*The Friedmann equation can be obtained from the field equation. The basic form can also be obtained through Newtonian mechanics. If the object to be analyzed has spherical symmetry, from the second Newton’s law,

By adding pressure, we can create an acceleration equation.

Let’s look at the origin of mass density ρ here! What does ρ come from?
It comes from the total mass M inside the shell. The universe is a combined state because it contains various various matter(galaxies...), radiation, and energy.
Therefore, the total mass m^* including the binding energy must be entered, not the mass “2m” in the free state.“m^∗ = 2m + (−m_gp)”, i.e. gravitational potential energy must be considered.
In addition, since the acceleration equation can be derived from Newtonian mechanics, it can be seen that the Newtonian mechanical estimate has some validity.

If we find the Mass energy (Mc^2; M is the equivalent mass of positive energy.) and Gravitational potential energy (U_gp=(-M_gp)c^2) values at each range of gravitational interaction, Mass energy is an attractive component, and the gravitational potential energy (or gravitational self-energy) is a repulsive component. Critical density value p_c = 8.50 x 10^-27[kgm^-3] was used.

[Result summary]
At R=16.7Gly, U_gp = (-0.39)Mc^2
|U_gp| < (Mc^2) : Decelerating expansion period

At R=26.2Gly, U_gp = (-1.00)Mc^2
|U_gp| = (Mc^2) : Inflection point (About 5-7 billion years ago, consistent with standard cosmology.)

At R=46.5Gly, U_gp = (-3.08)Mc^2
|U_gp| > (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 negative gravitational potential energy is larger than positive mass energy, so the universe has accelerated expansion. The Gravitational Potential Energy Model describes decelerating expansion, inflection points, and accelerating expansion.

Since mass energy is proportional to M, whereas gravitational potential energy is proportional to -M^2/R, as mass increases, the ratio of (negative) gravitational potential energy to (positive) mass energy increases.

Therefore, as the universe ages and the range of gravitational interaction expands, a situation arises where the negative gravitational potential energy becomes greater than the positive mass energy, and thus the universe is accelerating expansion.

If we roughly calculate the value of the cosmological constant using the gravitational potential energy model,

Λ_gp = (6πGRρ/5c^2)^2 = 2.455 x 10^-52[m^-2]

This value is almost identical to the cosmological constant value obtained through the Planck satellite.

Λ_obs = 1.1056 x 10^-52[m^-2]

With a little correction, we can get the values to match exactly. Dark energy is not a cosmological constant, it is a function of R and ρ, and dark energy changes over time.

#Paper
Dark Energy is Gravitational Potential Energy or Energy of the Gravitational Field

 

[Jim Franklin]

I argue that Gravitational Potential Energy (or gravitational field's energy) is the source of dark energy!
In the standard cosmology model, dark energy is described as having a positive energy density and exerting negative pressure. However, since the source of accelerated expansion is unknown, it is named dark energy, so it is also a hypothesis that it has positive energy density and acts on negative pressure. Currently, the ΛCDM model is leading the way, but there is a possibility that the answer will be wrong.

1.The ΛCDM model may be wrong

1)The Dark Energy Survey team(2024.01)
The Dark Energy Survey team, an international collaborative team of more than 400 scientists, announced the results of an analysis of 1,499 supernovae. (2024.01) This figure is approximately 30 times more than the 52 supernovae used by the team that reported the accelerated expansion of the universe in 1998.

https://noirlab.edu/public/news/noirlab2401/?lang



2)Dark Energy Spectroscopic Instrument team(2024.04 / 2024.11)
https://arstechnica.com/science/2024/04/dark-energy-might-not-be-constant-after-all/#gsc.tab=0


1.1 ΛCDM model does not explain the origin of dark energy, or the cosmological constant Λ. In the case of vacuum energy, which was presented as a strong candidate, there is a huge difference of 10^120 times (depending on some models, it can be reduced to 10^60 times) between observed values and theoretical predictions. Cosmological Constant Problem and Cosmological Constant Coincidence Problem are unresolved.

1.2 In the case of CDM as dark matter, candidates such as MACHO (Massive Astrophysical Compact Halo Object), black hole, and neutrino failed one after another, and even WIMP, which was presented as a strong candidate, was not detected in several experiments. In addition, no suitable candidate for CDM was found in particle accelerators, which are a completely different methodological approach from WIMP detection.

1.3 Hubble tension problem: This is a discrepancy between the Hubble constant observed through cosmic background radiation (CMB) and the Hubble constant value obtained by observing actual galaxies, which implies the possibility that dark energy is not a cosmological constant.

1.4 The Dark Energy Survey team's large-scale supernova analysis results: suggest the possibility that dark energy is not a cosmological constant, but a function of time.

1.5. The Dark Energy Spectroscopic Instrument team also suggested that the dark energy density may not be constant but a function of time, meaning that the cosmological constant model may be wrong.

Therefore, we must consider whether there are other possibilities to the existing interpretation.


2.The logic behind the success of the ΛCDM model
We are faced with the possibility that the ΛCDM model is a successful model in some ways and a wrong model in others. Therefore, there is a need to analyze what makes the ΛCDM model seem like a successful model.

Let’s put the results obtained from the ΛCDM model into the acceleration equation.
matter:4.9%, dark matter:26.8%, dark energy:68.3%

In the acceleration equation,
(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(-ρ_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 standard cosmology 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 density is twice the positive mass density. And if the entire mass of the observable universe is in a negative mass state, the phenomenon of accelerated expansion can be explained.

So, is there a physical quantity that can play the role of negative energy (mass) as above? Yes!


3. Gravitational Potential Energy or Gravitational Field's Energy
*Gravitational potential energy = gravitational self-energy = - gravitational binding energy ≃ gravitational field's energy

When a binding system exerts gravitational force, the gravitational potential energy has a negative equivalent mass and exerts gravitational force.
Because the universe is a structure in which countless masses exist, the gravitational potential energy between masses must be considered.

1) Mass defect effect due to gravitational binding energy (gravitational potential energy)

● ----- r ----- ●

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 equivalent mass. If we introduce the negative equivalent mass "-m_gp" for the gravitational potential energy,

When a binding system exerts gravitational force, the gravitational potential energy has a negative equivalent mass and acts as a gravitational force (anti-gravity).

F_gp= +G(m_gp)(m_3)/R^2

In general, gravitational potential energy is small compared to mass energy, so it can be ignored. However, on a cosmic scale, the situation is different.
If we calculate the values of the gravitational potential energy of celestial bodies, we get surprising results.

In the case of spherical uniform distribution, gravitational self-energy

It can be seen that the gravitational potential energy is about 1/10000 of the (free state) mass energy in the case of the sun and 30% of the (free state) mass of the black hole at the event horizon of the black hole.

When the mass is large, it can be seen that the negative gravitational potential energy cannot be ignored.
Therefore, we need to calculate what the magnitude of gravitational potential energy is for the observable universe.


4. In the observable universe, positive mass energy and negative gravitational potential energy
The universe is almost flat, and its mass density is also very low. Thus, Newtonian mechanics approximation can be applied. And, the following reasoning should not be denied by the assertion that “it is difficult to define the total energy in general relativity.”

When it is difficult to find a complete solution, we have found numerous solutions through approximation. The success of this approximation or inference must be determined by the model’s predictions and observations of the universe.

*The Friedmann equation can be obtained from the field equation. The basic form can also be obtained through Newtonian mechanics. If the object to be analyzed has spherical symmetry, from the second Newton’s law,

By adding pressure, we can create an acceleration equation.

Let’s look at the origin of mass density ρ here! What does ρ come from?
It comes from the total mass M inside the shell. The universe is a combined state because it contains various various matter(galaxies...), radiation, and energy.
Therefore, the total mass m^* including the binding energy must be entered, not the mass “2m” in the free state.“m^∗ = 2m + (−m_gp)”, i.e. gravitational potential energy must be considered.
In addition, since the acceleration equation can be derived from Newtonian mechanics, it can be seen that the Newtonian mechanical estimate has some validity.

If we find the Mass energy (Mc^2; M is the equivalent mass of positive energy.) and Gravitational potential energy (U_gp=(-M_gp)c^2) values at each range of gravitational interaction, Mass energy is an attractive component, and the gravitational potential energy (or gravitational self-energy) is a repulsive component. Critical density value p_c = 8.50 x 10^-27[kgm^-3] was used.

[Result summary]
At R=16.7Gly, U_gp = (-0.39)Mc^2
|U_gp| < (Mc^2) : Decelerating expansion period

At R=26.2Gly, U_gp = (-1.00)Mc^2
|U_gp| = (Mc^2) : Inflection point (About 5-7 billion years ago, consistent with standard cosmology.)

At R=46.5Gly, U_gp = (-3.08)Mc^2
|U_gp| > (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 negative gravitational potential energy is larger than positive mass energy, so the universe has accelerated expansion. The Gravitational Potential Energy Model describes decelerating expansion, inflection points, and accelerating expansion.

Since mass energy is proportional to M, whereas gravitational potential energy is proportional to -M^2/R, as mass increases, the ratio of (negative) gravitational potential energy to (positive) mass energy increases.

Therefore, as the universe ages and the range of gravitational interaction expands, a situation arises where the negative gravitational potential energy becomes greater than the positive mass energy, and thus the universe is accelerating expansion.

If we roughly calculate the value of the cosmological constant using the gravitational potential energy model,

Λ_gp = (6πGRρ/5c^2)^2 = 2.455 x 10^-52[m^-2]

This value is almost identical to the cosmological constant value obtained through the Planck satellite.

Λ_obs = 1.1056 x 10^-52[m^-2]

With a little correction, we can get the values to match exactly. Dark energy is not a cosmological constant, it is a function of R and ρ, and dark energy changes over time.

#Paper
Dark Energy is Gravitational Potential Energy or Energy of the Gravitational Field

Try reading this.

https://academic.oup.com/mnrasl/article/537/1/L55/7926647?login=false