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

 

[Ignat]

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

The model of the universe as a part of infinite matter removes the contradictions of the cosmological singularity and can explain such exotic concepts as dark matter and dark energy.

Indeed, dark matter manifests itself by gravitational effects, which can be explained by the influence of the external environment on our universe. The same applies to dark energy – it is the energy of external influence on our universe. As a result, we do not see "darkness", but a completely understandable picture of the material world, which does not need fairy tales like the Big Bang.

 

[Jim Franklin]

The model of the universe as a part of infinite matter removes the contradictions of the cosmological singularity and can explain such exotic concepts as dark matter and dark energy.

Indeed, dark matter manifests itself by gravitational effects, which can be explained by the influence of the external environment on our universe. The same applies to dark energy – it is the energy of external influence on our universe. As a result, we do not see "darkness", but a completely understandable picture of the material world, which does not need fairy tales like the Big Bang.

With all due respect, that posts demonstrates to me that you do not understand the concepts of which you speak, not fully at least, and you are clutching at straws - which is fine, many researchers have clutched at straws in history that whilst they were shown to be misguided or plain wrong, the results led them down the path of discovery. .

However, there is much we need to know, much we simply cannot comprehend with our ape brains and one of the most important ones - GRAVITY. You may think we understand it, but in reality we have only scratched the surface.

 

[Ignat]

With all due respect, that posts demonstrates to me that you do not understand the concepts of which you speak, not fully at least, and you are clutching at straws - which is fine, many researchers have clutched at straws in history that whilst they were shown to be misguided or plain wrong, the results led them down the path of discovery. .

Gravity is a universal fundamental interaction between material bodies with mass. (Wikipedia)Please explain which concepts I don't understand. Do you think my assumption is unbelievable in the material world? How do you understand gravity?

 

[Jim Franklin]

Gravity is a universal fundamental interaction between material bodies with mass. (Wikipedia)Please explain which concepts I don't understand. Do you think my assumption is unbelievable in the material world? How do you understand gravity?

The hypothesis that gravitational potential energy (or the energy of the gravitational field) is the source of dark energy is an intriguing and creative idea. However, several points in this argument lack consistency with established physics, and key assumptions require further scrutiny. Here’s a detailed refutation.

1. The ΛCDM Model and Observational Evidence

The ΛCDM model has been incredibly successful in explaining a vast array of cosmological observations, including:

• The cosmic microwave background (CMB) anisotropies
• Large-scale structure formation
• Type Ia supernovae luminosity distances
• Baryon acoustic oscillations (BAO)

Counterpoints to Criticisms

1.1 Dark Energy and the Cosmological Constant Problem
The author points out the "cosmological constant problem," but this does not necessarily imply that the ΛCDM model is wrong. The problem is related to the fine-tuning of vacuum energy, which remains unresolved but does not undermine the model's empirical success.

1.2 Hubble Tension
The Hubble tension problem (a discrepancy in measured Hubble constants) suggests refinements to ΛCDM but does not invalidate it. Possible solutions include evolving dark energy, interactions between dark matter and dark energy, or new physics, but these remain speculative.

1.3 Time-Dependent Dark Energy
Observations by the Dark Energy Survey and the Dark Energy Spectroscopic Instrument hint at the possibility of evolving dark energy, but the evidence remains inconclusive. This doesn't support replacing ΛCDM outright but suggests modifications to the dark energy equation of state.

2. Gravitational Potential Energy as Dark Energy

This hypothesis proposes that the negative gravitational potential energy (GPE) of the universe acts as the source of dark energy and explains accelerated expansion.
Critical Flaws in the Argument

2.1 Gravitational Potential Energy as Anti-Gravity

While gravitational potential energy is negative, it does not inherently produce a repulsive force. GPE arises from the binding energy of a system, but the forces it describes remain attractive. The concept of "anti-gravity" requires explicit physics beyond GPE.

2.2 Newtonian Approximation of Cosmology

The argument relies heavily on Newtonian mechanics for a system as large and relativistic as the universe. General Relativity (GR), which governs cosmic-scale physics, treats energy-momentum and spacetime curvature in a way that cannot be captured by simple Newtonian approximations.

2.3 Mass Energy and GPE Balancing

The claim that negative gravitational potential energy can outweigh positive mass energy is problematic:

• Energy conservation in GR is complex and does not allow for simple subtraction of "mass energy" and "gravitational energy."
• The dynamics of spacetime expansion (described by the Friedmann equations) depend on the total stress-energy tensor, including pressure, rather than a direct GPE-mass energy balance.

2.4 Cosmological Constant Derivation

The derived value of the cosmological constant based on GPE (Λ_gp) is numerically close to observed Λ, but this could be coincidental:

• The derivation does not stem from a fundamental theory or mechanism, and fitting observations by tweaking parameters is not proof of validity.
• The Planck satellite results and other observations strongly support Λ being constant, with no definitive evidence yet for time variability.

2.5 Dark Energy Equation of State

Observations of dark energy suggest it has an equation of state parameter w≈−1w \approx -1w≈−1, consistent with a cosmological constant. Gravitational potential energy, being tied to mass distribution and distance, cannot produce a constant w=−1.

3. Misinterpretation of Observations
3.1 Inflection Points and Accelerated Expansion

The hypothesis claims to explain the universe's inflection point and accelerated expansion through GPE, but this is already well-modeled by the ΛCDM framework using a cosmological constant.
3.2 Large-Scale Structure and CMB Predictions

The gravitational potential energy hypothesis does not account for critical observational successes of ΛCDM, such as:

• The specific angular power spectrum of the CMB.
• The detailed growth of cosmic structures.

4. Conclusion

The idea of gravitational potential energy as the source of dark energy is an interesting speculative framework, but it has significant flaws:

• It oversimplifies the role of gravitational potential energy in General Relativity.
• It fails to explain key cosmological observations that are well-accounted for by ΛCDM.
• Its derivation of the cosmological constant value is mathematically convenient but lacks a solid theoretical foundation.

Refinement or replacement of ΛCDM must address these issues while maintaining agreement with observational data. Gravitational potential energy, as proposed here, does not meet this criterion, hence the theory is wrong.

Does that make my position on this clearer for you?

 

[Ignat]

The hypothesis that gravitational potential energy (or the energy of the gravitational field) is the source of dark energy is an intriguing and creative idea. However, several points in this argument lack consistency with established physics, and key assumptions require further scrutiny. Here’s a detailed refutation.

The established cosmology with the ΛCDM model is collapsing with the new discoveries of the Webb telescope. As for the successful explanation of processes in space by this model, it only means that the wrong model can sometimes give correct results. For example, the theory of circuits is based on Kirchhoff's laws, and he considered the movement of positively charged particles to be current.It is unclear why the gravitational forces of objects external to our universe cannot affect it.

 

[Jim Franklin]

The established cosmology with the ΛCDM model is collapsing with the new discoveries of the Webb telescope. As for the successful explanation of processes in space by this model, it only means that the wrong model can sometimes give correct results. For example, the theory of circuits is based on Kirchhoff's laws, and he considered the movement of positively charged particles to be current.It is unclear why the gravitational forces of objects external to our universe cannot affect it.

You are conflating totally unconnected ideas and topics. I stand by my post, the information within it and that it is a wholly incorrect idea.

We may not understand what gravity is and where it comes from, other than it is the product of mass (in simple terms), but we also do know what it is NOT - and it is NOT responsible for the expansion of the Universe.

 

[Ignat]

We may not understand what gravity is and where it comes from, other than it is the product of mass (in simple terms), but we also do know what it is NOT - and it is NOT responsible for the expansion of the Universe.

I'm not saying that gravity is responsible for the expansion of our universe. I have already shown why the universe does not expand in the post The infinity cannot expand. There is simply a movement of objects along different trajectories, and gravity may well be involved in this.

 

[SMyers]

perhaps cosmic expansion is not accelerating, but is steady. adhering to a rigid dogma concerning the shape of the universe necessitates the need to create novel solutions to why the standard model's geometry does not jive with the known matter in the universe. that's because it is most likely incorrect.

alternate geometries, such as a hypersphere, negate the need to have Dark Solutions, or voids that can be stretched with fancy math.

 

[SMyers]

i have an essay that addresses this topic but so far the admin here has deleted all attempts at posting a link and my content has been locked "waiting approval" for half a day. more than happy to share content over private message to anyone who is interested, as that seems to be the only way i have permission.

 

[SMyers]

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

i have to agree here, the current model's interpretation of the geometry of space needs to be revisited. whatever shape it is, it is not flat, it curves.

as well as the concept of Time being just another Euclidean dimension. the Euclidean axes compound linearly, but Time compounds deterministically (exponentially). meaning they are not the same and cannot be treated the same.

a better geometric fit is a hyperball, consisting of the time axis as the radius, and the three Euclidean's comprising the 3-dimensional hypersphere surface. the math is quite simple, actually.

 

[COLGeek]

i have an essay that addresses this topic but so far the admin here has deleted all attempts at posting a link and my content has been locked "waiting approval" for half a day. more than happy to share content over private message to anyone who is interested, as that seems to be the only way i have permission.

I will contact you directly. Nothing is pending approval.

 

[7icarus7]

1.1 Dark Energy and the Cosmological Constant Problem
The author points out the "cosmological constant problem," but this does not necessarily imply that the ΛCDM model is wrong. The problem is related to the fine-tuning of vacuum energy, which remains unresolved but does not undermine the model's empirical success.

1.2 Hubble Tension
The Hubble tension problem (a discrepancy in measured Hubble constants) suggests refinements to ΛCDM but does not invalidate it. Possible solutions include evolving dark energy, interactions between dark matter and dark energy, or new physics, but these remain speculative.

1.3 Time-Dependent Dark Energy
Observations by the Dark Energy Survey and the Dark Energy Spectroscopic Instrument hint at the possibility of evolving dark energy, but the evidence remains inconclusive. This doesn't support replacing ΛCDM outright but suggests modifications to the dark energy equation of state.

*This analysis was probably written by ChatGPT?

The issues presented above are some of the issues that are clearly being debated within the scientific community, and despite ChatGPT's counterarguments, these issues have not been resolved by the supporters of the Lambda CDM model or ChatGPT.

If ChatGPT were asked to refute the Lambda CDM model, ChatGPT would also refute the Lambda CDM model by including the five points I pointed out and adding other opinions.

Therefore, just because ChatGPT refuted my points, it does not mean that ChatGPT's argument is correct, and there are still arguments on both sides, and it is an unresolved issue and a debate.

It seems that we will have to wait a few more years for the final result on whether dark energy is not a cosmological constant and whether dark energy depends on time.

2.1 Gravitational Potential Energy as Anti-Gravity

While gravitational potential energy is negative, it does not inherently produce a repulsive force. GPE arises from the binding energy of a system, but the forces it describes remain attractive. The concept of "anti-gravity" requires explicit physics beyond GPE.

This claim by ChatGPT is incorrect.

First, ChatGPT acknowledged that gravitational potential energy is negative energy.

If gravitational potential energy is negative energy, then by the mass-energy equivalence principle, it should have a negative equivalent mass, and therefore, it should exert a repulsive force.

What Chat-GPT is confusing is that,
When a mass deficiency occurs in a bound system or object, and when we analyze its gravity, the energy of the entire system, including the gravitational potential energy, is still in a positive energy, positive mass state, so ultimately, an attractive force exists. It is not because gravitational potential energy does not exert a repulsive force, but because the equivalent mass of the negative gravitational potential energy is smaller than the mass of the object in its free state, the object is still in a positive mass state, and therefore, an attractive force exists.

In the above case,
=====
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,

======

What we, who are outside the system, are observing is the total mass or equivalent mass of the bound system, m^* = (2m - m_gp).

In many situations, even if we consider the gravitational potential energy, which has a negative value, the total mass m^* of the system is positive, so the gravity that the system exerts on the outside is an attractive force.

However, as we have seen in cases such as Newtonian mechanics and special relativity, we know that at the extremes of some physical quantities, the two models can differ from each other and different physical phenomena can occur.

In special relativity, such a situation occurred when the speed approached the speed of light c.
In problems that require consideration of gravitational potential energy, since the total gravitational potential energy function is proportional to M^2/R, a large effect generally occurs when M is large or R is small. Therefore, it is difficult to observe the repulsive effect due to gravitational potential energy in the situations around us.

In particular, the situations where the negative gravitational potential energy exceeds the positive mass energy and the repulsive phenomenon can be observed are very limited, such as 1) the inside of a black hole and 2) the observable universe.

Since humanity does not have the ability to observe the inside of a black hole, we can currently only observe it on the scale of the observable universe.

The total energy of the system, including gravitational potential energy, is

Average density of the universe = 8.50 x 10^-27[kgm^-3]
At R=46.5Gly,
Positive mass energy Mc^2 = 2.71 x 10^71 [kgm^2s^-2]
Negative gravitational potential energy U = -(3/5)(GM^2)/R = -8.35 x 10^71 [kgm^2s^-2]

E_T = Mc^2 - (3/5)(GM^2)/R < 0

According to this model, since negative gravitational potential energy is greater than positive mass energy, a repulsive force, i.e. antigravity, exists, and the universe undergoes accelerated expansion.

---------
Although you may have a strong objection and antipathy to the negative mass (density), you need to look at the logical structure of standard cosmology.

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

=====
Negative Mass?
Actually the first indication of the discovery!
=====

The High-z Supernova Search team : if Λ=0, Ω_m = - 0.38(±0.22) : negative mass density
Supernova Cosmology Project team : if Λ=0, Ω_m = - 0.4(±0.1) : negative mass density
*This is from the paper that awarded the Nobel Prize in Physics for the discovery of the accelerated expansion of the universe.

They had negative thoughts about negative mass. So, they discarded the negative mass (density) without sufficient scientific review. They corrected the equation and argued that the accelerated expansion of the universe was evidence of the existence of a cosmological constant.

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, it has only lessened the antipathy of people by the name change. It cannot change the essence.

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
You need to look at the logical structure of standard cosmology. Let's look at the expression expressing (ρ+3P) as the critical density of the universe.

In the second Friedmann 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(-(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= (ρ_c)+(-2ρ_c)= −ρ_c

ρ+3P ≃ (+1)ρ_c + (-2)ρ_c = (−1)ρ_c

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 the total mass of the observable universe is the negative mass state.

In order for the universe to expand at an accelerated rate, (p+3P)<0 must hold, and according to the results of dimensional analysis, a negative mass density is required.

The mainstream achieves negative mass density by introducing negative pressure, and my model achieves negative mass density through the equivalent mass density of negative gravitational potential energy.

The gravitational potential energy hypothesis does not account for critical observational successes of ΛCDM, such as:

• The specific angular power spectrum of the CMB.
• The detailed growth of cosmic structures.

In the previous few cases, I obtained the values of negative gravitational potential energy and positive mass energy.

What we can learn from these few real cases is that gravitational potential energy can be very small compared to mass energy.

In the case of Moon, U_gs-Moon = - (1.89 x 10^-11)(M_Moon)c^2
In the case of Earth, U_gs-Earth = - (4.17 x 10^-10)(M_Moon)c^2
That is, in the gravitational potential energy model, during the CMB epoch, since the universe is young, the total positive equivalent mass M within the gravitational interaction radius is relatively small, and therefore, the gravitational potential energy is negligibly small compared to the mass energy. Therefore, the gravitational potential energy model does not make any claims different from those of the standard cosmology during the CMB epoch. The growth of the structure of the universe is beyond my ability, so we have to wait until experts simulate it.

The gravitational potential energy model clearly suggests the source of dark energy, and the observed dark energy value is also derived through the gravitational potential energy term.

In addition, the gravitational potential energy used is a type of binding energy, and since the universe is a state of binding of various substances and energies, it is a physical quantity that should have been considered. Since gravitational potential energy is negative energy, it has a repulsive effect, and therefore can cause accelerated expansion. I present the dark energy term as a function of time.

Through the model, the point where negative gravitational potential energy becomes equal to positive mass energy can be found as an inflection point, and through this, the time when the effect of dark energy becomes similar to the attractive effect of matter and radiation can be theoretically found, so it can be verified.

However, although I provide the core idea and some calculations, since my learning is lacking, from here on, serious research by someone better than me is needed.

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

 

[SMyers]

*This analysis was probably written by ChatGPT?

haaaa ! i was soo gonna say this. from the first post i read from this guy all i could think was "he's using chatGPT". but i didn't wanna be accused of antagonizing.

and then he proceeds to belittle others and then give them a "grade" .... thanks for calling this out lol.