# The source of dark energy is total gravitational potential energy!

#### icarus2

Registered Senior Member
The source of dark energy is gravitational self-energy or total gravitational potential energy!

1. The need for negative energy density
1) Negative energy (mass) density in standard cosmology
From the second Friedmann equation or acceleration equation,

In standard cosmology, it is explained by introducing an entity that has a positive mass density but exerts a negative pressure.
ρ_Λ + 3P_Λ = ρ_Λ+3(-ρ_Λ) = - 2ρ_Λ
However, If we rearrange the dark energy term, the final result is a negative mass density of "- 2ρ_Λ" .

There are too many people who have an aversion to negative energy (mass). However, in the standard cosmology, accelerated expansion is impossible without negative mass density. It is just that the negative mass density term is called negative pressure, so it is not recognized.

2) The energy of a gravitational field is negative
In his lecture, Alan Guth said:
The energy of a gravitational field is negative! The positive energy
of the false vacuum was compensated by the negative energy of gravity.

Stephen Hawking also argued that
Zero energy state could be maintained when mass energy and gravitational potential energy were offset each other at the inflation period only.

3) Earth's and Moon's Gravitational self-energy

Treating the Earth as a continuous, classical mass distribution (with no gravitational self-energy in the elementary, subatomic particles), we find that its gravitational self-energy is about 4.6 x 10^-10 times its rest-mass energy. The gravitational self-energy of the Moon is smaller, only about 0.2 x 10^- 10 times its rest-mass energy. - GRAVITATION AND SPACETIME

4) Mass defect due to binding energy

Consider situations a) and c)

In a), the total mass of the two particle system is 2m, and the total energy is E_T=2mc^2
In c), is the total energy of the two-particle system E_T=2mc^2 ?
In c), when the two particle system act gravitationally on an external particle, will they act gravitationally with a gravitational mass of " 2m "?

Are a) and c) the same mass or same state?
If you do not apply negative binding energy, the conclusions you get will not match the actual results.

In c), the total energy of the two particle systems is

In the dimension analysis of energy, E has kg(m/s)^2, so all energy can be expressed in the form of mass x (speed)^2. So, E=mc^2 (Here, m is not used as a word for rest mass, but for mass.) holds true for all kinds of energy. If we introduce the equivalent mass -m_gp for the gravitational potential energy,

In the dimension analysis of energy, E has kg(m/s)^2, so all energy can be expressed in the form of mass x (speed)^2. So, E=mc^2 (Here, m is not used as a word for rest mass.) holds true for all kinds of energy. If we introduce the equivalent mass -m_gp for the gravitational potential energy,

The gravitational force acting on a relatively distant third mass m3 is

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 should be considered. Alternatively, the gravitational force acting on the bound system can be decomposed into a free-state mass term and an equivalent mass term of binding energy.

While we usually use the mass m* of the bound system, we forget that m* is (m - m_binding-energy). Gravitational potential energy is also a kind of binding energy.

The same is true in cosmology. We have to consider not only mass energy, but also gravitational binding energy.

5) Our common sense was wrong long ago
Our conventional wisdom is already wrong about the accelerated expansion of the universe and the rotation curve of galaxies. So, instead of thinking about whether negative energy exists, we should focus on whether the universe is explained by the introduced physical quantity. For those of you who are still reluctant to negative energy, first assume that gravitational potential energy is negative energy, and then look at the following logic.

#On the solution of the strong gravitational field the solution of the Singularity problem the origin of Dark energy and Dark matter
https://www.researchgate.net/publication/359329109

The source of dark energy is gravitational self-energy or total gravitational potential energy!

2. Comparison of magnitudes of mass energy and gravitational self-energy in the observable universe

1)Total mass energy (include radiation energy) of the observable universe (particle horizon)
Simply put, the particle horizon is important because it means the range of the interaction. The critical density value p_c = 8.50 X 10^-27[kgm^-3 ] was used. Observable universe (particle horizon) radius : 46.5Gly.

Since the universe is almost flat spacetime, the total mass energy in the particle horizon is

The repulsive force component is approximately 3.04 times the attractive force component. The universe is accelerating expansion.

For reference, assuming the current average density, in the cosmic horizon 16.7Gly, U/Mc^2 = -0.39 is obtained.

At the cosmic horizon 16.7Gly,the repulsive force component is smaller than the attractive force component, suggesting that it is a period of decelerated expansion.

3. Find the inflection point where the attractive and repulsive components are equal
I searched for the point at which the universe transitions from decelerated expansion to accelerated expansion.

I do not know the magnitude R_gs at which the positive mass energy and the negative gravitational potential energy are equal, since I do not have the data of the density. We only need to understand the general flow and possibility, so let's get ? by putting in the current critical density value.

R_gs = 26.2Gly

Assuming that the average density is approximately 1.25 times the current average density, we get R_gs = 23.7Gly.
Assuming that the average density is approximately 2 times the current average density, we get R_gs = 18.7Gly.

Comparing the data from the existing particle horizon graph, it is estimated that it is approximately 5 to 7 billion years ago from the present. It is necessary to review this model because it includes the transition of the universe to the period of decelerated expansion, the inflection point, and the period of accelerated expansion.

Particle horizon vs time. We need to know the average density to get an accurate value. However, as a rough estimate, according to this model, it is estimated that the transition to accelerated expansion was approximately 5-7 billion years ago.

4. The ratio of increase in gravitational self-energy to increase in mass energy

If the particle horizon increases and a positive mass is produced by M, the equivalent mass of negative gravitational potential energy is produced by -5.14 M.

This value is not a fixed value, it depends on the density and the size of the particle horizon.

5. Increase in dark energy (gravitational self-energy) due to increase in particle horizon
1)Particles and galaxies spread almost uniformly throughout the universe through the inflation process.

2)Galaxies move according to the Hubble-Lemaitre law.

3)On the other hand, the propagation speed of the field, the range of interaction (particle horizon), has the fastest speed, the speed of light in expanding space.

4)Thus, over time, many new substances (matters and galaxies) enter the particle horizon. In other words, the newly entering materials undergo gravitational interaction, resulting in an increase in mass energy and an increase in gravitational potential energy in the region within the particle horizon.

5)By the way, while mass energy is proportional to M, total gravitational potential energy (gravitational self-energy) is proportional to - M^2/R. As M increases, the gravitational potential energy increases faster. Accordingly, the repulsive force component increases faster than the attractive force component.

6)The increase in gravitational potential energy due to the newly incorporated matter into the particle horizon is causing the dark energy. The same principle is applicable to the birth of energy within a particle horizon. That is, when the mass energy increases by M, the gravitational self-energy increases by - M^2/R.

7)In the present universe, it is predicted that the dark energy effect (repulsive effect) surpassed the gravitational effect of matter and dark matter about 5 billion years ago. According to this model, it is the point at which the positive mass energy and the negative gravitational self-energy are equal. Knowing the average density function, we can get the exact value.

8)Gravitational potential energy is a concept that already exists and is negative energy that can create repulsive force. This model produces similar results to the phenomenon of applying negative pressure while having positive (inertial) mass density. As the particle horizon expands, the positive mass increases(New influx or birth of matter), but the negative gravitational potential energy created by these positive masses is greater. While having a positive inertial mass, it is creating a negative gravitational mass that is larger than the positive inertial mass. Because of this factor, this model should be reviewed.

6. How to validate the dark energy model that gravitational self-energy is the source of dark energy
1)Find the expressions of p(t) and R_ph(t)
p(t) is the average density inside the particle horizon. R_ph(t) is the particle horizon.

2)At each time, within the particle horizon
Find E = M(t)c^2 and U_gs = - (3/5)(GM(t)^2/R
E = M(t)c^2 is the attractive energy component and U_gs is the repulsive energy component.

3)Compare U_gs/E with the observations
Anyone familiar with particle horizons and density functions can verify this model.

*The potential of this model
1. Description of the current accelerated expansion
R = 46.5Gly, the ratio of the attractive component to the repulsive force component, U/Mc^2= - 3.04, and the negative energy component and the repulsive force component are larger, explaining the accelerated expansion.

2. Numerically, it represents the change from decelerated expansion to accelerated expansion, and by calculating the inflection point, it can be compared with the observed value. The roughly calculated inflection point is 5 to 7 billion years ago, So this model has potential.

3. In standard cosmology, dark energy is an object that has a positive energy density and exerts a negative pressure. The gravitational self-energy provides an explanation for this bizarre property.

1) Characteristics: It has a positive mass (energy) density and acts as a negative gravitational mass.
2) Size: Produces a negative gravitational mass density that is greater than the positive inertial mass density. The repulsive component is greater than the attractive component.

The gravitational self-energy accounts for both of these properties.
Mass energy is positive energy and is attractive, whereas gravitational self-energy is negative energy and has repulsive properties.

Mass energy is proportional to M. On the other hand, gravitational self-energy is proportional to -M^2/R. At a size smaller than R_gs (The magnitude at which the positive mass energy and the negative gravitational self-energy are equal.), the mass energy is greater than the gravitational self-energy created by positive masses, and at a size larger than R_gs , the gravitational self-energy created by positive masses is greater than the mass energy.

4. Since gravitational self-energy is pointed out as the source of dark energy, verification is possible.

#On the solution of the strong gravitational field the solution of the Singularity problem the origin of Dark energy and Dark matter
https://www.researchgate.net/publication/359329109

i read it all both posts
but i cant do the maths

i read it all both posts
but i cant do the maths
I can't do the maths
can't do the English

I can't do the maths
can't do the English
View attachment 4711

i could teach myself what the equations mean and then work them to see if they make sense
but my brain doesn't like thinking like that
calculus and algebra are quite difficult for me & i have not retained any ability in either.

im slightly tempted because im very interested in gravity drives
and thats the core scientific reality of the science
being able to fly to other star systems

i could teach myself what the equations mean and then work them to see if they make sense
but my brain doesn't like thinking like that
calculus and algebra are quite difficult for me & i have not retained any ability in either.

im slightly tempted because im very interested in gravity drives
and thats the core scientific reality of the science
being able to fly to other star systems
Myself I really really don't get negative mass
OR
negative energy

Anti mass and anti matter I'm a bit more relaxed with but still long long way looonnng way from understanding

How would you get negative mass? Start with a lump of mass, start taking bits of it away and when you have none left, TAKE MORE AWAY?????

How does that work?

negative mass

would be a state of energy
like light
lack of light is dark
but in this case instead of attract it repels

matter has gravity which attracts but is still traveling with the expansion being driven by something
while being held by something else while being under observable gravitation fields

gets a bit timey wimey if your not read a little into the common language

creating negative mass would create a gravity drive while allowing inertia to remain the same so you dont get squashed by G force

the recent publications on the theoretical creation of a warp drive define this formula as an envelope around something

would be a state of energy
like light
lack of light is dark
but in this case instead of attract it repels

Don't think so
Lack of light is dark go with that

But you don't get lack of MORE light giving you MORE dark

But you don't get lack of MORE light giving you MORE dark

space is moving

1. Nobel Prize-winning lecture by Adam Riess : 11:00~
https://www.nobelprize.org/mediaplayer/?id=1729

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

=====

They had negative thoughts about negative mass. So, they discarded the negative mass 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.

However, it still remains unresolved. In any case, it also means that the presence of negative mass density explains the accelerated expansion.

2. Mass defect due to binding energy

Consider situations a) and c)

In a), the total mass of the two particle systems is 2m, and the total energy is ET=2mc^2
In c), is the total energy of the two-particle system ET=2mc^2 ?
In c), when the two particle systems act gravitationally on an external particle, will they act gravitationally with a gravitational mass of " 2m "?
Are a) and c) the same mass or same state?

If you do not apply negative binding energy, the conclusions you get will not match the actual results.

In c), the total energy of the two particle systems is

In the dimension analysis of energy, E has kg(m/s)^2, so all energy can be expressed in the form of mass x (speed)^2. So, E=mc^2 (Here, m is not used as a word for rest mass, but for mass.) holds true for all kinds of energy. If we introduce the equivalent mass -m_gp for the gravitational potential energy,

The gravitational force acting on a relatively distant third mass m_3 is

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 should be considered. Alternatively, the gravitational force acting on the bound system can be decomposed into a free-state mass term and an equivalent mass term of binding energy.

While we usually use the mass m* of the bound system, we forget that m* is (m - m_binding-energy). Gravitational potential energy is also a kind of binding energy.

Even in universe, the gravitational potential energy term must be considered.

So, the universe is accelerating expansion.

There are too many people who have an aversion to negative energy (mass). However, in the standard cosmology, accelerated expansion is impossible without negative mass density. It is just that the negative mass density term is called negative pressure, so it is not recognized.
In other words if you start out assuming negative mass exists and then use that in your analysis you end up proving negative mass exists, which is circular logic and not very useful.

the universe is accelerating expansion.
I took the accelerating expansion to be a continuation of the Big Bang (Rapid Expansion) having no resistance ahead of the expansion and as the expansion continues less gravitational attraction (decreasing mass) behind to hinder (pull back) the expansion

[ summary ]
1. Gravitational potential energy is negative energy
In Wikipedia, refer to the gravitational binding energy entry,
Two bodies, placed at the distance R from each other and reciprocally not moving, exert a gravitational force on a third body slightly smaller when R is small. This can be seen as a negative mass component of the system, equal, for uniformly spherical solutions, to: -M_binding = -(3/5)GM^2/Rc^2

In the dimensional analysis of energy, E has kg(m/s)^2, so all energy can be expressed in the form of (mass) x (speed)^2. So, E=Mc^2 holds true for all kinds of energy. "-M_gs" is the equivalent mass of gravitational self-energy. It is a negative equivalent mass term. The greater the mass, the greater the gravitational self-energy ratio.

Earth's -M_gs= (- 4.17 x 10^-10)M_Earth
Sun's -M_gs= (- 1.27 x 10^-4)M_Sun
Black hole's -M_gs= (- 0.3)M_black-hole

2. In the universe, if we calculate the gravitational self-energy
Since the particle horizon is the range of interaction, if we find the mass energy (Mc^2) and gravitational self-energy ((-M_gs)c^2)values at each particle horizon, Mass energy is an attractive component, and the equivalent mass of gravitational self-energy is a repulsive component. Critical density value p_c = 8.50 x 10^-27[kgm^-3] was used.

At particle horizon R=16.7Gly, (-M_gs)c^2= (-0.39M)c^2: decelerated expansion period
At particle horizon R=26.2Gly, (-M_gs)c^2= (-1.00M)c^2: inflection point (About 5-7 billion years ago, consistent with standard cosmology.)
At particle horizon R=46.5Gly, (-M_gs)c^2 = (-3.04M)c^2 : accelerated expansion period

3. What was discovered in 1998 was not a cosmic constant, but a negative mass?
The two research teams(HSS and SCP team) who discovered the accelerated expansion of the universe, The first thing the two teams discovered was negative mass density.

1) Nobel Prize Lecture by Adam Riess : https://www.nobelprize.org/mediaplayer/?id=1729 11m : 40s~

Negative Mass? Actually the first indication of the discovery!

2) 1998 paper : The paper that won the Nobel Prize for the discovery of the accelerated expansion of the universe

https://arxiv.org/abs/astro-ph/9805201 Refer to 14P

If we instead demand that Ω_Λ=0, we are forced to relax the requirement that Ω_M ≥ 0 to locate a global minimum in our χ^2 statistic. Doing so yields an unphysical value of Ω_M = −0.38 ± 0.22 and Ω_M = −0.52 ± 0.20 for the MLCS ~

When the two teams(HSS and SCP team) obtained a negative mass density, they chose to modify the equation, considering negative mass density to be an unphysical value. Resurrecting the cosmological constant, claiming that this is evidence of the existence of the cosmological constant. However, a number of problems(origin, 10^120 error, fine tuning, CCC Problem,...) still remain unresolved.

-------

Even in the universe, gravitational self-energy must be considered.
And, in fact, if we calculate the value, since gravitational self-energy is larger than mass energy, so the universe has accelerated expansion.
Gravitational self-energy accounts for decelerated expansion, inflection point, and accelerated expansion.​

https://www.researchgate.net/publication/359329109

*I think this will be my last post on this topic.

Friedmann's equations and the dark energy term from the gravitational self-energy model

I used the existing gravitational self-energy equation, but there are some problems with applying this equation to cosmology.

1) The existing gravitational self-energy equation is an equation obtained by Newtonian mechanics. It does not reflect the general relativistic idea that all energy is a source of gravity.
For example, when calculating the gravitational self-energy equation, use M' as the internal mass. At this time, the internal mass M' also has its own gravitational energy value, which contributes as a negative mass. These contents are not reflected.

2) In the universe, there are objects that are strongly bound by gravity, such as stars, black holes, and galaxies. The gravitational self-energy of these objects is already reflected in the total mass of the object (observed from the outside). By the way, the gravitational self-energy equation assumes a uniform distribution and is a structure in which all the gravitational potential energy terms of all infinitesimal mass are added. Therefore, there is a possibility that expression U_gs=-(3/5)GM^2/R overestimates gravitational self-energy.

3) Because of the propagation velocity of the field, it is possible that some matter within the particle horizon is not participating in gravitational interactions
That is, it is possible that the gravitational field has not yet been transmitted from one end to the other. There is a possibility of overcalculation of gravitational self-energy.

In addition to 1) - 3) mentioned here, there may be factors that need to be corrected. Therefore, β(t) is introduced as a correction term by these factors. The universe structure correction variable β(t) is a variable, but it is thought to change very slowly since the change will be relatively small after the formation of the galactic structure. So, it is assumed that after the formation of the galactic structure, it can be thought of almost like a constant.

Existing vacuum energy model is known to have a difference of 10^120 times between the theoretical predicted value and the observed value.
In the gravitational self-energy model, excluding the universe structure correction variable, the difference is not even by a factor of 10^1 order. Gravitational potential energy is a concept that has already existed, and does not assume a bizarre existence that has a positive inertial mass and exerts a negative pressure. There are no problems like fine tuning or CCC problem.

a(t)R is the particle horizon at the point in time to be analyzed. In the gravitational self-energy model, if p(t) ? 1/a(t)R, it is possible that the density of dark energy seems to be constant.

In standard cosmology, the energy density of dark energy is a constant. However, in the gravitational self-energy model, dark energy density is a variable. There is no cosmological constant and the dark energy is a function of time. Thus, this model can be verified.

# Dark energy is the gravitational potential energy or gravitational self-energy