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Fraser
2011-Apr-18, 12:20 PM
Since the late 20th century, astronomers have been aware of data that suggest the universe is not only expanding, but expanding at an accelerating rate. According to the currently accepted model, this accelerated expansion is due to dark energy, a mysterious repulsive force that makes up about 73% of the energy density of the universe. [...]

More... (http://www.universetoday.com/84934/antigravity-could-replace-dark-energy-as-cause-of-universes-expansion/)

Noclevername
2011-Apr-18, 12:29 PM
But we've made antimatter here on Earth, haven't we? Shouldn't we have some idea of how gravity affects it?

Strange
2011-Apr-18, 01:07 PM
But we've made antimatter here on Earth, haven't we? Shouldn't we have some idea of how gravity affects it?

The problem is that gravity is very weak, so detecting its effects on a tiny amount of matter is hard.

I don't know if it would be possible to do something like this with anti-neutrons: http://www.bbc.co.uk/news/science-environment-13097370 (the article is a bit vague about how it works).

caveman1917
2011-Apr-18, 01:37 PM
I'm wondering, if it is due to gravitational repulsion between anti-matter and matter, shouldn't the expansion decrease?
If the repulsion falls of with 1/r², and the voids keep getting bigger, shouldn't the repulsive force between the center of the voids (where the anti-matter should coalesce) and the matter concentrations decrease?

IsaacKuo
2011-Apr-18, 02:46 PM
I'm wondering, if it is due to gravitational repulsion between anti-matter and matter, shouldn't the expansion decrease?
If the repulsion falls of with 1/r², and the voids keep getting bigger, shouldn't the repulsive force between the center of the voids (where the anti-matter should coalesce) and the matter concentrations decrease?
The force may decrease, but it would still be an outward repulsive force--meaning the expansion would still be accelerating.

Think about how two protons repel each other. The amount of repulsion decreases with distance, but it's still repulsion so they are still accelerating away from each other.

caveman1917
2011-Apr-18, 03:10 PM
The force may decrease, but it would still be an outward repulsive force--meaning the expansion would still be accelerating.

Think about how two protons repel each other. The amount of repulsion decreases with distance, but it's still repulsion so they are still accelerating away from each other.

Yes, but this acceleration is decreasing, where it should be increasing.
For a cosmological constant, the scale factor evolves by e^t.
This means that if we want to view it as two particles accelerating away from eachother, the force on them should be increasing over time, not decreasing.

Unless i'm missing something of course.

ETA:
for succesive points in time, t (using 2^t). d = distance between protons, v = speed of proton from this point to the next
t d v
1 2 1
2 4 2
3 8 4
4 16 8
...

Grey
2011-Apr-18, 06:49 PM
Although the direct experiment has not yet been done (although there are a few researchers getting close), there are some pretty straightforward theoretical arguments (arising from simple, well-tested principles like conservation of energy) that anti-matter and matter attract each other normally via gravity. I think it extremely unlikely that this suggestion will pan out.

IsaacKuo
2011-Apr-18, 07:25 PM
Yes, but this acceleration is decreasing, where it should be increasing.
For a cosmological constant, the scale factor evolves by e^t.
This means that if we want to view it as two particles accelerating away from eachother, the force on them should be increasing over time, not decreasing.
As I understand it, a cosmological constant is a theory that is consistent with observations, not something which is proven by observations. That is, our observations do not provide enough data.

caveman1917
2011-Apr-18, 11:18 PM
As I understand it, a cosmological constant is a theory that is consistent with observations, not something which is proven by observations. That is, our observations do not provide enough data.

That is true, but the general shape of the curve seems to be wrong. It looks as such a mechanism would provide a decelerating expansion, rather than an accelerating one. Unless i'm missing the obvious of course :)

caveman1917
2011-Apr-18, 11:30 PM
I'm also wondering about something else. If this antimatter is responsible for what we termed dark energy, then doesn't \Omega << 1, implying a hyperbolic universe (counter to WMAP measurements)? We double the baryonic and dark matter densities, but leave out the energy density due to what we now consider dark energy. This leaves us a lot short to achieve a flat universe. Unless again i'm missing the obvious.

IsaacKuo
2011-Apr-18, 11:35 PM
That is true, but the general shape of the curve seems to be wrong. It looks as such a mechanism would provide a decelerating expansion, rather than an accelerating one. Unless i'm missing the obvious of course :)
Like I said, it would be accelerating expansion. The force is outward, so the acceleration is outward. The force gets smaller with time, but it's still an outward force so the acceleration is still outward.

caveman1917
2011-Apr-18, 11:41 PM
Like I said, it would be accelerating expansion. The force is outward, so the acceleration is outward. The force gets smaller with time, but it's still an outward force so the acceleration is still outward.

No it isn't. The acceleration of expansion is an increase in the first derivative scale factor over time, an increase in the velocity of two points moving away from eachother is not enough. The condition is d^3s/dt^3 > 0, the proposal seems to be (at least the way we've been considering it as the two-proton system) d^3s/dt^3 < 0

ETA:
Yes, you're right. I was comparing d(t) to d(t-1) instead of to d0

ETA2:
Just for clarity, the condition is indeed, as IsaacKuo alluded to, d^2s/dt^2 > 0 which the proposal conforms to. I was incorrectly considering a(t) \propto ds/dt rather than the correct a(t) \propto s(t), the error of the extra derivative not showing up when using e^t

Jeff Root
2011-Apr-19, 01:50 AM
This has been my pet idea I've been nurturing since the mid-1970's.
I only learned that anyone else had thought of it a couple of years ago.

A graph showing a possible expansion history based on gravity
between matter and antimatter being repulsive:

http://www.freemars.org/jeff2/expansn1.png

-- Jeff, in Minneapolis

Jeff Root
2011-Apr-19, 02:13 AM
The only difference I see from that article between Villata's concept
and mine is that he places the antimatter in the voids, while I think
it constitutes half the visible matter. Clusters of matter galaxies
pushing away from clusters of antimatter galaxies form sheets.

-- Jeff, in Minneapolis

.

Grey
2011-Apr-19, 06:52 AM
The only difference I see from that article between Villata's concept
and mine is that he places the antimatter is in the voids, while I think
it constitutes half the visible matter. Clusters of matter galaxies
pushing away from clusters of antimatter galaxies form sheets.So your idea is just about as unlikely as his to be correct. ;)

astromark
2011-Apr-19, 08:07 AM
So your idea is just about as unlikely as his to be correct. ;)

An opinion you are perfectly entitled to have... BUT...

Now I can not know because I simply do not have the depth of knowledge as to be assertive of a view.

I too have a opinion. As does Jeff Root and I would suspect a good many other regular contributors here.

It is a little unkind to be so blunt without backing it up with good science.

I have seen this as a news release.. challenge the idea but do not shoot the messenger...

I will step across the line and add that I have never been happy with the accelerating expansion being driven by

73% of the Universe being unseen and called Dark Energy..

I can not have proof of a conviction I do not entirely understand.

This little development of a method. A explanation that does not require Dark Energy....

It might need some deeper explanation., but it could be the beginning of a new clarity.

Matter and anti-matter. The way they exist and interact could be the beginning of a new understanding...

I like it. It makes sense.. and I think Jeff and others might be on to something...

Jeff Root
2011-Apr-19, 11:51 AM
I have a real problem explaining the Pound-Rebka experiment,
but to my knowledge, that's the only problem. But eventually
the people at CERN will measure the response of antimatter
to Earth's gravity for the first time, and we'll know. That will
probably be sometime after 2015. They're going to try to
measure electromagnetic properties first, getting spectra,
before moving on to the more difficult gravity measurement.

-- Jeff, in Minneapolis

Grey
2011-Apr-19, 03:32 PM
It is a little unkind to be so blunt without backing it up with good science.

I have seen this as a news release.. challenge the idea but do not shoot the messenger...I never attacked Jeff, I have the highest regard for him. However, I said his idea is very unlikely to be true, which is accurate (and I even included a smiley, to make it clear that I wasn't attacking him). We've discussed this before several times (here (http://www.bautforum.com/showthread.php/109619-Antimatter-Atom-still-responds-normally-to-gravity?p=1826767#post1826767) and here (http://www.bautforum.com/showthread.php/88748-Question-about-repulsive-gravity?p=1633822#post1633822), for example). Jeff is exactly right that the results of the Pound-Rebka experiment are pretty hard to explain if conservation of energy holds, but antimatter and matter repel each other gravitationally. I'd be curious to know how (or if) Villata addresses this problem.

We also have other indirect evidence, such as the fact that the antineutrinos and the neutrinos from SN 1987A arrived at the same time. Calculations suggest that the travel time of these neutrinos was changed by about five months, so if it affected the neutrinos and antineutrinos differently, there should have been two spikes at completely different times. That's not what we observed.

The folks at CERN are going to be doing the direct experiment relatively soon, which I think is pretty cool. But it's extremely likely that they will confirm what we already suspect, rather than overturning the foundation of general relativity.

Jeff Root
2011-Apr-19, 11:48 PM
Okay, TWO problems. Pound-Rebka and SN 1987A neutrino observations.

Two is still a pretty small number. :)

-- Jeff, in Minneapolis

Noclevername
2011-Apr-20, 01:48 AM
Ahhh, at last a way to get a flying car! ;)

MrObvious
2011-Jun-07, 02:37 AM
I will step across the line and add that I have never been happy with the accelerating expansion being driven by

73% of the Universe being unseen and called Dark Energy..

I can not have proof of a conviction I do not entirely understand.

Maybe a quick description of something else will help.
The Sun releases vast energy every day and has done so since it first shone. So has every other star in the Universe.
In the case of our Sun that has been a few billion years.
The vast majority of that energy we cannot observe but we know it is out there. Indeed, we can only see the energy headed directly to us from the Sun but will never observe it in the opposite direction.
Likewise for every star.
If the Sun is 4.5billion years old, then the amount of energy it has put out is 4.5billion times what it puts out each year now, assuming it provided the same output through that time.
Basically we are limited in what we can see but we also know that the energy is there.
How much energy is there in the Universe from star light?
Now that would be a complicated calculation.

So technically, above is an example of star "light" energy that is dark to us simply because it is unobservable from our position in the Universe, but, we know it exists and we know it is a lot of energy that is out there.

frankuitaalst
2011-Oct-26, 08:46 PM
I have a real problem explaining the Pound-Rebka experiment,
but to my knowledge, that's the only problem. But eventually
the people at CERN will measure the response of antimatter
to Earth's gravity for the first time, and we'll know. That will
probably be sometime after 2015. They're going to try to
measure electromagnetic properties first, getting spectra,
before moving on to the more difficult gravity measurement.

-- Jeff, in Minneapolis
I just read this (older) post Jeff .
Can you explain the difficulty you have with the Pound Rebka experiment in case of antigravitating antimatter ?
To be honest I also feel uncomfortable with the idea that we need to invent dark energy and dark matter in order to explain what we observe.

Grey
2011-Oct-26, 09:16 PM
I just read this (older) post Jeff .
Can you explain the difficulty you have with the Pound Rebka experiment in case of antigravitating antimatter ?
To be honest I also feel uncomfortable with the idea that we need to invent dark energy and dark matter in order to explain what we observe.I'm not Jeff, but here's the basic issue. Imagine you have a particle and its antiparticle on top of a tall tower. You have them annihilate, and send the resulting photons down to the bottom. From general relativity, we know that they'll be blueshifted, so we'll get more energy out of them then we had originally. So we can recreate the particle-antiparticle pair, and use the extra bit of energy to send them back to the top of the tower. The Pound-Rebka experiment measures the amount of blueshift, and it's consistent with the gravitational potential energy you'd need to lift a normal matter particle (currently measured to within 0.02%). So if antimatter is affected differently from normal matter by more than 0.04% (falling up would be a difference of 200%), you'd violate conservation of energy, and running this loop one way or the other would be a way to generate energy out of nothing. Take a look here (http://www.ps.uci.edu/~markm/antihydrogen/Does%20Antimatter%20Fall%20Up%20or%20Down_.pdf) for a more detailed analysis.

You may not be comfortable with dark energy, but if anti-matter were to behave opposite matter in a gravitational field, there are even more fundamental issues that would be raised.

frankuitaalst
2011-Oct-26, 09:55 PM
I'm not Jeff, but here's the basic issue. Imagine you have a particle and its antiparticle on top of a tall tower. You have them annihilate, and send the resulting photons down to the bottom. From general relativity, we know that they'll be blueshifted, so we'll get more energy out of them then we had originally. So we can recreate the particle-antiparticle pair, and use the extra bit of energy to send them back to the top of the tower. The Pound-Rebka experiment measures the amount of blueshift, and it's consistent with the gravitational potential energy you'd need to lift a normal matter particle (currently measured to within 0.02%). So if antimatter is affected differently from normal matter by more than 0.04% (falling up would be a difference of 200%), you'd violate conservation of energy, and running this loop one way or the other would be a way to generate energy out of nothing. Take a look here (http://www.ps.uci.edu/~markm/antihydrogen/Does%20Antimatter%20Fall%20Up%20or%20Down_.pdf) for a more detailed analysis.

You may not be comfortable with dark energy, but if anti-matter were to behave opposite matter in a gravitational field, there are even more fundamental issues that would be raised.
Thanks for the reply Grey . Much more people would feel less comfortable when antigarvity is proven to be true , I realize :-)
I went quickly through the article in the link you posted above but got stuck at the 3th formula , when the photon is captured at the bottom and is transformed to a new pair of proton - antiproton and asked myself : whats happening with the other photon which must go upwards , while total, momentum (=0) must be maintained .

Grey
2011-Oct-27, 12:01 PM
I went quickly through the article in the link you posted above but got stuck at the 3th formula , when the photon is captured at the bottom and is transformed to a new pair of proton - antiproton and asked myself : whats happening with the other photon which must go upwards , while total, momentum (=0) must be maintained .You send both photons down to the bottom. You can't be guaranteed that either one will be going in the direction you want, but you could reflect gamma rays with a series of grazing mirrors, or you could absorb them and re-emit them in the right direction. Of course, if you actually set this up in practice, you'd never be able to make that work with 100% efficiency, but that's not really important. It's a thought experiment, and conservation of energy should hold in principle (and has done so in every test we've done), regardless of whether a perfect practically realizable apparatus could be built.

icarus2
2011-Oct-27, 03:21 PM
I agree that "Antigravity Could Replace Dark Energy as Cause of Universe’s Expansion"
But antigravity originated not antiparticle but negative energy(mass).

1. Video simulation :

2. Big bang simulation from the Zero Energy State!

frankuitaalst
2011-Oct-27, 03:39 PM
Hello Grey ,
I don't get it . Let' s assume that the proton / anti-proton pair is in rest at the time of annihilation . The momentum is zero at the time they annihilate .
To conserve the momentum they should emit at least two photons in opposite direction , or maybe more in whatever direction .
In the simplest case let's assume we have two photons . One is going down with half of the total energy , the other is going upwards , also with half of the energy .
If we want them to form a pair of proton/antiproton again , we should consider both rays , isn't it ?
We can't use mirrors to deflect them and send them both downwards because the simple fact of using mirrors adds some action to the mirror .
If I remember corectly the thought experiment using mirrors is one of the experiments to prove the E=mc² relationship .
I haven't gone through the formulas fully but this may be a flaw in the tought experiment , maybe resultung in an equation which says : 0= 0 .
I don't want to go ATM , but I am only expressing I don't understand why both photons are send down in this tought experiment .

Grey
2011-Oct-27, 04:11 PM
We can't use mirrors to deflect them and send them both downwards because the simple fact of using mirrors adds some action to the mirror .Reflection from a mirror doesn't change the energy of a photon, at least in principle. No real mirror is 100% efficient, but there's no theoretical restriction on the efficiency, it's just a practical engineering issue. So in principle, we can indeed direct both photons downward with no net change in energy (the momenta of the photons do change here, but the argument doesn't concern itself with momentum).

frankuitaalst
2011-Oct-27, 04:23 PM
Ok Grey I understand what you mean , no energy difference usng mirrors , that's correct .
Still having diffuculty with the "momentum" issue which changes sign .
I'll go through the formulas to get a better insight in what happens.
( glad we have the same time -shedule :-) ) .
In the mean time I've send an e-mail to Mr Massimo Villato - the author - what's he thinking about this issue .

frankuitaalst
2011-Oct-31, 08:37 PM
Grey ,
I went through the article you mentionned in another post :
http://johanw.home.xs4all.nl/PhysFAQ/ParticleAndNuclear/antimatter_fall.html
and to which you referred above .
If the experiment is done so that two opposite photons are emitted ( instead of one beam ) , the result seems to be the same as in the paper .
So this means that antimatter has the same gravitational direction just as normal matter . The proof is easy and uses only well accepted and tested ideas .
Going through the calculations I got convinced myself also . Thanks for the link

icarus2
2013-Feb-02, 08:10 AM
[ Antigravity is the source of dark energy (accelerating expansion) ]

A. Gravitational potential energy, when antigravity exists.

We are aware of what gravitational self-energy (gravitational binding energy) as the sum of gravitational potential energy is displayed as follows, when matters show a three-dimensional spherical distribution.

{U_S} = - \frac{3}{5}\frac{{G{M^2}}}{r}
(r: radius, M: the mass of the sphere)
=========
http://en.wikipedia.org/wiki/Gravitational_binding_energy
=========

Because we are planning to apply this to cosmology,
Assumption: For simple modeling, we will suppose that antigravity source has a uniform distribution on a cosmological scale of a level of cluster of galaxies.

When gravitational self-energy by ordinary matters is as below in our universe,

{U_M} = - \frac{3}{5}\frac{{G{M^2}}}{r}

Because we don't know how big gravitational potential energy by antigravity is, let's introduce and indicate a constant {k_h} which is easy for comparison as below, for a simple comparison.

{U_{DE}} = {k_h}\frac{{G{M^2}}}{r}

(**Refer to http://vixra.org/abs/0907.0015 eq.(91)
{U_{DE}} = {U_{-+}} ={k_c}\frac{{G{M^2}}}{r})

B. Force generated by positive gravitational potential energy.

\vec F = - \Delta {U_{DE}} = - \frac{{\partial {U_{DE}}}}{{\partial r}}\hat r = - \mathop {\lim }\limits_{\Delta r \to 0} \frac{{{U_{DE}}(r + \Delta r) - {U_{DE}}(r)}}{{\Delta r}}\hat r

{U_{DE}(r)} = {k_h}\frac{{G{M^2}}}{r} = {k_h}\frac{{G{{(\frac{{4\pi }}{3}{r^3}{\rho _r})}^2}}}{r} = {k_h}G{(\frac{{4\pi }}{3})^2}{\rho _r}^2{r^5}

{U_{DE}}(r + \Delta r) = {k_h}G{(\frac{{4\pi }}{3})^2}{\rho _{r + \Delta r}}^2{(r + \Delta r)^5}

When considering the law of conservation of mass-energy,
{\rho _r}{r^3} = {\rho _{r + \Delta r}}{(r + \Delta r)^3}

{\rho _{r + \Delta r}} = {\rho _r}{(\frac{r}{{r + \Delta r}})^3} = {\rho _r}(1 - 3\frac{{\Delta r}}{r} + 6{(\frac{{\Delta r}}{r})^2}...)

{\rho _{r + \Delta r}}^2 = {\rho _r}^2(1 - 6\frac{{\Delta r}}{r} + 21{(\frac{{\Delta r}}{r})^2}...)

{(r + \Delta r)^5} = {r^5}{(1 + \frac{{\Delta r}}{r})^5} = {r^5}(1 + 5\frac{{\Delta r}}{r} + 10{(\frac{{\Delta r}}{r})^2} + \cdots )

F = - \mathop {\lim }\limits_{\Delta r \to 0} \frac{{{k_h}G{{(\frac{{4\pi }}{3})}^2}[{\rho _{r + \Delta r}}{}^2{{(r + \Delta r)}^5} - \rho _r^2{r^5}]}}{{\Delta r}}

F \approx - \mathop {\lim }\limits_{\Delta r \to 0} \frac{{{k_h}G{{(\frac{{4\pi }}{3})}^2}{\rho _r}^2{r^5}[(1 - 6\frac{{\Delta r}}{r} + 21{{(\frac{{\Delta r}}{r})}^2})(1 + 5\frac{{\Delta r}}{r} + 10{{(\frac{{\Delta r}}{r})}^2}) - 1]}}{{\Delta r}}

F \approx - \mathop {\lim }\limits_{\Delta r \to 0} \frac{{{k_h}G{{(\frac{{4\pi }}{3})}^2}{\rho _r}^2{r^5}[(1 + (5 - 6)\frac{{\Delta r}}{r} + (10 - 30 + 21){{(\frac{{\Delta r}}{r})}^2}) - 1]}}{{\Delta r}}

Let's mark it to the secondary term, for verification of model!
F \approx - \mathop {\lim }\limits_{\Delta r \to 0} {k_h}G{(\frac{{4\pi }}{3})^2}{\rho _r}^2{r^5}[ - \frac{1}{r} + (\frac{{\Delta r}}{{{r^2}}})]

F \approx + {k_h}G{(\frac{{4\pi }}{3})^2}{\rho _r}^2{r^5}[\frac{1}{r} - (\frac{{\Delta r}}{{{r^2}}})]

F = + {k_h}G{(\frac{{4\pi }}{3})^2}{\rho _r}^2{r^5}[\frac{1}{r} - \frac{{\Delta r}}{{{r^2}}}] = + {k_h}G(\frac{{4\pi }}{3})(\frac{{4\pi }}{3}{\rho _r}{r^3}){\rho _r}{r^2}[\frac{1}{r} - \frac{{\Delta r}}{{{r^2}}}] = + {k_h}G(\frac{{4\pi }}{3})M{\rho _r}r[1 - \frac{{\Delta r}}{r}]

Therefore, the force by antigravity source which uniformly distributes
\vec F = + (\frac{{4\pi G }}{3}){k_h}M{\rho _r}r(1 - \frac{{\Delta r}}{r})\hat r

As a \vec F = + k\hat r shape, this force is repulsive force, and is proportional to r like dark energy.
If we assume that this force is the same as the existing force related to dark energy,
(\frac{{4\pi G}}{3}){k_h}M{\rho _r}r = \frac{1}{3}\Lambda M{c^2}r

\Lambda = \frac{{4\pi G{k_h}{\rho _r}}}{{{c^2}}}

Here, the total mass, M was used, as the force by gravitational potential energy affects all particles in the three-dimensional sphere.
We can see that \Lambda is also a constant, since G,{k_h},{\rho _r} and c are all constants. This is an evidence of why cosmological constant related to the present dark energy looks like a constant.

Then, let's figure out constant k_h from the current observation results, and verify whether \Lambda calculated by us is a right value.
Not mass-energy, we are measuring a gravitational effect from the observation of the universe, and supposing the existence of mass-energy corresponding to the gravitational effect.
The ratio of magnitude of gravitational effects of the present dark energy and matters can be yielded as below.

\frac{{DarkEnergy}}{{Matter}} \approx \frac{{72.1}}{{4.6}} = 15.67 = |\frac{{{U_{ - + }}}}{{{U_{ + + }}}}|

{k_h} = 15.67 \times \frac{3}{5} = 9.40

\Lambda = \frac{{4\pi G{k_h}{\rho _r}}}{{{c^2}}} = \frac{{4 \times 3.14 \times (6.67 \times {{10}^{ - 10}}{m^3}k{g^{ - 1}}{s^{ - 2}}) \times {k_h} \times (4.17 \times {{10}^{ - 28}}kg{m^{ - 3}})}}{{9 \times {{10}^{16}}{m^2}{s^{ - 2}}}}
\Lambda = \frac{{4\pi G{k_h}{\rho _r}}}{{{c^2}}} = 3.64 \times {10^{ - 52}}[\frac{1}{{{m^2}}}]

This value is in accord with the dimension of cosmological constant that is being inferred from the existing observation results, and is similar with the prediction, too

http://en.wikipedia.org/wiki/Cosmological_constant
=========
Thus, the current standard model of cosmology, the Lambda-CDM model, includes the cosmological constant, which is measured to be on the order of 10^−52 m^−2, in metric units.
=========

According to this hypothesis that our universe consists of negative energy and positive energy of the same scale, it appears that the total mass accelerated by positive gravitational potential energy is 2M. Thus, cosmological constant value can be reduced by 1/2.

Anyways, we can see that the force generated from gravitational potential energy by antigravity has the same shape as the force by dark energy, and that it is possible to accurately explain its magnitude and repulsive effect.
Moreover, we figured out the secondary term to verify whether this model would be right,

The force generated from gravitational potential energy by antigravity can be indicated like

F = (\frac{{4\pi G}}{3}){k_h}M{\rho _r}r(1 - \frac{{\Delta r}}{r}) = \frac{1}{3}\Lambda M{c^2}r(1 - \frac{{\Delta r}}{r})

Since the previous analysis of dark energy was proportional to radial distance r, we can find out whether the model is right or wrong using (\frac{{\Delta r}}{r}) term of the above formula.

C. Meanings including proof

1) The essence of dark energy is antigravity.

2) The force by U_{-+}(GPE between negative mass and positive mass, positive gravitational potential energy) is

\vec F = (\frac{{4\pi G}}{3}){k_h}M{\rho _r}r(1 - \frac{{\Delta r}}{r})\hat r = \frac{1}{3}\Lambda M{c^2}r(1 - \frac{{\Delta r}}{r})\hat r

shaped, and it is needed to conduct an observatory experiment of (\frac{{\Delta r}}{r}) term, for verification of this model.

3) The above evidence explains why dark energy looks like a constant.

4) "Negative energy(mass)" and "antimatter with a possibility of generating antigravity" can be candidates of antigravity source.

5) The above evidence only considered forms of matters, but implies that dark energy is a function of time, considering radiation or the secondary term. There is a need of figuring out a relativistic formula including radiation.

6) Even if mass-energy of antigravity source is equal to mass-energy of gravity source, the repulsive gravity effect could be 15 times bigger than the gravitational effect resulting from gravity source.

7) We can answer the CCC(Cosmological Constant Coincidence) problem of "Why does dark energy have the similar scale with matters?". It is because it has the same gravitational effect as them.

8) We can consider a general shape, U = k{r^n} (n is real number) as a cause for dark energy, and thus there is a high possibility that it is no accident that the above evidence is valid.

9) While the existing cosmological constant or vacuum energy is a concept not to conserve energy, gravitational potential energy is conserved.

--- Icarus2

The Change of Gravitational Potential Energy And Dark Energy in the Zero Energy Universe
http://vixra.org/abs/1110.0019

Strange
2013-Feb-02, 08:42 AM