Could dark energy be gravitational potential energy?

  • #1
370
0

Main Question or Discussion Point

I was wondering if dark energy might actually be gravitational potential energy.

If one assumes that space is flat and that the Universe is approximately a sphere with mass M and the Hubble radius R then we find that we have the approximate relation:

[itex] \frac{G M }{R} = c^2 [/itex]

A mass m at the center of the sphere would have approximate gravitational potential energy

[itex] PE = - \frac{G M m}{R} = - m c^2 [/itex]

This potential energy would have a gravitational repulsion that might counteract the gravitational attraction due to mass m causing the Universal expansion to accelerate.

I would be interested to hear what you think of this line of thought.
 

Answers and Replies

  • #2
bcrowell
Staff Emeritus
Science Advisor
Insights Author
Gold Member
6,723
422
No. As explained in our FAQ, general relativity doesn't have a conserved scalar mass-energy that can be defined in all spacetimes: https://www.physicsforums.com/showthread.php?t=506985 Therefore the PE you're discussing can't be meaningfully defined in cosmology.

Also, the negative sign of the PE in Newtonian gravity represents its attractive nature. (If you flip the sign, you get a universe in which gravity is repulsive, like the electrical repulsion between like charges.) So you can't use it to explain a repulsion.

The nonrelativistic limit of GR with [itex]\Lambda=0[/itex] is Newtonian gravity, so you can't use Newtonian gravity to derive [itex]\Lambda\ne0[/itex].

A mass m at the center of the sphere
There's no center. We also have a FAQ about this: https://www.physicsforums.com/showthread.php?t=506991 [Broken]
 
Last edited by a moderator:
  • #3
938
9
Well, it's not entirely far fetched. The standard model of cosmology describes the matter of the universe as a homogeneous and isotropic ideal fluid of dust particles. Now, we know that on the scales of galaxies and galaxy clusters, the universe is far from homogeneous today.

As one coarse grains the description of "dust" to larger and larger scales, effects of the gravity become more and more unclear. For the FRW metric to apply at all scales, one needs to be able to carry out this coarse graining up to scales of galaxy clusters and beyond, at which point the "particles" of ideal fluid can be themselves expanding or contracting.
 
  • #4
6,814
11
I was wondering if dark energy might actually be gravitational potential energy.
Nope.

A mass m at the center of the sphere would have approximate gravitational potential energy

[itex] PE = - \frac{G M m}{R} = - m c^2 [/itex]

This potential energy would have a gravitational repulsion that might counteract the gravitational attraction due to mass m causing the Universal expansion to accelerate.
Aside from the problems with calculating total energy with GR, you run into the problem that you flipped a sign. Things with negative potential energy are *attractive*. As you move two objects closer together, the potential energy goes lower, which means that the negative sign in the potential energy causes objects to *attract*.
 
  • #5
370
0
Also, the negative sign of the PE in Newtonian gravity represents its attractive nature. (If you flip the sign, you get a universe in which gravity is repulsive, like the electrical repulsion between like charges.) So you can't use it to explain a repulsion.
I am assuming that the negative PE is itself a source of gravitational repulsion on normal matter. It is as though it is a gravitational source with negative mass.

No. As explained in our FAQ, general relativity doesn't have a conserved scalar mass-energy that can be defined in all spacetimes
I admit my argument is only Newtonian with the addition of the equivalence of mass and energy.

There's no center. We also have a FAQ about this
I'm not assuming a particular center of the Universe. I'm just considering the gravitational potential at any particle due to the rest of the Universe around it.
 

Related Threads for: Could dark energy be gravitational potential energy?

Replies
0
Views
2K
Replies
9
Views
3K
Replies
9
Views
3K
  • Last Post
Replies
6
Views
850
Replies
7
Views
1K
Replies
5
Views
1K
Replies
3
Views
1K
  • Last Post
2
Replies
45
Views
10K
Top