Dark Energy as repulsive gravity

[Staticboson]

TL;DR Summary

Dark Energy has been referred as a repulsive gravity, however their effects are fundamentally different.

Mass has an effect on the surrounding space which causes two massive objects within the extent of this effect to fall towards each other by crossing the space between them. There is a point source and a direction for the field.

The effect of Dark energy causes an expansion of space itself and the increased separation between objects is not by crossing space. The field has no direction and is uniform throughout.

Speed of light is a constant within local frames, however this constant does not carry to large distances in a uniformly expanding universe (from my perspective a photon from my flashlight moving away from me is slower than a photon 10 Gly away moving away from me). However I don't believe a gravitational field can have such an effect on c regardless of its theoretical strength or extent (I'm not sure about this).

In any case, it seems like equaling Dark energy to repulsive gravity is be misleading because although both forces act on space, they do in fundamentally different ways. Dark energy doesn't care about objects, while gravity is all about objects. Dark energy doesn't cause an increase of space between objects, while gravity causes a decrease of space between objects. Am I looking at this wrong?

 

[PeterDonis]

Speed of light is a constant within local frames, however this constant does not carry to large distances in a uniformly expanding universe (from my perspective a photon from my flashlight moving away from me is slower than a photon 10 Gly away moving away from me).

A better way of saying this would be that you can't measure the "speed" of a photon 10 Gly away moving away from you. You can calculate a coordinate speed, and this number will indeed be larger than the speed you actually measure for a photon from your flashlight. But that coordinate speed doesn't correspond to anything anyone will actually measure. Someone 10 Gly away from you would measure the speed of the photon 10 Gly away from you to be c.

I don't believe a gravitational field can have such an effect on c

A gravitational field--or more correctly spacetime curvature--can certainly affect the behavior of light. That effect is not best viewed as an "effect on c", but that's because no physical effect is best viewed as an "effect on c". It's better to not look at coordinate speeds at all.

 

[DennisN]

However I don't believe a gravitational field can have such an effect on c regardless of its theoretical strength or extent (I'm not sure about this).

A gravitational field--or more correctly spacetime curvature--can certainly affect the behavior of light.

@Staticboson, here are some examples of gravitational field/spacetime curvature affecting light:

• Gravitational Deflection of Light (HyperPhysics)
• Light Deflection and Space-time Curvature (HyperPhysics)
• Gravitational Lens (HyperPhysics)
• and here's a little video introduction to it (Sixty Symbols).

 

[Staticboson]

here are some examples of gravitational field/spacetime curvature affecting light

Hi Dennis, thank you for the links, I will read them.
However I want to make clear that in my post I was referring to the effect of gravity on "c" (the speed of light), I am fairly well aware of the effects of gravity and curvature on light otherwise.

 

[PeroK]

Hi Dennis, thank you for the links, I will read them.
However I want to make clear that in my post I was referring to the effect of gravity on "c" (the speed of light), I am fairly well aware of the effects of gravity and curvature on light otherwise.

In SR we have the postulate that the speed of light is invariant across all inertial reference frames.

In GR this is essentially replaced by the postulate that light travels on null spacetime paths. And, of course, if you focus on a local inertial reference frame, then a null path is equivalent to the invariant speed $c$ in that reference frame.

In an expanding universe it becomes difficult to say what you mean by the overall "speed" of light over large distances that cannot even be approximated by a local inertial frame, owing to the expansion of space. The light travels locally at $c$ throughout its journey. That's all you can say.

The local curvature of spacetime and the global expansion of space tell you about the spacetime in which the light moves. In one sense this does not affect the light in any way. You can say that light is"bent" around a star. But, equally, you can say that light encountered a region of spacetime near a massive body and followed its usual null path. It's only the interpretation on Earth based on the angle at which we receive the light that leads to the conclusion that the light did something different from what it would have done if the intervening star was not there.

The same is true of redshift. There is no sense in which light is absolutely changing as it redshifts or blueshifts. Redshift and blueshift are functions of the relationship between the source and the receiver. Not of any physical process affecting the light per se. You can always redshift or blueshift light by moving relative to the source. The light itself is not changing; only your measurement of it because of your relationship to the source.

 

[DennisN]

However I want to make clear that in my post I was referring to the effect of gravity on "c" (the speed of light), I am fairly well aware of the effects of gravity on light otherwise.

Ok, great.
PeterDonis has already addressed your question, and here's my take on it:

Speed of light is a constant within local frames

Yes, correct.

however this constant does not carry to large distances in a uniformly expanding universe (from my perspective a photon from my flashlight moving away from me is slower than a photon 10 Gly away moving away from me).

This is not because c is changing. It is because space is changing (expanding), in your case the space between you and the photon 10 Gly away. The photon at 10 Gly has a larger distance to travel to you than it would in a static universe because there is more space between the photon and you (more space than there would be in a static universe).

However I don't believe a gravitational field can have such an effect on c regardless of its theoretical strength or extent (I'm not sure about this).

...so this is not about gravitational fields, it is about the metric expansion of space.

Edit: I now saw PeroK replied while I was writing my reply.

The light travels locally at c throughout its journey. That's all you can say.

And that was one thing I intended to say with my reply.

 

[Staticboson]

In SR we have the postulate that the speed of light is invariant across all inertial reference frames.

In GR this is essentially replaced by the postulate that light travels on null spacetime paths. And, of course, if you focus on a local inertial reference frame, then a null path is equivalent to the invariant speed $c$ in that reference frame.

In an expanding universe it becomes difficult to say what you mean by the overall "speed" of light over large distances that cannot even be approximated by a local inertial frame, owing to the expansion of space. The light travels locally at $c$ throughout its journey. That's all you can say.

The local curvature of spacetime and the global expansion of space tell you about the spacetime in which the light moves. In one sense this does not affect the light in any way. You can say that light is"bent" around a star. But, equally, you can say that light encountered a region of spacetime near a massive body and followed its usual null path. It's only the interpretation on Earth based on the angle at which we receive the light that leads to the conclusion that the light did something different from what it would have done if the intervening star was not there.

The same is true of redshift. There is no sense in which light is absolutely changing as it redshifts or blueshifts. Redshift and blueshift are functions of the relationship between the source and the receiver. Not of any physical process affecting the light per se. You can always redshift or blueshift light by moving relative to the source. The light itself is not changing; only your measurement of it because of your relationship to the source.

That was a great explanation, I appreciate you taking the time to put that together.