> Your statement that matter has average uniform density in all directions around us is obviously only correct in sufficiently large frames of reference
Yes, agreed. But the distance to our cosmological horizon is large enough that the averaging assumption is fine on that scale.
> You should expand on why the cosmological horizon does not function in the same way the GP's "event horizon" analogue does
Fair enough. But first I'll reference an excellent paper by Davis & Lineweaver (2003) [1]. You can find much more detail there than I'm going to give here.
Some simple facts about our cosmological horizon are:
(1) It is currently receding from us very slowly (in terms of proper distance); and asymptotically it will be at a constant distance from us forever (in more technical language, our universe approaches de Sitter spacetime asymptotically, as all other matter and energy becomes negligible compared to dark energy; and in de Sitter spacetime the cosmological horizon is at a constant distance forever). It certainly is not receding from us at the speed of light.
(It is true that the horizon is a lightlike surface--but that does not mean it's receding from us at the speed of light. In fact, counterintuitively, to the extent it is "moving", locally, in any direction, that direction is towards us, not away from us! But due to the curvature of spacetime, its proper distance from us will asymptotically be constant.)
(2) It is not a boundary between things that can affect us gravitationally and things that can't. To the extent there is such a boundary in GR, it's our past light cone (which is shown in the diagrams in Figure 1 of the paper I referenced). But one also has to consider the other caveats I gave in my earlier post.
(3) The cosmological horizon is a boundary in spacetime, not space. It is a boundary between the region of spacetime that will be able to causally affect us into the infinite future, and the region that won't. Particular objects, as they recede from us, will move beyond the cosmological horizon and will then no longer be able to causally affect us. But events that occurred in those objects before they moved beyond the horizon will still be able to causally affect us--though of course it will take time for those effects to propagate to us. For example, the light we see from distant objects is a causal effect, but we see the objects not as they are "now" but as they were when the light was emitted. It's quite possible for a distant galaxy whose light we are seeing now to be beyond our event horizon "now", but they weren't when they emitted the light.
The spacetime diagrams in Figure 1 of the paper I referenced can be very helpful in making all this clearer.
> expand on how large the frame would have to be to achieve reasonable uniformity.
A few billion light years is certainly large enough. Our cosmological horizon is quite a bit further away than that (about 16 billion light years, according to the paper I referenced).
Yes, agreed. But the distance to our cosmological horizon is large enough that the averaging assumption is fine on that scale.
> You should expand on why the cosmological horizon does not function in the same way the GP's "event horizon" analogue does
Fair enough. But first I'll reference an excellent paper by Davis & Lineweaver (2003) [1]. You can find much more detail there than I'm going to give here.
Some simple facts about our cosmological horizon are:
(1) It is currently receding from us very slowly (in terms of proper distance); and asymptotically it will be at a constant distance from us forever (in more technical language, our universe approaches de Sitter spacetime asymptotically, as all other matter and energy becomes negligible compared to dark energy; and in de Sitter spacetime the cosmological horizon is at a constant distance forever). It certainly is not receding from us at the speed of light.
(It is true that the horizon is a lightlike surface--but that does not mean it's receding from us at the speed of light. In fact, counterintuitively, to the extent it is "moving", locally, in any direction, that direction is towards us, not away from us! But due to the curvature of spacetime, its proper distance from us will asymptotically be constant.)
(2) It is not a boundary between things that can affect us gravitationally and things that can't. To the extent there is such a boundary in GR, it's our past light cone (which is shown in the diagrams in Figure 1 of the paper I referenced). But one also has to consider the other caveats I gave in my earlier post.
(3) The cosmological horizon is a boundary in spacetime, not space. It is a boundary between the region of spacetime that will be able to causally affect us into the infinite future, and the region that won't. Particular objects, as they recede from us, will move beyond the cosmological horizon and will then no longer be able to causally affect us. But events that occurred in those objects before they moved beyond the horizon will still be able to causally affect us--though of course it will take time for those effects to propagate to us. For example, the light we see from distant objects is a causal effect, but we see the objects not as they are "now" but as they were when the light was emitted. It's quite possible for a distant galaxy whose light we are seeing now to be beyond our event horizon "now", but they weren't when they emitted the light.
The spacetime diagrams in Figure 1 of the paper I referenced can be very helpful in making all this clearer.
> expand on how large the frame would have to be to achieve reasonable uniformity.
A few billion light years is certainly large enough. Our cosmological horizon is quite a bit further away than that (about 16 billion light years, according to the paper I referenced).
[1] https://arxiv.org/abs/astro-ph/0310808