The point is that gravitational interaction through space is not within a time slice, but across time. The gravitational effect of distant matter on us today represents the past. So there is a gradient over space when there is a gradient over time, which there likely is by the moving particle horizon.At any time slice in a homogeneous and isotropic universe there is no gravitational potential difference to cause a time dilation other than local effects such as stars BH's etc. However these are only small, local regions compared to the universe as a whole.
at any time slice in our universes history the universe as a whole is considered homogeneous and isotrophic. So how can a universal time dilation occur?
"Slows down" by what criterion? Certainly not the FRW metric; in that metric, coordinate time is the same as proper time for comoving observers. Once again, if you want to talk about GR, and not your personal speculations, you need to talk about what GR actually says.And IMO it slows down, while space expands (these go together, just as in the Schwarzschild metric).
Whether it "could" or not in some hypothetical model, it doesn't in the actual model GR uses, the FRW model.Picture what happens if one increases the central mass in the Schwarzschild spacetime. The increase of total mass within the expanding particle horizon could generate the same effect.
This is true; a more precise way of saying it is to say that the spacetime curvature observed at any event in spacetime can be explained entirely by the presence of mass-energy in the past light cone of that event. This is true for FRW spacetime, since it's true of any spacetime in GR; that is, it's true of any spacetime that is a solution of the Einstein Field Equation.The point is that gravitational interaction through space is not within a time slice, but across time. The gravitational effect of distant matter on us today represents the past.
...does not follow from the above; FRW spacetime is a counterexample. In the standard "comoving" coordinate chart, there is a gradient of spacetime curvature with time (because the scale factor changes with time), but not with space (because the scale factor is the same everywhere in space).So there is a gradient over space when there is a gradient over time
The Milne universe is empty (no matter-energy present), so it's not a good example. You may be confusing the Milne universe with the critical density FRW universe, which has flat spatial slices (so the spatial geometry is easy to conceptualize), but nonzero energy density (since the energy density has to be just at the critical value such that the expansion rate of the universe goes to zero as the time goes to infinity).lets look at the flight path of a photon emitted from the CMB in a Milne universe.
Not in the Milne universe, it isn't; it's zero for all time in the Milne universe. The statement is true for a critical density FRW universe.at the time of emission the average density of the universe is higher than it is today
The Milne universe is not "close to flat"; it's exactly flat. (Put another way, the Milne universe is just a region of Minkowski spacetime, with an unusual coordinate chart on it.) That's why photon flight paths in the Milne universe are straight lines; spacetime is flat because the energy density is zero.however their is no localized gravity well, so the photon flight path is still determined by the Universe geometry (which is close to flat).
Yes, you are, even aside from what I pointed out above. In the Milne universe, "comoving" observers are observers moving outward from the "Big Bang" (which is just an event at the origin of a Minkowski coordinate chart in which the Milne universe is the "upper wedge", the interior of the future light cone of the origin) at all possible velocities (i.e, all possible timelike worldlines through the origin). Since these observers are obviously in relative motion with respect to a global inertial frame, you would expect to see "time dilation" between them.So where would you expect to see a time dilation or am I missing something?
Ok, then show me another metric that correctly describes the universe as a whole but also allows a meaningful "gravitational time dilation" to be defined. Just waving your hands and saying "cosmic potential" doesn't mean any such metric consistent with GR does exist.if something is different from the FRW metric that doesn't mean it is in conflict with GR. Your statement is in effect: there is no gravitational time dilation, because it is not in the FRW metric. That doesn't mean it does not exist.
None of the clues you have mentioned so far are "within GR context"; they are either speculations on alternative theories to GR that didn't pan out, or dealing with other theoretical frameworks altogether (such as quantum mechanics).I think it's not there, because we simply don't know (yet) how to calculate the cosmic potential and how it evolves. But I believe their are some clues, as I indicated before, which could help us moving forward on this, all within GR context.
Modeling dark energy in the FRW model is easy: it's a positive cosmological constant. If that's not enough for you because we don't know what microphysics produces a positive cosmological constant, that's not a problem with the FRW model; *any* large-scale model that produced the same predictions would be open to the same objection.FRW model is not free from interrogation as long as we have no acceptable answer to what dark energy is supposed to be.
Btw, I haven't commented on this before: according to the best current model of the universe (the one with a positive cosmological constant, aka "dark energy"), the total mass within our particle horizon is *decreasing*, not increasing. That's because the expansion of the universe is accelerating, and the effect of the accelerating expansion (which moves matter outside the particle horizon) outweighs the effect of the increasing age of the universe (which increases the distance to the particle horizon).The increase of total mass within the expanding particle horizon
What you are calling the "fundamental observer" is what is usually called a "comoving observer". Those observers see the universe as homogeneous and isotropic. An observer in relative motion to the comoving observer in his vicinity will *not* see the universe as homogeneous and isotropic.if an observer is in relative motion to the fundamental observer and to the fundamental observer the universe is homogeneous and isotropic. Am I correct in thinking that the com-moving observer would not see the universe as isotropic?