The Hubble flow: an observer's perspective

Abstract

In this methodological note we discuss some details and peculiarities of the cosmic expansion as viewed by a realistic observer. We show that the velocity v Θ related to a change (measured by observer's clock) of the angular distance, plays an important role in formation of a meaningful observed picture of the expansion of the universe. Usage of this velocity and the angular distance (in addition to the standard approach -proper distance and corresponding velocity) allows to present the cosmic expansion in a more illustrative manner. These parameters play a key role in visualization of the expansion.

Unified approach to redshift in cosmological/black hole spacetimes and synchronous frame

“…If, in addition to this, we set an observer at the origin of coordinate system (as usually done in FRW cosmology), we can see that equation (29) for the redshift is still valid and coincides with the known cosmological result (see, for example, [16]). As for equation (22), it gives us the famous Hubble law…”

“…As noted above, in FRW cosmology, these formulas are valid only for the de Sitter solution (see more comments on this in the following). For other regimes, the dependence between the redshift and the velocity at emission (in FRW metrics, it is reasonable to set the velocity of observer to zero) is more complicated; see, for example, [16].…”

“…The geodesic equations for radial light propagation in the static frame are the following (see equation (16)…”

Velocities of distant objects in General Relativity revisited

“…These two simple formulas give us the Hubble law v = Hd which in the FRW Universe is an exact relation. For other proposals for FRW cosmology see, for example, [5,6].…”

“…Time is increasing along the null-geodesic, so we can write x 0 = x 0 (x 1 ) (other coordinates are constant). Then we rewrite (5) :…”