The Cosmological Spacetime

TL;DR

This paper derives observer-dependent transformations of cosmological metrics to better understand the cosmic horizon and its implications for dark energy, challenging the notion of a cosmological constant.

Contribution

It provides explicit formulas for the cosmic horizon in various cosmologies and analyzes the divergence of cosmological time at this boundary, impacting dark energy interpretations.

Findings

Cosmic horizon radius expressed in measurable terms.

Divergence of cosmological time at the horizon.

Challenges the cosmological constant model of dark energy.

Abstract

We present here the transformations required to recast the Robertson-Walker metric and Friedmann-Robertson-Walker equations in terms of observer-dependent coordinates for several commonly assumed cosmologies. The overriding motivation is the derivation of explicit expressions for the radius R_h of our cosmic horizon in terms of measurable quantities for each of the cases we consider. We show that the cosmological time dt diverges for any finite interval ds associated with a process at R -> R_h, which therefore represents a physical limit to our observations. This is a key component required for a complete interpretation of the data, particularly as they pertain to the nature of dark energy. With these results, we affirm the conclusion drawn in our earlier work that the identification of dark energy as a cosmological constant does not appear to be consistent with the data.