Cosmological Redshift in FRW Metrics with Constant Spacetime Curvature

TL;DR

This paper investigates the origin of cosmological redshift in FRW metrics with constant curvature, demonstrating that its interpretation as space expansion is coordinate-dependent and can be explained through kinematics and gravity.

Contribution

It challenges the conventional view by showing redshift's dependence on symmetry and coordinate choice, suggesting it need not imply space expansion.

Findings

Redshift interpretation varies with coordinate system.

Redshift can be derived from kinematic and gravitational effects.

Space expansion is not the only explanation for redshift in these models.

Abstract

Cosmological redshift z grows as the Universe expands and is conventionally viewed as a third form of redshift, beyond the more traditional Doppler and gravitational effects seen in other applications of general relativity. In this paper, we examine the origin of redshift in the Friedmann-Robertson-Walker metrics with constant spacetime curvature, and show that---at least for the static spacetimes---the interpretation of z as due to the "stretching" of space is coordinate dependent. Namely, we prove that redshift may also be calculated solely from the effects of kinematics and gravitational acceleration. This suggests that its dependence on the expansion factor is simply a manifestation of the high degree of symmetry in FRW, and ought not be viewed as evidence in support of the idea that space itself is expanding.