Almost-homogeneity of the universe in higher-order gravity

TL;DR

This paper demonstrates that in higher-order gravity theories, specifically $R+ ext{alpha} R^2$, the universe's geometry is nearly FRW if massless particles are nearly isotropic, extending previous GR results to early universe conditions.

Contribution

It extends the isotropy-FRW relation from general relativity to higher-order gravity theories, linking anisotropies in relic backgrounds to early universe geometry.

Findings

Almost isotropic massless particle distributions imply nearly FRW spacetime in $R+\alpha R^2$ gravity.

Results applicable to relic graviton backgrounds and early universe conditions.

Provides a theoretical basis for interpreting future anisotropy observations.

Abstract

In the $R+\alpha R^2$ gravity theory, we show that if freely propagating massless particles have an almost isotropic distribution, then the spacetime is almost Friedmann-Robertson-Walker (FRW). This extends the result proved recently in general relativity ($\alpha=0$), which is applicable to the microwave background after photon decoupling. The higher-order result is in principle applicable to a massless species that decouples in the early universe, such as a relic graviton background. Any future observations that show small anisotropies in such a background would imply that the geometry of the early universe were almost FRW.