Order rho^2 Corrections to Randall-Sundrum I Cosmology

TL;DR

This paper calculates order rho^2 corrections to the Friedmann equation in Randall-Sundrum I cosmology, revealing that such corrections are absent for inflaton energy density on the same brane but present for the opposite brane, affecting early universe dynamics.

Contribution

It provides a detailed derivation of rho^2 corrections in RS-I cosmology including radion stabilization effects, highlighting the asymmetric impact on different branes and implications for inflation and baryogenesis.

Findings

Inflaton on a brane experiences no order rho^2 correction in Hubble rate.

Opposite brane's energy density causes rho^2 corrections.

Electroweak phase transition corrections are large but have the wrong sign for baryogenesis.

Abstract

We derive the corrections to the Friedmann equation of order rho^2 in the Randall-Sundrum (RS) model, where two 3-branes bound a slice of five-dimensional Anti-deSitter space. The effects of radion stabilization by the Goldberger-Wise mechanism are taken into account. Surprisingly, we find that an inflaton on either brane will experience no order rho^2 corrections in the Hubble rate H due to its own energy density, although an observer on the opposite brane does see such a correction. Thus there is no enhancement of the slow-roll condition unless inflation is simultaneously driven by inflatons on both branes. Similarly, during radiation domination, the rho^2 correction to H on a given brane vanish unless there is nonvanishing energy density on the opposite brane. During the electroweak phase transition the correction can be large, but is has the wrong sign for causing sphalerons to go out of thermal equilibrium, so it cannot help electroweak baryogenesis. We discuss the differences between our results and exact solutions in RS-II cosmology.