Asymptotically Safe Cosmology

TL;DR

This paper investigates quantum effects on cosmology using renormalisation group techniques, identifying fixed points and conditions for inflation in asymptotically safe gravity models.

Contribution

It introduces a method to incorporate renormalisation group running into cosmological evolution equations and classifies fixed points in asymptotically safe cosmology.

Findings

Identification of two types of cosmological fixed points.

Conditions for inflation at ultraviolet fixed points.

Classification of fixed points with and without gravity.

Abstract

We study quantum modifications to cosmology in a Friedmann-Robertson-Walker universe with and without scalar fields by taking the renormalisation group running of gravitational and matter couplings into account. We exploit the Bianchi identity to relate the renormalisation group scale with scale factor and derive the improved cosmological evolution equations. We find two types of cosmological fixed points where the renormalisation group scale either freezes in, or continues to evolve with scale factor. We discuss the implications of each of these, and classify the different cosmological fixed points with and without gravity displaying an asymptotically safe renormalisation group fixed point. We state conditions of existence for an inflating ultraviolet cosmological fixed point for Einstein gravity coupled to a scalar field. We also discuss other fixed point solutions such as "scaling" solutions, or fixed points with equipartition between kinetic and potential energies.