Inflation in asymptotically safe f(R) theory

TL;DR

This paper investigates inflationary solutions within a class of polynomial f(R) gravity theories that are asymptotically safe, showing that high-order polynomials yield reliable inflationary solutions consistent with quantum gravity expectations.

Contribution

It demonstrates the existence of inflationary solutions in asymptotically safe f(R) theories and establishes their reliability at high polynomial orders.

Findings

Existence of power law and exponential inflationary solutions.

Solutions are reliable for sufficiently high polynomial order.

Modified Friedmann equations are derived assuming cutoff proportional to Hubble parameter.

Abstract

We discuss the existence of inflationary solutions in a class of renormalization group improved polynomial f(R) theories, which have been studied recently in the context of the asymptotic safety scenario for quantum gravity. These theories seem to possess a nontrivial ultraviolet fixed point, where the dimensionful couplings scale according to their canonical dimensionality. Assuming that the cutoff is proportional to the Hubble parameter, we obtain modified Friedmann equations which admit both power law and exponential solutions. We establish that for sufficiently high order polynomial the solutions are reliable, in the sense that considering still higher order polynomials is very unlikely to change the solution.