Late-time quantum backreaction of a nonminimally coupled massless scalar on FLRW

Abstract

We investigate whether quantum fluctuations can have a significant impact on the evolution of the universe, by studying the (late-time) backreaction of a massless scalar field with a possible coupling xi to the Ricci scalar on an FLRW background. The main motivation for this work is the observed late-time acceleration of the universe, for which no satisfactory explanation has been given yet. At the same time, cosmological perturbation theory establishes that we can take quantum fluctuations in a gravitational setting seriously, and some of their effects are well studied and in agreement with observations. This opens up the question if the energy density and pressure of these quantum fluctuations could account for the observed late-time acceleration of the universe. In addition to the usually assumed history of the universe (an inflationary, radiation and matter dominated period), we assume an initial radiation period in order to resolve IR divergences that are otherwise present in two point correlation functions for nonzero $\xi$. We canonically quantize the field and compute the one loop expectation value of the energy-momentum tensor with respect to the Bunch-Davies vacuum during radiation and matter domination. We compare the expectation values with the background quantities in order to estimate the significance of the quantum backreaction. For xi<0, we find that this backreaction can become significant, but the quantum energy density is negative during inflation and radiation. For xi<-0.057, the quantum energy density becomes comparable to the background energy density already during inflation, which makes late-time predictions for these values unreliable. For -0.057<xi<0, we find a transient phenomenon when the conformal Hubble rate becomes comparable to the conformal Hubble rate at the beginning of inflation. That is, when those scales become comparable, the quantum energy density goes from a period where it is negative but grows with respect to the background to a period where it is positive but decays with respect to the background. In between, there is a period where the energy density seems to grow from negative to positive rather quickly and during which the quantum fluid has negative pressure. We can tune the duration of inflation and the value of xi such that the backreaction is not too big during inflation and radiation and for which this transient behavior becomes significant at low redshift, rendering it potentially observable.