Backreaction of a massless minimally coupled scalar field from inflationary quantum fluctuations

Abstract

In this paper we study a massless, minimally coupled scalar field in a Friedmann-Lemaître-Robertson-Walker space-time with periods of different constant deceleration parameter. We assume the Bunch-Davies vacuum during inflation and then use a sudden matching approximation to match it onto a radiation era and subsequently onto a matter era. We then proceed to calculate the one-loop energy-momentum tensor from the inflationary quantum vacuum fluctuations in different eras. The energy-momentum tensor has the form of an ideal (quantum) fluid, characterized by an equation of state. When compared with the background, far away from the matching the quantum energy density in the radiation era exhibits a contribution that grows logarithmically with the scale factor. In the matter era the ratio of the quantum to classical fluid settles eventually to a tiny constant, ρ q /ρ≃(ℏH 0 ) 2 /(4πm 2 P c 4 )∼10 −13 for a grand unified scale inflation. Curiously, the late time scaling of quantum fluctuations suggests that they contribute a little to the dark matter of the Universe, provided that it clusters as cold dark matter, which needs to be checked.