Late-time quantum backreaction from inflationary fluctuations of a nonminimally coupled massless scalar

Abstract

We consider the late-time one-loop quantum backreaction from inflationary fluctuations of a nonminimally coupled, massless scalar field. The scalar is assumed to be a spectator field in an inflationary model with a constant principal slow-roll ϵ parameter. We regulate the infrared by matching onto a preinflationary radiation era. We find a large late-time backreaction when the nonminimal coupling ξ is negative (in which case the scalar exhibits a negative mass term during inflation). The one-loop quantum backreaction becomes significant today for moderately small nonminimal couplings, ξ ∼ −1=20, and it changes sign (from negative to positive) at a recent epoch when inflation lasts not much longer than what is minimally required, N ≳ 66. Since currently we do not have a way of treating the classical fluid and the quantum backreaction in a self-consistent manner, we cannot say decidedly whether the backreaction from inflationary quantum fluctuations of a nonminimally coupled scalar can mimic dark energy.

Stochastic dark energy from inflationary quantum fluctuations

“…This idea goes back a while ago to [23,24] where it was noted that quantum fluctuations of a very light scalar could provide a CC-like contribution to the Friedmann equations. In recent years, similar ideas were examined [25][26][27][28][29][30]. Most recently in [30] it was shown that, for certain ranges of model parameters, the backreaction remains small throughout the expansion of the Universe, and becomes relevant only at late times in matter era where it behaves approximately like a cosmological constant.…”

“…The dominant contribution to the light scalar field correlators in inflation comes from the superhorizon modes (of wavelengths k > 1/aH). This is also true for the very light or massless scalar fields in subsequent evolution of the Universe, namely during radiation and matter periods [28,30]. The slow-roll approximation usually employed to derive the stochastic equations need not be correct in situations when the scalar becomes very massive, meaning m H. Since during decelerating periods of expansion the Hubble rate decays, this can eventually become true.…”

“…An example of such computation was done in the context of reheating in [31], but it still presents a challenging numerical problem. Instead of the numerical approach we make use of the observation from the analytic computations [26,28,30] that the quantum backreaction for very light fields is dominated by the infrared (IR) modes not only during inflation, but throughout the history, and that the spectrum of these modes is inherited from the inflation era. The evolution of IR modes (which are largely amplified) during inflation (for small enough nonminimal coupling) is very accurately described by the formalism of stochastic inflation fully formulated in [33] (though some of its simplest applications were already used in [32]).…”

Light scalars on cosmological backgrounds

“…From now on we will only consider situations where (3.5) is satisfied and this is required for the validity of the derivation in [12,63]. Situations where this restriction cannot be imposed can also be approached analytically, see for example the works [54,64,65] Following [12] we will first introduce a physical UV cut-off as…”

The effect of backreaction on inflationary Brans–Dicke cosmology

“…In the following, we use WKB approximation to achieve a UV expansion for the mode functions. 17,18 Since a basis of solutions for large k is given by {e −ikη , e ikη }, which are normalized by the Wronskian, thus the full positive frequency solutions of the mode equation (2.18) can be written as a…”