Superhorizon effects on the gauge invariant effective energy density inf(R)gravity

Abstract

In this article we study the gauge invariant effective energy momentum tensor for cosmological perturbations in f (R) gravity during the inflationary epoch. Considering the super-horizon regime, we derive the effective energy density up to the one-loop corrections. It describes the back-reaction effect of the fluctuations on the background space-time. introductionAccording to the inflationary scenario, the fluctuations of a scalar field, called inflaton, along with the metric perturbations, provide the original seeds for the structure formation of our recent universe, see [1]-[6] and references therein. Due to the non-linearity of Einstein field equations, there is a non-vanishing back-reaction effect through which the fluctuations change the Friedmann-Lematre-Robertson-Walker (FLRW) background metric. This effect could appear in the power spectrum of the cosmic fluctuations of CMB [6]. In general relativity (GR), considering the subhorizon and super-horizon regimes, the back-reaction effects have studied in many articles [7,8,9,10]. Some issues like local observability and causality [11] cause the super-horizon modes have been less studied than the sub-horizon modes. In [12], Unruh has claimed that the effect of long wavelength perturbation is invisible for any local observer but in the recent articles of Brandenberger and his collaborators [13], they mention how the super-horizon modes could affect the local physics. In GR, during the slow roll inflation, it is shown that the light scalar field fluctuations along with the scalar metric perturbations lead to a strong infrared enhancement in the gauge invariant energy momentum tensor (EMT) due to the super-horizon modes, but a combination of slow roll parameters can regulate this infrared enhancement [14,15,16]. In this article we would like to consider the effective EMT in a gauge invariant manner up to the one loop quantum correction of the scalar and tensor perturbations in f (R) gravity with an extra scalar field. Although f (R) gravity can produce an inflationary era in the early universe, inclusion of some additional scalar fields to it, can lead to non-adiabatic perturbations. These fields are responsible for primordial non-Gaussianity in the density perturbation [17]. Moreover multifield inflationary models have rich dynamics and according to [18] there is no particular reason to believe that a single scalar field drives the inflationary expansion of the universe. These models may also be motivated by high-energy physics, such as supersymmetric theories in which there are many superpartners scalar