Abstract
We have considered the perturbation equations governing the growth of fluctuations during inflation in generalized scalar tensor theory f(R,phi ). We have found that the scalar metric perturbations at very early times are negligible compared to the scalar field perturbation, just like general relativity. At sufficiently early times, when the physical momentum of perturbation mode, q / a is much larger than the Hubble parameter H, i.e. q/agg H, we have obtained the metric and scalar field perturbation in the form of WKB solutions up to an undetermined coefficient. Then we have quantized the scalar fluctuations and expanded the metric and the scalar field perturbations with the help of annihilation and creation operators of the scalar field perturbation. The standard commutation relations of annihilation and creation operators fix the unknown coefficient. Going over to the gauge invariant quantities which are conserved beyond the horizon, we have obtained the initial condition of the generalized Mukhanov–Sasaki equation. Then a similar procedure is performed for the case of tensor metric perturbation. As an example of the generalized Mukhanov–Sasaki equation and its initial condition, we have proposed a power-law functional form as f(R,phi )=f_0 R^m phi ^n and obtained an exact inflationary solution. In this background, then we have discussed how the scalar and tensor fluctuations grow.
Highlights
The inflationary mechanism provides the initial condition for cosmic perturbations observed in the cosmic background radiation (CMB) today
At these very early times, the perturbations are essentially quantum fields which can be expanded in terms of creation and annihilation operators satisfying the standard commutation relations
The evolution of cosmological fluctuations for radiation dominated universe depends on the initial conditions through scalar and tensor gauge invariant quantities, Rq0 and Dq0 respectively
Summary
The inflationary mechanism provides the initial condition for cosmic perturbations observed in the cosmic background radiation (CMB) today. The cosmological dynamics of dark energy models based on f (R, φ) gravity leads to some conditions on the form of the potential ( of φ) to realize a sequence of radiation, matter, and accelerated epochs [15,16,17] This theory can give the correct amount of inflation in agreement with the cosmological data while provides at the same time a graceful exit from the inflationary epoch [18,19]. Hwang et al have applied the conformal equivalence of generalized gravity theories with general relativity minimally coupled to a scalar field, in the absence of ordinary matter They have studied the evolution of the curvature perturbation considering the second order action. We have found the appropriate range of the free parameters of the solution to cover the observational constraints
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