On the initial conditions of scalar and tensor fluctuations in $f(R,\varphi )$ gravity

Abstract

We have considered the perturbation equations governing the growth of fluctuations in generalized scalar tensor theory during inflation. we have found that the scalar metric perturbations at very early times are negligible compared with the scalar field perturbation, just like general relativity. At sufficiently early times, when $q/a\gg H$, 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. And a similar procedure is performed for the case of tensor metric perturbation.

arXiv comment11 pages

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Cited by in corpus (3)

• Testing scale-invariant inflation against cosmological data
• Trans-Planckian Effect in $f(R)$ Cosmology
• Super-horizon effects on the gauge invariant effective energy density in f(R) gravity