Cosmological perturbations in a generalized gravity including tachyonic condensation

TL;DR

This work develops a unified framework for cosmological perturbations in a generalized gravity theory with action $S = \int d^4 x \sqrt{-g} \left[ {1 \over 2} f(R, \phi, X) + L_m \right]$, encompassing $f(\phi,R)$ gravity, $p(\phi,X)$ models, and tachyonic condensation. It derives a general prescription to obtain primordial power spectra from vacuum fluctuations during slow-roll inflation, introducing gauge-invariant variables and effective quantities $Q$ and $c_A^2$ that modify both scalar and tensor perturbations. The formalism recovers standard Einstein results as a special case and applies to tachyonic slow-roll inflation with an exponential potential, yielding nearly scale-invariant spectra, a generalized consistency relation, and suppressed tensor modes. Overall, the paper provides a robust toolkit for predicting inflationary perturbations in a broad class of modified gravity theories, with direct implications for CMB and large-scale structure observations.

Abstract

We present unified ways of handling the cosmological perturbations in a class of gravity theory covered by a general action in eq. (1). This gravity includes our previous generalized $f(φ,R)$ gravity and the gravity theory motivated by the tachyonic condensation. We present general prescription to derive the power spectra generated from vacuum quantum fluctuations in the slow-roll inflation era. An application is made to a slow-roll inflation based on the tachyonic condensation with an exponential potential.