Constraints from Inflation on Scalar-Tensor Gravity Theories

TL;DR

This work analyzes how inflationary perturbations constrain general scalar-tensor gravity with a two-field setup (inflaton $\sigma$ and dilaton $\psi$). By formulating slow-roll dynamics and the full perturbation theory in this two-field scalar-tensor framework, the authors derive expressions for the scalar tilt $n_s$, tensor tilt $n_g$, and tensor-to-scalar ratio $R$ in terms of the slow-roll parameters $\epsilon_\sigma$, $\eta_\sigma$, $\epsilon_\psi$, $\eta_\psi$ and the couplings encoded in $\alpha(\psi)$. They show that non-adiabatic perturbations can drive evolution of the curvature perturbation $\zeta$ on super-Hubble scales, though GR is typically recovered as an attractor when the coupling tends to zero ($\alpha(\psi)\to0$). The paper identifies two limiting regimes—$\psi$-dominated extended inflation and $\sigma$-dominated chaotic inflation—with distinct predictions for $n_s$ and $R$, and demonstrates that current and future observations can place meaningful bounds on $\alpha$ and $\alpha'$ that are competitive with, or stronger than, primordial nucleosynthesis and solar-system constraints. In a concrete chaotic-inflation example, they show that keeping $n_s\approx0.95$ requires both $a_1$ and $a_2$ (the parameters controlling the scalar-tensor coupling) to be small, yielding quantitative bounds on the deviations from general relativity during inflation.

Abstract

We show how observations of the perturbation spectra produced during inflation may be used to constrain the parameters of general scalar-tensor theories of gravity, which include both an inflaton and dilaton field. An interesting feature of these models is the possibility that the curvature perturbations on super-horizon scales may not be constant due to non-adiabatic perturbations of the two fields. Within a given model, the tilt and relative amplitude of the scalar and tensor perturbation spectra gives constraints on the parameters of the gravity theory, which may be comparable with those from primordial nucleosynthesis and post-Newtonian experiments.