Planck constraints on inflation in auxiliary vector modified $f(R)$ theories

TL;DR

This paper explores how auxiliary vector fields modify $f(R)$ inflation models, connecting them to $ ext{α}$-attractors and Brans-Dicke theories, and constrains these models using Planck CMB data.

Contribution

It introduces a new class of inflationary models with auxiliary vector fields in $f(R)$ theories and derives observational constraints from Planck data.

Findings

The auxiliary vector field modifies the $f(R)$ inflation models to include $ ext{α}$-attractor features.

The Brans-Dicke parameter $eta$ is constrained to be less than 25 at 68% confidence level.

The models are consistent with Planck measurements of the scalar spectral index and tensor-to-scalar ratio.

Abstract

We show that the universal $\alpha$-attractor models of inflation can be realized by including an auxiliary vector field $A_{\mu}$ for the Starobinsky model with the Lagrangian $f(R)=R+R^2/(6M^2)$. If the same procedure is applied to general modified $f(R)$ theories in which the Ricci scalar $R$ is replaced by $R+A_{\mu} A^{\mu}+\beta \nabla_{\mu}A^{\mu}$ with constant $\beta$, we obtain the Brans-Dicke theory with a scalar potential and the Brans-Dicke parameter $\omega_{\rm BD}=\beta^2/4$. We also place observational constraints on inflationary models based on auxiliary vector modified $f(R)$ theories from the latest Planck measurements of the Cosmic Microwave Background (CMB) anisotropies in both temperature and polarization. In the modified Starobinsky model, we find that the parameter $\beta$ is constrained to be $\beta<25$ (68\,\%\,confidence level) from the bounds of the scalar spectral index and the tensor-to-scalar ratio.