Inflation due to non-minimal coupling of $f(R)$ gravity to a scalar field

Abstract

In this work we investigate a inflationary scenario generated by a large scalar field $\varphi$ that non-minimally couples to a $f(R)$ modified gravity model. For a Starobinsky's like model, it is found that along a particular flat direction, the scalar potential takes a simple form $V=(M_p^4/4)[V(\varphi )/\alpha (\varphi {)}^2]$ where $\alpha (\varphi )$ is a non-minimal coupling to Ricci scalar $R$ in the model. The inflation, therefore, is effectively represented as a single field inflaton scenario. For a specific example, such as a scalar potential $V(\varphi )={\mu }_1{\varphi }^2+{\mu }_2{\varphi }^4$, we found that the predictions match nicely in the $1\sigma$ confidence level of \textit{Plank} TT, TE, EE+lowP combination data of Planck 2015 CMB data for $0<{\mu }_3\le 100$, where ${\mu }_3:=|{\mu }_1|/({\mu }_2{M}_p^2)$. For example, taking ${\mu }_3=0.01$ the scalar-to-tensor ratio $r=0.0004$ and and spectral index $n_s=0.96985$ for $N_{\ast }=50$ while taking ${\mu }_3=100.0$ produces $r=0.03$ and $n_s=0.96359$ for $N_{\ast }=60$.

Comments: 10 pages, 1 figure