 Starobinsky inflation

Starobinsky inflation can be formulated as a metric theory of gravity with a squared Ricci scalar in the action. In a convention with positive de Sitter Ricci scalar, use natural units, reduced Planck mass $M$ and mass scale $m>0$:The higher-curvature term carries an extra scalar degree of freedom, the scalaron. Set $F=1+R/(3m^2)>0$ and perform a conformal transformation to $g_{\mu \nu }^E=F{g}_{\mu \nu }$, with canonical field $\varphi =\sqrt{3/2}M\log F$. Its Einstein frame scalar potential isThis scalar representation explains the flat large-field plateau without assuming an unrelated matter potential. The pure $R+R^2$ contribution has this scalar representation.^[ref].

Near $\varphi =0$, $V\simeq m^2{\varphi }^2/2$, allowing an oscillatory post-inflationary phase. On the plateau, the leading slow-roll approximation gives ${ϵ}_V\simeq 3/(4N^2)$ and ${\eta }_V\simeq -1/N$ for $N$ remaining number of e-folds. Hence $n_s\simeq 1-2/N$ and $r\simeq 12/N^2$. These are model predictions, not an observational measurement; the mapping from $N$ to a measured scale also depends on reheating.

Starobinsky inflation is a theoretical model of cosmic inflation proposed by Russian physicist Alexei Starobinsky in the early 1980s. This model provides an explanation for the rapid expansion of the early universe, which is thought to have occurred just after the Big Bang. The key features of Starobinsky inflation include: 1. **Scalar Curvature Action**: The model is based on a modification of Einstein's general relativity which includes a scalar curvature term in the action.