Inflation in a nutshell: From basics to latest advances

Abstract

Inflation is an elegant paradigm for the very early Universe. It not only offers a simple solution to the flatness and horizon puzzles of the standard hot Big Bang model, but also generates quantum fluctuations that seed CMB anisotropies and the formation of large-scale structure. In particular, both the spatial flatness of the Universe and a nearly Gaussian, scale-invariant power spectrum of the curvature perturbation predicted by inflation have been confirmed by various observations. Recently, a larger spectral index of curvature perturbation is preferred when combining with ACT DR6, and particularly when further including the $H_0$ prior from SH0ES, and then the Starobinsky inflation model is disfavored at more than $95\%$ confidence level. Even though modified reheating histories and non-minimal couplings have been proposed to achieve a larger value of the spectral index, the model with higher-order curvature corrections to Starobinsky inflation offers a concise and well-motivated explanation.