Alexei Starobinsky and Modern Cosmology

TL;DR

This paper surveys Starobinsky inflation and its generalizations through conformal and α-attractor frameworks, highlighting how diverse origins converge on plateau-like potentials that yield robust predictions for the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$. It traces the connection between the original $R^2$ gravity model and its Einstein-frame scalar-tensor form, then develops the conformal-attractor and α-attractor families (including T-models and E-models) and their universal predictions, while addressing current observational status from Planck, BICEP/Keck, ACT, SPT, and DESI. A key theme is the unity of attractor models under a common pole structure in the kinetic sector and the role of hyperbolic geometry, with implications for single- and multi-field realizations, higher-curvature extensions, and non-minimal couplings. The latest data tensions with DESI, though, motivate exploring non-minimal chaotic inflation and two-field attractors, underscoring that future measurements (CMB-S4, LiteBIRD) are crucial to test and refine this unified attractor framework.

Abstract

Alexei Starobinsky is one of the main authors of inflationary cosmology. Here I will discuss the Starobinsky model and its generalizations, including the theory of $α$-attractors. I will then describe the current status of these models in light of the latest observational results from ACT, SPT, and DESI.

Figures (4)

• Figure 1: Inflation in the Starobinsky model (\ref{['starf']}) combined with the chaotic inflation mode ${m^{2}\over 2}\chi^{2}$. The first stage of inflation begins at large $\chi$, as in the simple chaotic inflation model. After the field $\chi$ rolls to $\chi = 0$, the second stage of inflation begins, which is described by the model (\ref{['starf']}). This solves the problem of initial conditions for inflation in the model (\ref{['starchaot']}).
• Figure 2: BICEP/Keck results for $n_{s}$ and $r$BICEP:2021xfz superimposed with the predictions of the simplest $\alpha$-attractor T-model with the potential $\tanh^{2} {\varphi\over \sqrt{6\alpha}}$ and E-models (yellow lines for $N_{e} = 50, 60$) with the potential $(1-e^{-\sqrt{{2\over 3\alpha}}\varphi} )^{2}$ (red lines for $N_{e} = 50, 60$).
• Figure 3: The figure from "Snowmass2021 Cosmic Frontier: Cosmic Microwave Background Measurements White Paper" Chang:2022tzj. It shows the predictions of T-model $\alpha$-attractors with unconstrained values of $\alpha$ (gray area), the predictions for $3\alpha= 7,6,5,4,3,2,1$ (purple lines), as well as Higgs inflation, $R^2$ inflation (red disks). The predictions are for $47 < N_e< 57$.
• Figure 4: The potential of the model (\ref{['JordanChaot']}) in the Einstein frame as a function of the canonical inflaton field $\varphi$. As one can see, it is similar to the potential in the Starobinsky model (red dashed line) and in the E-models of $\alpha$-attractors Kallosh:2013yoa, but it approaches the plateau more slowly.