Generalized non-local $R^2$-like inflation

Understand

The $R^2$ inflation which is an extension of general relativity (GR) by quadratic scalar curvature introduces a quasi-de Sitter expansion of the early Universe governed by Ricci scalar being an eigenmode of d'Alembertian operator.

• In this paper, we derive a most general theory of gravity admitting $R^2$ inflationary solution which turned out to be higher curvature non-local extension of GR.
• We study in detail inflationary perturbations in this theory and analyse the structure of form-factors that leads to a massive scalar (scalaron) and massless tensor degrees of freedom.
• We argue that the theory contains only finite number of free parameters which can be fixed by cosmological observations.