Note on Nariai and Tomita's and Starobinsky's cosmological solutions in the R^2 modified gravity

TL;DR

This paper compares early cosmological solutions in R^2 modified gravity, showing how Nariai and Tomita's solution relates to Starobinsky's inflationary model, and discusses the emergence of inflation and singularity avoidance.

Contribution

It demonstrates the connection between different R^2 gravity solutions and clarifies the mechanisms of inflation and singularity avoidance using conformal transformations.

Findings

Nariai and Tomita's solution describes early de Sitter expansion.

Starobinsky's solution corresponds to the later inflationary phase.

The models explain how inflation arises and singularities are avoided.

Abstract

Cosmological solutions derived by Nariai and Tomita (1971) and by Starobinsky (1980) are compared, and it is shown that the former derived de Sitter expansion in the R^2 modified gravity (without cosmological constant) at the earliest stage, and nine years later the latter derived the well-known inflationary solution. Next the property of their simplified models is described using the method of conformal transformations, and how the inflation arises and the singularity is avoided is shown. Finally the initial and final states of the inflation are discussed.