Constraints on Non-Singular Cosmological Models with Quadratic Lagrangians

TL;DR

This paper investigates quadratic gravity theories with $R^2$ terms, analyzing conditions on parameters to ensure non-singular, inflationary cosmological models with positive energy density and realistic sound velocities.

Contribution

It identifies parameter ranges in quadratic Lagrangians that produce non-singular, inflationary cosmologies with physically acceptable matter properties.

Findings

Derived conditions on $eta$ for non-singular inflationary solutions.

Ensured positivity of energy density in quadratic gravity models.

Established constraints for realistic sound velocities.

Abstract

We consider the generalized set of theories of gravitation whose Lagrangians contain the term $R^{2}$ : $L=\sqrt{-g}(R+\beta R^{2})$. Inserting the RW metric with an imposed non-singular and inflationary behaviour of the scale factor $a(t)$, and using a arbitrary perfect fluid, we study the properties of $\rho $ and $p$ in this context. By requiring the positivity of the energy density, as well as real and finite velocity of sound, we can obtain the range of values of $\beta $ that ensure the inflationary behaviour and absence of singularity.