An exact solution of the higher-order gravity in standard radiation-dominated era

TL;DR

This paper derives an exact analytical solution for higher-order gravity theories during the radiation-dominated era, confirming standard cosmic evolution and simplifying tensor perturbation analysis, with implications for observational tests.

Contribution

It provides the first exact solution of sixth-order gravitational equations in a radiation-dominated universe, validating standard evolution within modified gravity frameworks.

Findings

Standard evolution $a \,\propto\, t^{1/2}$ is consistent with higher-order gravity.

Tensor perturbation equations reduce to standard form.

Potential observational signatures discussed for distinguishing models.

Abstract

We report that the standard evolution of radiation-dominated era (RDE) universe $a \propto t^{1/2}$ is a sufficient condition for solving a sixth order gravitational field equation derived from the Lagrangian containing $B R^{ab}R_{ab} + C R {R^{;c}}_{c}$ as well as a polynomial $f(R)$ for a spatially flat radiation FLRW universe. By virtue of the similarity between $R^{ab}R_{ab}$ and $R^2$ models up to the background order and of the vanishing property of ${R^{;c}}_{c}$ for $ H = 1/(2t)$, the analytical solution can be obtained from a special case to general one. This proves that the standard cosmic evolution is valid even within modified gravitational theory involving higher-order terms. An application of this background solution to the tensor-type perturbation reduces the complicated equation to the standard second order equation of gravitational wave. We discuss the possible ways to discriminate the modified gravity model on the observations such as the gravitational wave from the disturbed universe and primordial abundances.