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

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 $B{R}^{ab}{R}_{ab}+CR{R^{;c}}_c$ 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.

References in corpus (28)

• f(R) Theories Of Gravity
• f(R) theories
• Planck 2018 results. X. Constraints on inflation
• The Temperature of the Cosmic Microwave Background
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Effective Field Theory for Inflation
• Cosmic homogeneity demonstrated with luminous red galaxies
• Classical evolution and quantum generation in generalized gravity theories including string corrections and tachyon: Unified analyses
• Fourth order gravity: equations, history, and applications to cosmology
• Dark energy and dust matter phases from an exact $f(R)$-cosmology model
• Baryogenesis in $f(R)$-Theories of Gravity
• Higher-Order Corrections to the Effective Gravitational Action from Noether Symmetry Approach
• Relaxing Nucleosynthesis Constraints on Brans-Dicke Theories
• Einstein's 1917 Static Model of the Universe: A Centennial Review
• Beyond the Starobinsky model for inflation
• Higher-order extension of Starobinsky inflation: initial conditions, slow-roll regime, and reheating phase
• Light scalaron as dark matter
• The cosmological principle is not in the sky
• Cosmological Gravitational Wave in a Gravity with Quadratic Order Curvature Couplings
• Corrected constraints on big bang nucleosynthesis in a modified gravity model of $f(R)\propto R^n$
• CMASS galaxy sample and the ontological status of the cosmological principle
• The amplification of cosmological magnetic fields in Extended $f(T,B)$ Teleparallel Gravity
• Constraints on modified Gauss-Bonnet gravity during big bang nucleosynthesis
• Cosmological perturbations in a gravity with quadratic order curvature couplings
• The inflationary scenario in the $f(R)$ gravity model with a $R^4$ term
• A radiation-like era before inflation
• Optimal Boltzmann hierarchies with non-vanishing spatial curvature
• Perturbations and Linearization Stability of Closed Friedmann Universes

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• Oscillating cosmic evolution and constraints on big bang nucleosynthesis in the extended Starobinsky model
• Testing quantum gravity with primordial gravitational waves