Isotropic universe with almost scale-invariant fourth-order gravity

Abstract

We study a broad class of isotropic vacuum cosmologies in fourth-order gravity under the condition that the gravitational Lagrangian be scale-invariant or almost scale-invariant. The gravitational Lagrangians considered will be of the form L = f(R) + k(G) where R and G are the Ricci and Gauss-Bonnet scalars respectively. Specifically we take f(R) = R^2n and k(G) = G^n or k(G) = G ln G. We find solutions in closed form for a spatially flat Friedmann space-time and interpret their asymptotic early-time and late-time behaviour as well as their inflationary stages. One unique example which we discuss is the case of a very small negative value of the parameter b in the Lagrangian L = R^2 + b G ln G which leads to the replacement of the exact de Sitter solution from L = R^2 (being a local attractor) to a power-law inflation exact solution also representing a local attractor. This shows how one can modify the dynamics from de Sitter to power-law inflation by the addition of the G ln G-term.

several revisions included, 28 pages, J. Math. Phys. accepted

References in corpus (38)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• f(R,L_m) gravity
• The Cosmology of Modified Gauss-Bonnet Gravity
• Modified gravity models of dark energy
• Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology
• Fourth order gravity: equations, history, and applications to cosmology
• Dark energy from modified F(R)-scalar-Gauss-Bonnet gravity
• Cosmological evolution in exponential gravity
• Non-perturbative Gravity, Hagedorn Bounce & CMB
• On the $\Lambda$CDM Universe in $f(G)$ gravity
• Extended $f(R,L_m)$ gravity with generalized scalar field and kinetic term dependences
• On the Stability of a class of Modified Gravitational Models
• Reheating via a generalized non-minimal coupling of curvature to matter
• Stability of Schwarzschild-like solutions in f(R,G) gravity models
• Power-law cosmic expansion in f(R) gravity models
• Static Solutions for 4th order gravity
• Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke
• Master Equations for Gravitational Perturbations of Static Lovelock Black Holes in Higher Dimensions
• Inevitable ghost and the degrees of freedom in f(R,G) gravity
• Higher dimensional thin-shell wormholes in Einstein-Yang-Mills-Gauss-Bonnet gravity
• Massive Gravity with Mass Term in Three Dimensions
• Perihelion precession for modified Newtonian gravity
• Inflation with a Weyl term, or ghosts at work
• Gauss-Bonnet lagrangian G ln G and cosmological exact solutions
• Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions
• Eguchi-Hanson like space-times in F(R) gravity
• Stable Isotropic Cosmological Singularities in Quadratic Gravity
• Cosmological viability conditions for $f(T)$ dark energy models
• Cosmological entropy and generalized second law of thermodynamics in $F(R,G)$ theory of gravity
• Homogeneous cosmologies in generalized modified gravity
• R^n gravity and the chameleon
• Restricting Fourth Order Gravity via Cosmology
• A Born-Infeld-like f(R) gravity
• Exact $f(R)$-cosmological model coming from the request of the existence of a Noether symmetry
• Perihelion advance for orbits with large eccentricities in the Schwarzschild black hole
• Critical Cosmology in Higher Order Gravity
• On stability of power-law solution in multidimensional Gauss-Bonnet cosmology

Cited by in corpus (5)

• Scale Symmetry Breaking From Total Derivative Densities and the Cosmological Constant Problem
• Conformal Transformations and Weak Field Limit of Scalar-Tensor Gravity
• Why scalar-tensor equivalent theories are not physically equivalent?
• On the equivalence between different canonical forms of F(R) theory of gravity
• Field independent cosmic evolution