$f(R,\mathcal{G})$-cosmological dynamics in the FLRW background

Abstract

We examine the cosmological dynamics of Einstein-Gauss-Bonnet gravity models in a four-dimensional spatially flat FLRW metric. These models are described by $f\left(R,\mathcal{G}\right)=f\left(R+\mu \mathcal{G}\right)$ theory of gravity. They are equivalent to models linear in the Ricci scalar $R$ and in the Gauss-Bonnet scalar $\mathcal{G}$ with one nonminimally coupled scalar field without kinetic term. We analyze the stability of the de Sitter solutions and construct the phase space of the field equations to investigate the cosmological evolution. We show that $f\left(R+\mu \mathcal{G}\right)$-theory provides a double inflationary epoch, this can be used to unify the early-time and late-time acceleration phases of the universe. Moreover, we discuss the initial value problem for theory to be cosmologically viable. Finally, the effects of the cold dark matter in cosmic evolution are discussed.

18 pages, 3 figures

References in corpus (26)

• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• Are f(R) dark energy models cosmologically viable ?
• String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy
• Cosmological inflation in $F(R,\mathcal{G})$ gravity
• Cosmology and Astrophysical Constraints of Gauss-Bonnet Dark Energy
• Quintom cosmologies admitting either tracking or phantom attractors
• Exact solutions for the Einstein-Gauss-Bonnet theory in five dimensions: Black holes, wormholes and spacetime horns
• Ghost conditions for Gauss-Bonnet cosmologies
• Vacuum structure for scalar cosmological perturbations in Modified Gravity Models
• Inflation with a quartic potential in the framework of Einstein-Gauss-Bonnet gravity
• De Sitter solutions in Einstein-Gauss-Bonnet gravity
• Global stability analysis for cosmological models with non-minimally coupled scalar fields
• A note on differences between (4+1)- and (5+1)-dimensional anisotropic cosmology in the presence of the Gauss-Bonnet term
• On the superstring-inspired quantum correction to the Starobinsky model of inflation
• Possible evolution of a bouncing universe in cosmological models with non-minimally coupled scalar fields
• New slow-roll approximations for inflation in Einstein-Gauss-Bonnet gravity
• Cosmology in modified $f(\mathcal{G})$ gravity: a late time cosmic phenomena
• Global dynamics in Einstein-Gauss-Bonnet scalar field cosmology with matter
• Phase-space analysis of dark energy models in non-minimally coupled theories of gravity
• Cosmological stability in $f(\varphi ,\mathcal{G})$ gravity
• Five-dimensional compact stars in Einstein-Gauss-Bonnet gravity
• More accurate slow-roll approximations for inflation in scalar-tensor theories
• Dynamical system analysis in modified Galileon cosmology
• Attractor Solutions in Interacting Dark Energy Models
• Global Portraits of Inflation in Nonsingular Variables
• Onset of dark energy from cosmological scalarization and gravitational wave speed