f(G) Noether cosmology

Abstract

We develop the $n$-dimensional cosmology for $f(\mathcal{G})$ gravity, where $\mathcal{G}$ is the \emph{Gauss-Bonnet} topological invariant. Specifically, by the so-called Noether Symmetry Approach, we select $f(\mathcal{G})\simeq {\mathcal{G}}^k$ power-law models where $k$ is a real number. In particular, the case $k=1/2$ for $n=4$ results equivalent to General Relativity showing that we do not need to impose the action $R+f(\mathcal{G})$ to reproduce the Einstein theory. As a further result, de Sitter solutions are recovered in the case where $f(\mathcal{G})$ is non-minimally coupled to a scalar field. This means that issues like inflation and dark energy can be addressed in this framework. Finally, we develop the Hamiltonian formalism for the related minisuperspace and discuss the quantum cosmology for this model.

References in corpus (9)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Quantum Gravity at a Lifshitz Point
• Disappearing cosmological constant in f(R) gravity
• Extended Gravity Cosmography
• Cosmological inflation in $F(R,\mathcal{G})$ gravity
• Noether Symmetry Approach in $f(T,B)$ teleparallel cosmology
• Dark energy and dust matter phases from an exact $f(R)$-cosmology model
• Solutions of Higher Dimensional Gauss-Bonnet FRW Cosmology
• The gauge symmetries of f(R) gravity with torsion in the Cartan formalism

Cited by in corpus (35)

• Bouncing Cosmology in f(Q) Symmetric Teleparallel Gravity
• Non-Local Gravity Cosmology: an Overview
• Unification of a Bounce with a Viable Dark Energy Era in Gauss-Bonnet Gravity
• Big Bang Nucleosynthesis constraints on higher-order modified gravities
• Minisuperspace quantum cosmology in $f(Q)$ gravity
• Noether Symmetries and Quantum Cosmology in Extended Teleparallel Gravity
• Early and late time cosmology: the $f(R)$ gravity perspective
• Late-time constraints on modified Gauss-Bonnet cosmology
• Equivalence of non-minimally coupled cosmologies by Noether symmetries
• Tracing the cosmic history by Gauss-Bonnet gravity
• Canonical variational completion and 4D Gauss-Bonnet gravity
• Non-Local Curvature and Gauss-Bonnet Cosmologies by Noether Symmetries
• Existence of Wormholes in $f(\mathcal{G})$ Gravity using Symmetries
• Exact Solutions in Higher-Dimensional Lovelock and $Ad{S}_5$ Chern-Simons Gravity
• Reaching the sensitivity limit of a Sagnac gyroscope through linear regression analysis
• Non-Local Curvature Gravity Cosmology via Noether Symmetries
• Cosmological implications of Rastall-$f(R)$ theory
• Addressing Cosmological Tensions by Non-Local Gravity
• Minisuperspace Quantum Cosmology in Metric and Affine Theories of Gravity
• Renormalizability of alternative theories of gravity: differences between power counting and entropy argument
• Exploring departures from Schwarzschild black hole in $f(R)$ gravity
• Dynamical Complexity in Teleparallel Gauss-Bonnet Gravity
• The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity
• The Noether Symmetry Approach: Foundation and applications. The case of scalar-tensor Gauss-Bonnet gravity
• Late-time Cosmology of scalar field assisted $f(\mathcal{G})$ gravity
• Energy Conditions in Gauss-Bonnet Gravity
• Effective Actions for Loop Quantum Cosmology in Fourth-Order Gravity
• General analysis of Noether symmetries in Horndeski gravity
• Noether Symmetry Approach in Eddington-inspired Born-Infeld gravity
• Inflation and cosmological evolution with $F(R,G)$ gravity theory
• Linearized Field Equations and Extra Force in $f(R,{\mathbf{T}}^{(n)})$ Extended Gravity
• DNA Mutations via Chern-Simons Currents
• Noether symmetry approach in non-minimal derivative coupling gravity
• Noether gauge symmetry approach applying for the non-minimally coupled gravity to the Maxwell field
• Conflict between some higher-order curvature invariant terms