Modified Gauss-Bonnet gravity with Lagrange multiplier constraint as mimetic theory

Abstract

In this paper we propose and extensively study mimetic $f(\mathcal{G})$ modified gravity models, with various scenarios of cosmological evolution, with or without extra matter fluids. The easiest formulation is based on the use of Lagrange multiplier constraint. In certain versions of this theory, it is possible to realize accelerated expansion of the Universe or even unified evolution which includes inflation with dark energy, and at the same time in the same theoretical framework, dark matter is described by the theory. This is achieved by the re-parametrization of the metric tensor, which introduces a new degree of freedom in the cosmological equations and leads to appearance of the mimetic "dark matter" component. In the context of mimetic $f(\mathcal{G})$ theory, we also provide some quite general reconstruction schemes, which enable us to find which $f(\mathcal{G})$ gravity generates a specific cosmological evolution. In addition, we also provide the general reconstruction technique for Lagrange multiplier $f(\mathcal{G})$ gravity. All our results are accompanied by illustrative examples, with special emphasis on bouncing cosmologies.

Revised version, to appear in CQG

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• Ghost-free Gauss-Bonnet Theories of Gravity
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• Regular black holes in $f(G)$ gravity
• Ghost-Free $F(R)$ Gravity with Lagrange Multiplier Constraint
• From neutron stars to quark stars in mimetic gravity
• Unimodular-Mimetic Cosmology
• Late time cosmological approach in mimetic $f(R,T)$ gravity
• Event Horizon Telescope observations exclude compact objects in baseline mimetic gravity
• Braneworld Mimetic Cosmology
• Unimodular Mimetic $F(R)$ Inflation
• Inflation in mimetic f(G) gravity
• Reissner-Nordström Black Holes in Mimetic $F(R)$ Gravity
• Cuscuton gravity as a classically stable limiting curvature theory
• Late-time constraints on modified Gauss-Bonnet cosmology
• Thick brane in mimetic $f(T)$ gravity
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• Pleasant behavior of swampland conjectures in the face of specific inflationary models
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• Gauss-Bonnet modified gravity models with bouncing behavior
• A Note on Schwarzschild de Sitter Black Holes in Mimetic $F(R)$ Gravity
• Regular multihorizon black holes in $f(G)$ gravity with nonlinear electrodynamics
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• Unimodular $f(G)$ gravity
• Mimetic Black Strings
• Consistency between black hole and mimetic gravity -- Case of $(2+1)$-dimensional gravity
• Modifications of gravity via differential transformations of field variables
• Mimetic gravity in $(2+1)$-dimensions
• Mimetic Inflation
• New anisotropic star solutions in mimetic gravity
• Topological black holes in mimetic gravity
• Further Refining Swampland dS Conjecture in Mimetic f(G) Gravity
• Shape of Dark Energy: Constraining Its Evolution with a General Parametrization
• Structure formation in mimetic gravity
• Mimetic DBI Inflation in Confrontation with Planck2018 data
• Fundamental energy scale of the thick brane in mimetic gravity
• Reconstructing Mimetic Cosmology
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• Mimetic Weyl geometric gravity
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