Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics

Abstract

Mimetic gravity is a Weyl-symmetric extension of General Relativity, related to the latter by a singular disformal transformation, wherein the appearance of a dust-like perfect fluid can mimic cold dark matter at a cosmological level. Within this framework, it is possible to provide an unified geometrical explanation for dark matter, the late-time acceleration, and inflation, making it a very attractive theory. In this review, we summarize the main aspects of mimetic gravity, as well as extensions of the minimal formulation of the model. We devote particular focus to the reconstruction technique, which allows the realization of any desired expansionary history of the Universe by an accurate choice of potential, or other functions defined within the theory (as in the case of mimetic $f(R)$ gravity). We briefly discuss cosmological perturbation theory within mimetic gravity. As a case study within which we apply the concepts previously discussed, we study a mimetic Hořava-like theory, of which we explore solutions and cosmological perturbations in detail. Finally, we conclude the review by discussing static spherically symmetric solutions within mimetic gravity, and apply our findings to the problem of galactic rotation curves. Our review provides an introduction to mimetic gravity, as well as a concise but self-contained summary of recent findings, progresses, open questions, and outlooks on future research directions.

arXiv comment68 pages, invited review to appear in Advances in High Energy Physics

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• Initial Conditions for Imperfect Dark Matter
• d-dimensional non-asymptotically flat thin-shell wormholes in Einstein-Yang-Mills-Dilaton gravity
• Inflationary universe from higher derivative quantum gravity coupled with scalar electrodynamics
• A Cosmological Solution to Mimetic Dark Matter
• An Introduction to Cascading Gravity and Degravitation
• Mimetic $F(R)$ inflation confronted with Planck and BICEP2/Keck Array data
• Bi-scalar modified gravity and cosmology with conformal invariance
• Non-local $F(R)$-mimetic gravity
• Dark Energy and Equation of State Oscillations with Collisional Matter Fluid in Exponential Modified Gravity
• Thermodynamics of Horndeski black holes with non-minimal derivative coupling
• Thermodynamic instability of topological black holes in Gauss-Bonnet gravity with a generalized electrodynamics
• Cylindrical solutions in Mimetic gravity
• Inflationary Parameters in Renormalization Group Improved ${\varphi }^4$ Theory
• Conformal Invariant Teleparallel Cosmology
• Cosmology of a Lorentz violating Galileon theory
• Aspects of Late-time Evolution in Mimetic $F(R)$ Gravity
• Covariant Lagrange multiplier constrained higher derivative gravity with scalar projectors
• Singular deformations of nearly $R^2$ inflation potentials
• Beyond Fab Four
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• Curvature perturbations of quasidilaton non-linear massive gravity
• Gauged Nambu-Jona-Lasinio inflation
• Induced geometry from disformal transformation
• Newton law in covariant unimodular $F(R)$ gravity
• Flare-out conditions in static thin-shell wormholes
• Canonical invariance of spatially covariant scalar-tensor theory
• Black hole and de Sitter solutions in a covariant renormalizable field theory of gravity
• Quantum Corrected Schwarzschild Thin Shell Wormhole
• Wormholes leading to extra dimensions
• $f(\varphi )R$-models for inflation
• Mimetic Attractors
• Inhomogeneous Dark Energy
• Analyzing modified unimodular gravity via Lagrange multipliers
• 2+1-dimensional traversable wormholes supported by positive energy
• On FRW Model in Conformal Teleparallel Gravity
• Interacting Scalar Radiation and Dark Matter in Cosmology
• Lagrange Multiplier Modified Horava-Lifshitz Gravity
• Scalar tensor Horndeski models: simple cosmological applications
• Linearized gravity with matter time
• $R^n$ gravity is kicking and alive: the cases of Orion and NGC 3198
• van Vleck determinants: traversable wormhole spacetimes
• 3+1-dimensional thin-shell wormhole with deformed throat can be supported by normal matter
• Mutated hybrid inflation in $f(R,\square R)$-gravity
• Inflation without self-reproduction in $F(R)$ gravity
• Hamiltonian Analysis of Lagrange Multiplier Modified Gravity
• Some solutions for one of the cosmological constant problems
• Looking for empty topological wormhole spacetimes in $F(R)$-modified gravity
• Arnowitt-Deser-Misner representation and Hamiltonian analysis of covariant renormalizable gravity
• 2+1-dimensional wormhole from a doublet of scalar fields
• $k$-essence non-minimally coupled with Gauss-Bonnet invariant for inflation
• Ponderable aether
• Braneworlds with field derivative coupling to the Einstein tensor
• Notes on diffeomorphisms symmetry of $f(R)$ gravity in the cosmological context
• Structure of Aristotelian Electrodynamics
• Hypocycloidal throat for 2+1-dimensional thin-shell wormholes
• A Holographic Description of Negative Energy States
• Generic Scalar Potentials in Geometric Scalar Gravity
• Quanta of Geometry and Unification
• Covariant gravity with Lagrange multiplier constraint

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• Primordial regular black holes as all the dark matter. I. Time-radial-symmetric metrics
• Cosmological perturbations and stability of nonsingular cosmologies with limiting curvature
• Cuscuton gravity as a classically stable limiting curvature theory
• Anisotropic compact stars in the mimetic gravitational theory
• Generalized disformal Horndeski theories: cosmological perturbations and consistent matter coupling
• Fluctuations in cool quark matter and the phase diagram of Quantum Chromodynamics
• Black hole solutions in mimetic Born-Infeld gravity
• Thick brane in mimetic $f(T)$ gravity
• Spacetime and dark matter from spontaneous breaking of Lorentz symmetry
• On the origin of matter in the Universe
• Gauge Field Mimetic Cosmology
• Mimetic Euler-Heisenberg theory, charged solutions and multi-horizon black holes
• Thick branes with inner structure in mimetic gravity
• Higher order derivative coupling to gravity and its cosmological implications
• Non-covariance of the dressed-metric approach in loop quantum cosmology
• Trinity of black hole correspondences: Shadows, quasinormal modes, graybody factors, and cautionary remarks
• Tracing the cosmic history by Gauss-Bonnet gravity
• New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies
• Kinetically coupled dark energy
• Thick branes with inner structure in mimetic $f(R)$ gravity
• Spatially covariant gravity: Perturbative analysis and field transformations
• Swampland dS conjecture in Mimetic $f(R,T)$ gravity
• Forms of action for perfect fluid in General Relativity and mimetic gravity
• Limiting curvature mimetic gravity and its relation to Loop Quantum Cosmology
• Unified dark sectors in scalar-torsion theories of gravity
• Primordial Cosmology in Mimetic Born-Infeld Gravity
• Hayward black hole in scalar-Einstein-Gauss-Bonnet gravity in four dimensions
• Ghost-free Palatini derivative scalar-tensor theory: desingularization and the speed test
• Implications of cosmologically coupled black holes for pulsar timing arrays
• Non-relativistic limit of embedding gravity as General Relativity with dark matter
• Imprints of interacting dark energy on cosmological perturbations
• Is limiting curvature mimetic gravity an effective polymer quantum gravity?
• Two-field mimetic gravity revisited and Hamiltonian analysis
• Reconstruction of mimetic gravity in a non-singular bouncing universe from quantum gravity
• Disforming to Conformal Symmetry
• Limiting curvature mimetic gravity for group field theory condensates
• Inflation in mimetic $f(R,T)$ gravity
• The key role of Lagrangian multiplier in mimetic gravitational theory in the frame of isotropic compact star
• Disformally Coupled Quintessence
• Gravity in mimetic scalar-tensor theories after GW170817
• Supercomputers against strong coupling in gravity with curvature and torsion
• Modifications of gravity via differential transformations of field variables
• Large-scale structure in mimetic Horndeski gravity
• Mimetic Black Strings
• Consistency between black hole and mimetic gravity -- Case of $(2+1)$-dimensional gravity
• On the role of constraints and degrees of freedom in the Hamiltonian formalism
• Mimetic gravity in $(2+1)$-dimensions
• Anisotropic Mimetic Cosmology
• Importance of being nonminimally coupled: Scalar Hawking radiation from regular black holes
• Mimetic Inflation
• Towards a viable effective field theory of mimetic gravity
• New anisotropic star solutions in mimetic gravity
• Testing scale-invariant inflation against cosmological data
• Spatially covariant gravity with a dynamic lapse function
• Friedmann equations in the Codazzi parametrization of Cotton and extended theories of gravity and the Dark Sector
• Ghost from constraints: a generalization of Ostrogradsky theorem
• Topological black holes in mimetic gravity
• Further Refining Swampland dS Conjecture in Mimetic f(G) Gravity
• Dynamics of DiskMass Survey galaxies in refracted gravity
• Horndeski dark matter and beyond
• Structure formation in mimetic gravity
• Dynamical reconstruction of the $\Lambda$CDM model in the scalar-tensor representation of $f\left(Q,T\right)$ gravity
• New Dynamical Degrees of Freedom from Invertible Transformations
• A generalized Weyl structure with arbitrary non-metricity
• Topological regular black holes without Cauchy horizon
• Reconstructing Mimetic Cosmology
• Direct couplings of mimetic dark matter and their cosmological effects
• Solar chameleons: Novel channels
• Primordial regular black holes as all the dark matter. III. Covariant canonical quantum gravity models
• Creation of wormholes during the cosmological bounce
• Bose-Einstein Condensate dark matter models in the presence of baryonic matter and random confining potentials
• Fundamental energy scale of the thick brane in mimetic gravity
• First law of thermodynamics and entropy of FLRW universe in modified gravity
• Theories with limited extrinsic curvature and a nonsingular anisotropic universe
• Imprints of screened dark energy on nonlocal quantum correlations
• Mimetic f(T) Teleparallel gravity and cosmology
• Non-parametric modeling of the cosmological data, base on the ${\chi }^2$ distribution
• Dark matter from non-relativistic embedding gravity
• Hamiltonian analysis of Mimetic gravity with higher derivatives
• Inequivalence of mimetic gravity with models of loop quantum gravity
• Emergent scenario in mimetic gravity
• The geometry of null-like disformal transformations
• Light bending, static dark energy and related uniqueness of Schwarzschild-de Sitter spacetime
• Can Dark Matter be Geometry? A Case Study with Mimetic Dark Matter
• Black holes with Lagrange multiplier and potential in mimetic-like gravitational theory: multi-horizon black holes
• Multi-field Mimetic Gravity
• Note on bouncing backgrounds
• Dynamics of a higher-dimension Einstein-Scalar-Gauss-Bonnet cosmology
• Dark matter as a gravitational effect in the embedding theory approach
• A note on non singular Einstein-Aether cosmologies
• Stringballs and Planckballs for Dark Matter
• Cosmological Dark sector from a Mimetic-Metric-Torsion perspective
• Isotropic stellar model in mimetic theory
• Mimetic Curvaton
• Mimetic-Metric-Torsion with induced Axial mode and Phantom barrier crossing
• Physical Hamiltonian for mimetic gravity
• Hamiltonian Formulation of Ghost Free Mimetic Massive Gravity
• Tsallis holographic dark energy model with event horizon cutoff in modified gravity
• Extensions of two-field mimetic gravity
• Mimetic gravity: mimicking the dynamics of the primeval universe in the context of loop quantum cosmology
• Tidal virialization of dark matter haloes with clustering dark energy
• Mimetic-$f(Q)$ gravity: cosmic reconstruction and energy conditions
• Dark Coincidences: Small-Scale Solutions with Refracted Gravity and MOND
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Higher dimensional charged static and rotating solutions in mimetic gravity
• Analytical analysis of the origin of core-cusp matter density distributions in galaxies
• Mimetic Weyl geometric gravity
• Lower-dimensional Regge-Teitelboim gravity
• Holographic description of unified early and late universe in viscous mimetic gravity
• Energy-momentum pseudotensor and superpotential for generally covariant theories of gravity of general form
• The Impact of $f(\mathcal{G},T)$ Gravity on the Evolution of Cavity in the Cluster of Stars
• Higher order mimetic gravity after GW170817
• Possible types of dark matter condensation in embedding gravity
• K-nonizing
• Matter production effects and interacting scenario within a reconstructed mimetic cosmology for late times
• Mimetic Tensor-Vector-Scalar Cosmology: Incorporating Dark Matter, Dark Energy and Stiff Matter
• Dark matter candidate induced by Horndeski theory: dark matter halo and cosmological evolution
• Refracted Gravity Solutions from Small to Large Scales
• Black holes in $f(R,T)$ gravity coupled with Euler-Heisenberg electrodynamics
• Classification of ten-dimensional embeddings of spherically symmetric static metrics
• $\Lambda$CDM from broken diffeomorphisms
• Primordial Cosmology of an Emergent-like Universe from Modified Gravity: Reconstruction and Phenomenology Optimization with a Genetic Algorithm
• Dual models for p-form mimetic gravity and their connection to perfect fluids consisting of (p+1)-branes
• A simple ghost free and caustic free mimetic scalar field dark matter model
• Polyakov-like approach to the modified gravity and other geometric theories
• Investigation of Faddeev variant of embedding theory
• Dark Information in Black Hole with $\lambda \phi$ Fluid
• Nontrivial isometric embeddings for flat spaces
• Cosmology in the mimetic higher-curvature $f(R,R_{\mu \nu }{R}^{\mu \nu })$ gravity
• Noether currents in theories with higher derivatives and theories with differential field transformation in action (DFTA)
• Gravity as embedding theory and the distribution of matter in galaxies
• Sound Mode and Scale-Dependent Growth in Two-Fluid Dynamical Dark Energy