Mimetic Gravity Research Articles

The Mimetic Born-Infeld Gravity: The Primordial Cosmos and Spherically Symmetric Solutions

The Eddington-inspired-Born-Infeld (EiBI) model is reformulated within the mimetic approach. In the presence of a mimetic field, the model contains non-trivial vacuum solutions. We study a realistic primordial vacuum universe and we prove the existence of regular solutions. Besides, the linear instabilities in the EiBI model are found to be avoidable for some bouncing solutions. For a vacuum, static and spherically symmetric geometry, a new branch of solutions in which the black hole singularity that is replaced with a lightlike singularity is found.

Extended mimetic gravity: Hamiltonian analysis and gradient instabilities

We propose a novel class of degenerate higher-order scalar-tensor theories as an extension of mimetic gravity. By performing a noninvertible conformal transformation on “seed” scalar-tensor theories which may be nondegenerate, we can generate a large class of theories with at most three physical degrees of freedom. We identify a general seed theory for which this is possible. Cosmological perturbations in these extended mimetic theories are also studied. It is shown that either of tensor or scalar perturbations is plagued with gradient instabilities, except for a special case where the scalar perturbations are presumably strongly coupled, or otherwise there appear ghost instabilities.

Primordial cosmology in mimetic born-infeld gravity

The Eddington-inspired-Born-Infeld (EiBI) model is reformulated within the mimetic approach. In the presence of a mimetic field, the model contains non-trivial vacuum solutions which could be free of spacetime singularity because of the Born-Infeld nature of the theory. We study a realistic primordial vacuum universe and prove the existence of regular solutions, such as primordial inflationary solutions of de Sitter type or bouncing solutions. Besides, the linear instabilities present in the EiBI model are found to be avoidable for some interesting bouncing solutions in which the physical metric as well as the auxiliary metric are regular at the background level.

Forms of action for perfect fluid in general relativity and mimetic gravity

We consider various forms of action allowing us to describe a perfect fluid in the framework of General Relativity. First we consider a potential motion without pressure. Starting from an action in terms of the current density vector built similarly to the action of a single particle, we build a series of equivalent actions through various changes of variables. The results are then generalized to the cases of motion with vorticity and the presence of pressure. The obtained forms of action are compared to the previously known variants. We discuss the possibilities to use the obtained results to formulate the theories containing a description of a perfect fluid. A new form of action is proposed for mimetic gravity, which allows a motion with vorticity for mimetic matter as a perfect fluid.

Effective loop quantum cosmology as a higher-derivative scalar-tensor theory

Recently, Chamseddine and Mukhanov introduced a higher-derivative scalar-tensor theory which leads to a modified Friedmann equation allowing for bouncing solutions. As we note in the present work, this Friedmann equation turns out to reproduce exactly the loop quantum cosmology effective dynamics for a flat isotropic and homogeneous space-time. We generalize this result to obtain a class of scalar-tensor theories, belonging to the family of mimetic gravity, which all reproduce the loop quantum cosmology effective dynamics for flat, closed and open isotropic and homogeneous space-times.

Ghost-free F(R) gravity with Lagrange multiplier constraint

We propose two new versions of ghost-free generalized F(R) gravity with Lagrange multiplier constraint. The first version of such theory for a particular degenerate choice of the Lagrange multiplier, corresponds to mimetic F(R) gravity. The second version of such theory is just the Jordan frame description of mimetic gravity with potential. As we demonstrate, it is possible to realize several cosmological scenarios in such theory. In particular, de Sitter solutions may also be found.

A Non-Polynomial Gravity Formulation for Loop Quantum Cosmology Bounce

Recently the so-called mimetic gravity approach has been used to obtain corrections to the Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive this modified Friedmann equation via the so-called non-polynomial gravity approach, which consists of adding geometric non-polynomial higher derivative terms to Hilbert–Einstein action, which are nonetheless polynomials and lead to a second-order differential equation in Friedmann–Lemaître–Robertson–Walker space-times. Our explicit action turns out to be a realization of the Helling proposal of effective action with an infinite number of terms. The model is also investigated in the presence of a non-vanishing cosmological constant, and a new exact bounce solution is found and studied.

Recovering a MOND-like acceleration law in mimetic gravity

We reconsider the recently proposed mimetic gravity, focusing in particular on whether the theory is able to reproduce the inferred flat rotation curves of galaxies. We extend the theory by adding a non-minimal coupling between matter and mimetic field. Such coupling leads to the appearance of an extra force which renders the motion of test particles non-geodesic. By studying the weak field limit of the resulting equations of motion, we demonstrate that in the Newtonian limit the acceleration law induced by the non-minimal coupling reduces to a modified Newtonian dynamics (MOND)-like one. In this way, it is possible to reproduce the successes of MOND, namely the explanation for the flat galactic rotation curves and the Tully–Fisher relation, within the framework of mimetic gravity, without the need for particle dark matter. The scale-dependence of the recovered acceleration scale opens up the possibility of addressing the missing mass problem not only on galactic but also on cluster scales: we defer a full study of this issue, together with a complete analysis of fits to spiral galaxy rotation curves, to an upcoming companion paper.

Braneworld mimetic cosmology

We extend the idea of mimetic gravity to a Randall–Sundrum II braneworld model. As for the 4-dimensional mimetic gravity, we isolate the conformal degree of freedom of 5-dimensional gravity in a covariant manner. We assume the bulk metric to be made up of a non-dynamical scalar field Φ and an auxiliary metric G˜AB so that GAB=G˜CDΦ,CΦ,DG˜AB where A,B,... are the bulk spacetime indices. Then we show that the induced conformal degree of freedom on the brane as an induced scalar field, plays the role of a mimetic field on the brane. In fact, we suppose that the scalar degree of freedom which mimics the dark sectors on the brane has its origin on the bulk scalar field, Φ. By adopting some suitable mimetic potentials on the brane, we show that this brane mimetic field explains the late time cosmic expansion in the favor of observational data: the equation of state parameter of this field crosses the cosmological constant line in near past from quintessence to phantom phase in a redshift well in the range of observation. We show also that this induced mimetic scalar field has the capability to explain initial time cosmological inflation. We study parameter space of the models numerically in order to constraint the models with Planck2015 data set.

Mimetic Gravity: A Review of Recent Developments and Applications to Cosmology and Astrophysics

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 a 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 mimeticf(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, progress, open questions, and outlooks on future research directions.

De Sitter and power-law solutions in some models of modified gravity

Inspired by some recent works of Lovelock Brans–Dicke (BD) gravity and mimetic gravity, cosmology solutions in extensions of these two modified gravities are investigated. A nonlocal term is added to the Lovelock BD action and Gauss–Bonnet (GB) terms to the mimetic action, correspondingly. de Sitter and power scale factor solutions are then obtained in both theories. They can provide natural new approaches to a more accurate description of the unverse evolution.

Covariant Hořava-like and mimetic Horndeski gravity: cosmological solutions and perturbations

We consider a variant of the Nojiri–Odintsov covariant Hořava-like gravitational model, where diffeomorphism invariance is broken dynamically via a non-standard coupling to a perfect fluid. The theory allows one to address some of the potential instability problems present in Hořava–Lifshitz gravity due to explicit diffeomorphism invariance breaking. The fluid is instead constructed from a scalar field constrained by a Lagrange multiplier. In fact, the Lagrange multiplier construction allows for an extension of the Hořava-like model to include the scalar field of mimetic gravity, an extension which we thoroughly explore. By adding a potential for the scalar field, we show how one can reproduce a number of interesting cosmological scenarios. We then turn to the study of perturbations around a flat FLRW background, showing that the fluid in question behaves as an irrotational fluid, with zero sound speed. To address this problem, we consider a modified version of the theory, adding higher derivative terms in a way which brings us beyond the Horndeski framework. We compute the sound speed in this modified higher order mimetic Hořava-like model and show that it is non-zero, which means that perturbations therein can be sensibly defined. Caveats to our analysis, as well as comparisons to projectable Hořava–Lifshitz gravity, are also discussed. In conclusion, we present a theory of gravity which preserves diffeomorphism invariance at the level of the action but breaks it dynamically in the UV, reduces to General Relativity (GR) in the IR, allows the realization of a number of interesting cosmological scenarios, is well defined when considering perturbations around a flat FLRW background, and features cosmological dark matter emerging as an integration constant.

From neutron stars to quark stars in mimetic gravity

Realistic models of neutron and quark stars in the framework of mimetic gravity with Lagrange multiplier constraint are presented. We discuss the effect of mimetic scalar aiming to describe dark matter on mass-radius relation and the moment of inertia for slowly rotating relativistic stars. The mass-radius relation and moment of inertia depend on the value of mimetic scalar in the center of star. This fact leads to the ambiguity in the mass-radius relation for a given equation of state. {Such ambiguity allows to explain some observational facts better than in standard General Relativity}. The case of two mimetic potentials namely $V(\phi)\sim A\phi^{-2}$ and $V(\phi)\sim Ae^{B\phi^{2}}$ is considered in detail. The relative deviation of maximal moment of inertia is approximately twice larger than the relative deviation of maximal stellar mass. We also briefly discuss the mimetic $f(R)$ gravity. In the case of $f(R)=R+aR^2$ mimetic gravity it is expected that increase of maximal mass and maximal moment of inertia due to mimetic scalar becomes much stronger with bigger parameter $a$. The contribution of scalar field in mimetic gravity can lead to possible existence of extreme neutron stars with large masses.

Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations

We consider all degenerate scalar-tensor theories that depend quadratically on second order derivatives of a scalar field, which we have identified in a previous work. These theories, whose degeneracy in general ensures the absence of Ostrogradski instability, include the quartic Horndenski Lagrangian as well as its quartic extension beyond Horndeski, but also other families of Lagrangians. We study how all these theories transform under general conformal-disformal transformations and find that they can be separated into three main classes that are stable under these transformations. This leads to a complete classification modulo conformal-disformal transformations. Finally, we show that these higher order theories include mimetic gravity and some particular khronometric theories. They also contain theories that do not correspond, to our knowledge, to already studied theories, even up to field redefinitions.

Cylindrical solutions in mimetic gravity

This paper is devoted to investigate cylindrical solutions in mimetic gravity. The explicit forms of the metric of this theory, namely mimetic-Kasner (say) have been obtained. In this study we have noticed that the Kasner's family of exact solutions needs to be reconsidered under this type of modified gravity. A no-go theorem is proposed for the exact solutions in the presence of a cosmological constant.

Non-local F ( R ) $F(R)$ -mimetic gravity

In this paper, we study non-local $F(R)$-mimetic gravity. We implement mimetic gravity in the framework of non-local $F(R)$-theories of gravity. Given some specific class of models and using a potential on the mimetic field, we investigate some scenarios related to the early-time universe, namely the inflation and the cosmological bounce, compatibly with Einstein's gravity with cold dark matter at the late-time.

Unimodular-mimetic cosmology

We combine the unimodular gravity and mimetic gravity theories into a unified theoretical framework, which is proposed to provide a suggestive proposal for a framework that may assist in the discussion and search for a solution to the cosmological constant problem and the dark matter issue. After providing the formulation of the unimodular mimetic gravity and investigating all the new features that the vacuum unimodular gravity implies, by using the underlying reconstruction method, we realize some well known cosmological evolutions, with some of these being exotic for the ordinary Einstein–Hilbert gravity. Specifically we provide the vacuum unimodular mimetic gravity description of the de Sitter cosmology and of the perfect fluid with constant equation of state cosmology. As we demonstrate, these cosmologies can be realized by vacuum mimetic unimodular gravity, without the existence of any matter fluid source. Moreover, we investigate how cosmologically viable cosmologies, which are compatible with the recent observational data, can be realized by the vacuum unimodular mimetic gravity. Since in some cases, a graceful exit from inflation problem might exist, we provide a qualitative description of the mechanism that can potentially generate the graceful exit from inflation in these theories, by searching for the unstable de Sitter solutions in the context of unimodular mimetic theories of gravity.

Static spherically symmetric solutions in mimetic gravity: rotation curves and wormholes

In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend previous works by considering, in addition, a potential for the mimetic field. An appropriate choice of such a potential allows for the reconstruction of a number of interesting cosmological and astrophysical scenarios. We explicitly show how to reconstruct such a potential for a general static spherically symmetric space-time. A number of applications and scenarios are then explored, among which are traversable wormholes. Finally, we analytically reconstruct potentials, which leads to solutions to the equations of motion featuring polynomial corrections to the Schwarzschild space-time. Accurate choices for such corrections could provide an explanation for the inferred flat rotation curves of spiral galaxies within the mimetic gravity framework, without the need for particle dark matter.

Cosmological perturbations in mimetic Horndeski gravity

We study linear scalar perturbations around a flat FLRW background in mimetic Horndeski gravity. In the absence of matter, we show that the Newtonian potential satisfies a second-order differential equation with no spatial derivatives. This implies that the sound speed for scalar perturbations is exactly zero on this background. We also show that in mimetic G3 theories the sound speed is equally zero. We obtain the equation of motion for the comoving curvature perturbation (first order differential equation) and solve it to find that the comoving curvature perturbation is constant on all scales in mimetic Horndeski gravity. We find solutions for the Newtonian potential evolution equation in two simple models. Finally we show that the sound speed is zero on all backgrounds and therefore the system does not have any wave-like scalar degrees of freedom.

Mimetic Attractors

In this paper, we investigate the mathematical modeling for the cosmological attractors propagated in mimetic gravity upon which an interacting dark energy-dark matter is supposed to be existed. The average value of the interaction of these percentages, namely $\Gamma_i$ say, may be used to investigate generally the modeling of an attractor; the actual value could only be determined by data in any particular case. We have seen, for example, that it was led to investigate the subject of initially invariant submanifolds.