Starting from a local action for mimetic gravity that includes higher derivatives of a scalar field $ϕ$, we derive a gauge-fixed canonical action of the theory in the ADM canonical formalism in the time gauge $ϕ=t$. This reduced action reveals (i) a non-vanishing conserved physical Hamiltonian that is a sum of two terms, the expression for the Hamiltonian constraint of general relativity and a function of the expansion scalar, and (ii) a reduced symplectic structure that geometrically provides the Dirac brackets. As applications of our general analysis, we compute the physical Hamiltonians and canonical equations for perturbations around Minkowski spacetime, homogeneous cosmologies, and spherically symmetric spacetimes.
Mimetic gravity is analysed in the framework of some extensions of General Relativity, where a function of the Gauss-Bonnet invariant in four dimensions is considered. By assuming the so-called mimetic condition, the conformal degree of freedom is isolated and a pressureless fluid naturally arises. Then, the complete set of field equations for mimetic Gauss-Bonnet gravity is established and some inflationary models are analysed, for which the corresponding gravitational action is reconstructed. The spectral index and tensor-to-scalar ratio are obtained and compared with observational bounds fr…
We show that the mimetic theory with the constraint $g^{ρσ}\partial_ρϕ\partial_σϕ=1$ cannot realize the black hole geometry with the horizon(s). To overcome such issue, we may change the mimetic constraint a little bit by $ω(ϕ) g^{ρσ}\partial_ρϕ\partial_σϕ=-1,$ where $ω(ϕ)$ is a function of the scalar field $ϕ$. As an example, we consider $(2+1)$-dimensional mimetic gravity with the mimetic potential and construct black hole (BH) solutions by using this modified constraint. We study three different classes: In the first class, we assume the Lagrange multiplier and mimetic potential are vanishi…
In this paper, a modified version of the hydrostatic equilibrium equation based on the mimetic gravity in the presence of perfect fluid is revisited. By using the different known equation of states, the structural properties of neutron stars are investigated in general relativity and mimetic gravity. Comparing the obtained results, we show that, unlike general relativity, we can find the appropriate equation of states that support observational data in the context of mimetic gravity. We also find that the results of relativistic mean-field-based models of the equation of states are in better a…
One of the most important achievements in general relativity has been discovery of the $(2+1)$-dimensional black hole solutions of Einstein gravity in anti-de Sitter (AdS) spacetime [Phys. Rev. Lett. {\bf69}, 1849 (1992)]. In this paper, we construct, for the first time, the $(2+1)$-dimensional solutions of mimetic theory of gravity. These solutions may provide a powerful background to investigate the physical properties of mimetic gravity and examine its viability in lower spacetime dimensions. In particular, some physical properties of stationary black hole solutions of this theory in the pr…
We show that the scalar field of mimetic gravity could be used to construct diffeomorphism invariant models that reduce to Horava gravity in the synchronous gauge. The gradient of the mimetic field provides a timelike unit vector field that allows to define a projection operator of four-dimensional tensors to three-dimensional spatial tensors. Conversely, it also enables us to write quantities invariant under space diffeomorphisms in fully covariant form without the need to introduce new propagating degrees of freedom.
The idea of "asymptotically free" gravity is implemented using a constrained mimetic scalar field. The effective gravitational constant is assumed to vanish at some limiting curvature. As a result singularities in contracting spatially flat Friedmann and Kasner universes are avoided. The solutions in both cases approach de Sitter metric with a limiting curvature.We show that quantum metric fluctuations vanish when this limiting curvature is approached.
The energy conditions of mimetic-$f(R)$ gravity theory is analyzed. We will obtain the parameter space of the theory in some special forms of $f(R)$ in which the self-acceleration is allowed. In this sense, the parameter space is obtained in a way that it violates the strong energy condition while satisfying the weak, null and dominant energy conditions. We will also consider the condition that the Dolgov-Kawasaki instability is avoided. This condition will be further imposed in the parameter space of the theory. We will show that the parameter space of the mimetic-$f(R)$ gravity is larger tha…
Recently, it was shown that modified mimetic gravity, with a $f(\squareϕ)$ term, results in a singularity-free model of gravity, for both cosmological and black hole spacetimes [1, 2]. In this work, we analyze this model further and show that, since the function $f$ was tuned to vanish rapidly for small values of the argument, the non-singular bounce relies heavily on a subtle branch changing mechanism for the multi-valued function $f$. Furthermore, this mechanism has interesting implications for the proposed link between this model and loop quantum cosmology.
An interesting proposal has recently been made to extend massive gravity models beyond dRGT by a disformal transformation of the metric. In this Letter we want to note that it can be viewed as a mimetic extension of dRGT gravity which enormously simplifies the Hamiltonian analysis. In particular, pure gravity sector is equivalent to the usual dRGT gravity coupled to a constrained scalar field. And we also give some comments about possible matter couplings.
We present a detailed investigation of the dynamical behavior of mimetic gravity with a general potential for the mimetic scalar field. Performing a phase-space and stability analysis, we show that the scenario at hand can successfully describe the thermal history of the universe, namely the successive sequence of radiation, matter, and dark-energy eras. Additionally, at late times the universe can either approach a de Sitter solution, or a scaling accelerated attractor where the dark-matter and dark-energy density parameters are of the same order, thus offering an alleviation of the cosmic co…
In this paper, we employ mimetic $f(R,T)$ gravity coupled with Lagrange multiplier and mimetic potential to yield viable inflationary cosmological solutions consistent with latest Planck and BICEP2/Keck Array data. We present here three viable inflationary solutions of the Hubble parameter ($H$) represented by $H(N)=\left(A \exp βN+B α^N\right)^{γ}$, $H(N)=\left(A α^N+B \log N\right)^{γ}$, and $H(N)=\left(A e^{βN}+B \log N\right)^{γ}$, where $A$, $β$, $B$, $α$, $γ$ are free parameters, and $N$ represents the number of e-foldings. We carry out the analysis with the simplest minimal $f(R,T)$ fun…
Modified gravity models have been constantly proposed with the purpose of evading some standard gravity shortcomings. Recently proposed by A.H. Chamseddine and V. Mukhanov, the Mimetic Gravity arises as an optimistic alternative. Our purpose in this work is to derive Tolman-Oppenheimer-Volkoff equations and solutions for such a gravity theory. We solve them numerically for quark star and neutron star cases. The results are carefully discussed.
The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in thi…
Mimetic gravity analysis has been studied as a theory in various types of general relativity extensions, such as mimetic f(R) gravity, mimetic f(R, T) gravity, mimetic f(R, G) gravity, etc., in the literature. This paper presents a set of equations arising from mimetic conditions and studies cosmic inflation with a combination of mimetic f(G) gravity and swampland dS conjectures. We analyze and evaluate these results. Therefore, we first thoroughly introduce the mimetic f(G) gravity and calculate some cosmological parameters such as the scalar spectral index, the tensor-to-scalar ratio, and th…
We illustrate a general reconstruction procedure for mimetic gravity. Focusing on a bouncing cosmological background, we derive general properties that must be satisfied by the function $f(\Boxϕ)$ implementing the limiting curvature hypothesis. We show how relevant physical information can be extracted from power law expansions of $f$ in different regimes, corresponding e.g. to the very early universe or to late times. Our results are then applied to two specific models reproducing the cosmological background dynamics obtained in group field theory and in loop quantum cosmology, and we discuss…
Asymptotically free mimetic gravity has been introduced as a proposal for a classical limiting curvature theory with the purpose of singularity resolution. It was found that in a spatially flat universe an initial stage of exponential expansion with graceful exit is a generic consequence, regardless of the matter content. In this work I will analyze linear stability of cosmological perturbations in such a model, considering only the degrees of freedom of pure mimetic gravity. I show that the addition of Hořava-gravity-like higher order spatial curvature terms can lift the gradient instability …
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…
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.
In this brief note we investigate the conditions under which a Schwarzschild de Sitter black hole spacetime is a solution of the mimetic $F(R)$ gravity with Lagrange multiplier and potential. As we demonstrate, the resulting mimetic $F(R)$ gravity is a slight modification of the ordinary $F(R)$ gravity case, however the resulting perturbation equations are not in all cases identical to the ordinary $F(R)$ gravity case. In the latter case, the perturbation equations are identical to the ones corresponding to the Reissner-Nordström anti-de Sitter black hole.
We study cosmological perturbations in mimetic gravity in the presence of classified higher derivative terms which can make the mimetic perturbations stable. We show that the quadratic higher derivative terms which are independent of curvature and the cubic higher derivative terms which come from curvature corrections are sufficient to remove instabilities in mimetic perturbations. The advantage of working with the classified higher derivative terms is that we can control both the background and the perturbation equations allowing us to construct the higher derivative extension of mimetic dark…
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 solution search of the cosmological constant problem and of 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-Hilbe…
In this paper, we study the structure and gravitational resonances of thick branes generated by a mimetic scalar field in $f(R)$ gravity. We obtain several typical thick brane solutions for $f(R)=R+αR^2$. To study their stability, we analyze the tensor perturbation of the metric. It is shown that any thick brane model with $df/dR>0$ is stable and the graviton zero mode can be localized on the brane for each solution, which indicates that the four-dimensional Newtonian gravity can be restored. The effect of the parameter $α$ on the gravitational resonances is studied. As a brane splits into mul…
In this paper, we study a theory of gravity called mimetic $f(R, T)$ in the presence of swampland dS conjecture. For this purpose, we introduce several inflation solutions of the Hubble parameter H(N) from $f(R, T)= R+δT$ gravity model, in which R is Ricci scalar, and T denotes the trace of the energy-momentum tensor. Also, $δ$ and $N$ are the free parameter and a number of e-fold, respectively. Then we calculate quantities such as potential, Lagrange multiplier, slow-roll, and some cosmological parameters such as $n_{s}$ and $r$. Then we challenge the mentioned inflationary model from the swa…
We show that theories of mimetic gravity can be viewed as degenerate higher-order scalar-tensor (DHOST) theories that admit an extra local (gauge) symmetry in addition to the usual diffeomorphism invariance. We reformulate and classify mimetic theories in this perspective. Using the effective theory of dark energy, recently extended to include DHOST theories, we then investigate the linear perturbations about a homogeneous and isotropic background for all mimetic theories. We also include matter, in the form of a $k$-essence scalar field, and we derive the quadratic action for linear perturbat…
We perform the Hamiltonian analysis of several mimetic gravity models and compare our results with those obtained previously by different authors. We verify that for healthy mimetic scalar-tensor theories the condition for the corresponding part of the Hamiltonian to be bounded from below is the positive value of the mimetic field energy density $λ$. We show that for mimetic dark matter possessing a shift symmetry the mimetic energy density remains positive in time, provided appropriate boundary conditions are imposed on its initial value, while in models without shift symmetry the positive en…
Nonsingular bouncing cosmologies are realized in limiting curvature mimetic gravity by means of a multi-valued potential $f(\Boxϕ)$ depending on the d'Alembertian of a scalar field $ϕ$. We determine the functional form of such a potential so as to exactly reproduce the cosmological background dynamics obtained in the group field theory approach to quantum gravity. The original proposal made by Chamseddine and Mukhanov [JCAP 1703, no. 03, 009 (2017)], which was shown to lead to a background dynamics reproducing the effective dynamics of loop quantum cosmology, is here recovered as a particular …
We present the Hamiltonian formulation of the Ghost Free Mimetic Massive Gravity theory. The linearized theory is studied and the Hamiltonian equations of motion are analyzed. Poisson brackets are computed and closure is proved. To prove that this theory is ghost-free, the number of degrees of freedom is analyzed showing that we have only five degrees of freedom.
The recently proposed theory of "Asymptotically Free Mimetic Gravity" is extended to the general non-homogeneous, spatially non-flat case. We present a modified theory of gravity which is free of higher derivatives of the metric. In this theory asymptotic freedom of gravity implies the existence of a minimal black hole with vanishing Hawking temperature. Introducing a spatial curvature dependent potential, we moreover obtain non-singular, bouncing modifications of spatially non-flat Friedmann and Bianchi universes.
Two types of mimetic gravity models with higher derivatives of the mimetic field are analyzed in the Hamiltonian formalism. For the first type of mimetic gravity, the Ricci scalar only couples to the mimetic field and we demonstrate the number of degrees of freedom (DOFs) is three. Then in both Einstein frame and Jordan frame, we perform the Hamiltonian analysis for the extended mimetic gravity with higher derivatives directly coupled to the Ricci scalar. We show that different from previous studies working at the cosmological perturbation level, where only three propagating DOFs show up, this…
In this paper, thick branes generated by mimetic scalar field are investigated. Three typical thick brane models are constructed and the linear tensor and scalar perturbations are analyzed. These branes have different inner structures, some of which are absent in general relativity. For each brane model, the solution is stable under both tensor and scalar perturbations. The tensor zero modes are localized on the branes, while the scalar perturbations do not propagate and they are not localized on the brane. As the branes split into multi sub-branes for specific parameters, the potentials of th…
Reissner-Nordström Black Holes in Mimetic $F(R)$ Gravity
本文研究了在什么条件下Reissner-Nordström-anti de Sitter黑洞可以是具有Lagrange乘子和模拟标量势的真空模拟$F(R)$引力的解.正如我们所证明的，在模拟$F(R)$重力情况下得到的图像与普通$F(R)$重力情况相比是不同的，这两种描述导致了一组不同的约束，这些约束需要保持正确。我们还研究了在模拟$F(R)$引力情形下，对于Reissner-Nordström-anti de Sitter黑洞度规，在一阶扰动变量下的度规扰动.有趣的是，得到的方程与普通$F(R)$引力Reissner-Nordström-anti de Sitter黑洞的方程是相同的，至少在一阶上是相同的。我们把这个特征归因于Reissner-Nordström-anti de Sitter度量的特殊形式，并且我们推测在哪些情况下模仿和非模仿的情况之间可能存在差异。由于这两种情况下的扰动方程是相同的，所以在模拟$F(R)$引力的情况下也可能存在黑洞不稳定性，这可以解释为黑洞的反蒸发。
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 …
We study mimetic $F(R)$ gravity with potential and Lagrange multiplier constraint. In the context of these theories, we introduce a reconstruction technique which enables us to realize arbitrary cosmologies, given the Hubble rate and an arbitrarily chosen $F(R)$ gravity. We exemplify our method by realizing cosmologies that are in concordance with current observations (Planck data) and also well known bouncing cosmologies. The attribute of our method is that the $F(R)$ gravity can be arbitrarily chosen, so we can have the appealing features of the mimetic approach combined with the known featu…
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 …
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.
We revisit the two-field mimetic gravity model with shift symmetries recently proposed in the literature, especially the problems of degrees of freedom and stabilities. We first study the model at the linear cosmological perturbation level by quadratic Lagrangian and Hamiltonian formulations. We show that there are actually two (instead of one) scalar degrees of freedom in this model in addition to two tensor modes. We then push on the study to the full non-linear level in terms of the Hamiltonian analysis, and confirm our result from the linear perturbation theory. We also consider the case w…
We formulate mimetic theory in f(T) teleparallel gravity where T is torsion scalar. It is shown that the construction of the mimetic theory in the teleparallel gravity requires the vierbeins to be left unchanged and the confomal transformation performed on the Minkowski metric of the tangent space. It is further argued that the conformal degree of freedom in this teleparallel mimetic theory becomes dynamical and mimics the behavior of cold dark matter. We also show that it is possible to employ the Lagrange multipliers method to formulate the mimetic theory in an f(T) theory without any auxili…
We consider the recently introduced mimetic gravity, which is a Weyl-symmetric extension of the General Relativity and which can play a role of an imperfect fluid-like Dark Matter with a small sound speed. In this paper we discuss in details how this higher- derivative scalar-tensor theory goes beyond the construction by Horndeski, keeping only one scalar degree of freedom on top of two standard graviton polarizations. In particular, we consider representations of the theory in different sets of Weyl-invariant variables and connect this framework to the singular Brans-Dicke theory. Further, we…
We make a perturbative analysis of spatially covariant gravity only respecting spatial symmetries, of which the Lagrangian includes the dynamic lapse function and the coupling term of spatial curvature and extrinsic curvature. We show that the theory propagates 2 scalar degrees of freedom, as long as the kinetic terms are degenerate, it propagates a single scalar mode at the linear order. Then we calculate the scalar and tensor power spectra. Finally, we study cosmological perturbations in mimetic gravity in the presence of spatially covariant gravity. The original spatially covariant theory p…
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 techniq…
There is undetermined potential function $V(ϕ)$ in the action of mimetic gravity which should be resolved through physical means. In general relativity(GR), the static spherically symmetric(SSS) solution to the Einstein equation is a benchmark and its deformation also plays a crucial role in mimetic gravity. The equation of motion is provided with high nonlinearity, but we can reduce primal nonlinearity to a frequent Riccati form in the SSS case of mimetic gravity. In other words, we obtain an expression of solution to the functional differential equation of motion with any potential function.…
We present a theory of ghost-free massive gravity where the mass of the graviton is generated through the Brout-Englert-Higgs (BEH) mechanism and one of the four scalar fields used is that of mimetic gravity. The mass term is not of the Fierz-Pauli type and the constraint eliminates the Boulware-Deser ghost which is absent to all orders. We perform a detailed analysis using the methods of cosmological perturbation theory and consider quantum fluctuations of the degrees of freedom of massive graviton and mimetic matter. It is shown that for three of the degrees of freedom of the graviton of mas…
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 $G^3$ 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 sc…
We show that very general scalar-tensor theories of gravity (including, e.g., Horndeski models) are generically invariant under disformal transformations. However there is a special subset, when the transformation is not invertible, that yields new equations of motion which are a generalization of the so-called "mimetic" dark matter theory recently introduced by Chamsedinne and Mukhanov. These conclusions hold true irrespective of whether the scalar field in the action of the assumed scalar-tensor theory of gravity is the same or different than the scalar field involved in the transformation. …
We construct some new classes of topological black hole solutions in the context of mimetic gravity. We study the uncharged and charged black holes, separately. In the absence of a potential for the mimetic field, our solutions can address the flat rotation curves of spiral galaxies and alleviate the dark matter problem without invoking any kind of particle dark matter. Thus, mimetic gravity can provide a theoretical background for understanding flat galactic rotation curves through modification of the Schwarzschild spacetime. We also investigate the casual structure and physical properties of…
In this paper, we formulate the Mimetic theory of gravity in first-order formalism for differential forms, i.e., the mimetic version of Einstein-Cartan-Kibble-Sciama (ECKS) gravity. We consider different possibilities on how torsion is affected by conformal transformations and discuss how this translates into the interpolation between two different conformal transformations of the spin connection, parameterized with a zero-form parameter $λ$. We prove that regardless of the type of transformation one chooses, in this setting torsion remains as a non-propagating field. We also discuss the conse…
