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 scalartensor theory of gravity is the same or different than the scalar field involved in the transformation. The new equations of motion for our general mimetic theory can also be derived from an action containing an additional Lagrange multiplier field. The general mimetic scalar-tensor theory has the same number of derivatives in the equations of motion as the original scalar-tensor theory. As an application we show that the simplest mimetic scalar-tensor model is able to mimic the cosmological background of a flat FLRW model with a barotropic perfect fluid with any constant equation of state.

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 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. I. INTRODUCTIONRecently, mimetic gravity (called mimetic dark matter) [1], a modification of General Relativity (GR) leading to a scalar-tensor type theory, has attracted considerable attention in the cosmology community. The main reason is that the theory possesses some very attractive features. For example, it was shown that the original theory (called mimetic dark matter) [1] contains an extra scalar mode (of gravitational origin) which can mimic the behaviour of cold dark matter even in the absence of any form of matter. Soon after it was realised that with a small generalisation of the original theory the scalar mode could be used to mimic the behaviour of almost any type of matter and in this way one can have almost any desired expansion history of the universe [2].The mimetic scalar field was introduced in GR by doing a non-invertible conformal transformation in the Einstein-Hilbert action of the type g µν = −wℓ µν , where the physical metric is g µν , the auxiliary metric is ℓ µν , w is defined in terms of a scalar field ϕ as w = ℓ µν ∂ µ ϕ∂ ν ϕ [1-3]. Soon after it was realized [4] that the type of metric transformation that leads to mimetic gravity can be further generalised from the previous transformation to include also a disformal term [5] as g µν = A(ϕ, w)ℓ µν + B(ϕ, w)∂ µ ϕ∂ ν ϕ, where A and B are free functions of two variables and they must obey some conditions (see [6] and also [7] where the conditions for disformally coupled theories to have a so-called Jordan frame were discussed) so that the Lorentzian signature is preserved, the transformation is causal and regular, g µν exists and A and B are related as B = −A/w + b, where b is an arbitrary function of ϕ only and it should not cross zero. If A and B are arbitrary functions and do not obey the previous relation then the equations of motion that one obtains are just Einstein's equations [4].The stability of mimetic gravity against negative energy states, i.e. ghosts, was studied in [3], where it was shown that ghosts are absent if the energy density of the effective fluid is positive. Ref.[8] (see also [3] and [2]) showed that the original mimetic gravity can be derived from an action with a co...

We consider models of gravitation that are based on unimodular general coordinate transformations (GCT). These transformations include only those which do not change the determinant of the metric. We treat the determinant as a separate field which transforms as a scalar under unimodular GCT. We consider a class of such theories. In general, these theories do not transform covariantly under the full GCT. We characterize the violation of general coordinate invariance by introducing a new parameter. We show that the theory is consistent with observations for a wide range of this parameter. This parameter may serve as a test for possible violations of general coordinate invariance. We also consider the cosmic evolution within the framework of these models. We show that in general we do not obtain consistent cosmological solutions if we assume the standard cosmological constant or the standard form of non-relativistic matter. We propose a suitable generalization which is consistent with cosmology. We fit the resulting model to the high redshift supernova data. We find that we can obtain a good fit to this data even if include only a single component, either cosmological constant or non-relativistic matter.

We consider a model of gravity and matter fields which is invariant only under unimodular general coordinate transformations (GCT). The determinant of the metric is treated as a separate field which transforms as a scalar under unimodular GCT. Furthermore we also demand that the theory is invariant under a new global symmetry which we call generalized conformal invariance. We study the cosmological implications of the resulting theory. We show that this theory gives a fit to the high-z supernova data which is identical to the standard Big Bang model. Hence we require some other cosmological observations to test the validity of this model. We also consider some models which do not obey the generalized conformal invariance. In these models we can fit the supernova data without introducing the standard cosmological constant term. Furthermore these models introduce only one dark component and hence solve the coincidence problem of dark matter and dark energy. *

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 scalartensor 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 energy density can be maintained by simply replacing λ → e λ . The same result also applies to mimetic f (R) gravity, which is healthy if the usual stability conditions of the standard f (R) gravity are assumed and λ > 0. In contrast, if we add mimetic matter to an unhealthy seed action, the resulting mimetic gravity theory remains, in general, unstable. As an example, we consider a scalar-tensor theory with the higher-derivative term ( ϕ) 2 , which contains an Ostrogradski ghost. We also revisit results regarding stability issues of linear perturbations around the FLRW background of the mimetic dark matter in the presence of ordinary scalar matter.We find that the presence of conventional matter does not revive dynamical ghost modes (at least in the UV limit). The modes, whose Hamiltonian is not positive definite, are non-propagating (have zero sound speed) and are associated with the mimetic matter itself. They are already present in the case in which the ordinary scalar fluid is absent, causing a growth of dust overdensity.

In this paper, we propose to use the mimetic Horndeski model as a model for the dark universe. Both cold dark matter (CDM) and dark energy (DE) phenomena are described by a single component, the mimetic field. In linear theory, we show that this component effectively behaves like a perfect fluid with zero sound speed and clusters on all scales. For the simpler mimetic cubic Horndeski model, if the background expansion history is chosen to be identical to a perfect fluid DE (PFDE) then the mimetic model predicts the same power spectrum of the Newtonian potential as the PFDE model with zero sound speed. In particular, if the background is chosen to be the same as that of LCDM, then also in this case the power spectrum of the Newtonian potential in the mimetic model becomes indistinguishable from the power spectrum in LCDM on linear scales. A different conclusion may be found in the case of non-adiabatic perturbations. We also discuss the distinguishability, using power spectrum measurements from LCDM N-body simulations as a proxy for future observations, between these mimetic models and other popular models of DE. For instance, we find that if the background has an equation of state equal to -0.95 then we will be able to distinguish the mimetic model from the PFDE model with unity sound speed. On the other hand, it will be hard to do this distinction with respect to the LCDM

We study cosmic structures in the quadratic Degenerate Higher Order Scalar Tensor (qDHOST) model, which has been proposed as the most general scalar-tensor theory (up to quadratic dependence on the covariant derivatives of the scalar field), which is not plagued by the presence of ghost instabilities. We then study a static, spherically symmetric object embedded in de Sitter space-time for the qDHOST model. This model exhibits breaking of the Vainshtein mechanism inside the cosmic structure and Schwarzschild-de Sitter space-time outside, where General Relativity (GR) can be recovered within the Vainshtein radius. We then look for the conditions on the parameters on the considered qDHOST scenario which ensure the validity of the Vainshtein screening mechanism inside the object and the fulfilment of the recent GW170817/GRB170817A constraint on the speed of propagation of gravitational waves. We find that these two constraints rule out the same set of parameters, corresponding to the Lagrangians that are quadratic in second-order derivatives of the scalar field, for the shift symmetric qDHOST. The authors of Ref. [8,9] claimed that their extension of the Horndeski theory to the so-called Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theory, leads to a new class of models without the Ostrogradsky ghost instability. A later proposal showed that higher-order derivatives in the Lagrangian may not necessarily introduce Ostrogradsky ghosts, provided certain degeneracy conditions are met [10]. Indeed, "degenerate" Lagrangians with non-invertible kinetic matrix will ensure that the number of degrees of freedom is preserved, thus making the theory free from the Ostrogradsky ghost; this new class was named "degenerate higher order scalartensor" (DHOST) theory [11][12][13]. A particular extension of Horndeski was proposed earlier in Ref. [14], which appeared as a result of a disformal transformation on the Einstein-Hilbert action, later found a specific subclass of HOST theory. DHOST theory is categorised into several classes [13]. Class I DHOST theories are the only one which are healthy from the gradient instability, i.e., the square of the speed of the tensor modes (gravitational-wave speed) and that of the scalar mode (sound speed) do not have opposite sign, c 2 s ∝ −c T 2 [15]. Gravity is well tested and established on small scales (e.g. laboratory, solar system, ...). Therefore, there must be a screening mechanism able to suppress the fifth-force mediated by the new scalar degree of freedom, without destroying the modifications on large scales, while recovering GR on a small scale. In general, the so-called Vainshtein screening is widely used for higher-order scalar-tensor theories [16]. In the Vainshtein screening, the non-linear selfinteractions of the scalar field suppress the propagation of the fifth-force near the matter source [17,18]. The Vainshtein mechanism in the Horndeski framework has been studied intensively

No abstract