We study the stability of a recently proposed model of scalar-field matter called mimetic dark matter or imperfect dark matter. It has been known that mimetic matter with higher derivative terms suffers from gradient instabilities in scalar perturbations. To seek for an instability-free extension of imperfect dark matter, we develop an effective theory of cosmological perturbations subject to the constraint on the scalar field's kinetic term. This is done by using the unifying framework of general scalar-tensor theories based on the ADM formalism. We demonstrate that it is indeed possible to construct a model of imperfect dark matter which is free from ghost and gradient instabilities. As a side remark, we also show that mimetic F (R) theory is plagued with the Ostrogradsky instability.

The galilean genesis scenario is an alternative to inflation in which the universe starts expanding from Minkowski in the asymptotic past by violating the null energy condition stably. Several concrete models of galilean genesis have been constructed so far within the context of galileon-type scalar-field theories. We give a generic, unified description of the galilean genesis scenario in terms of the Horndeski theory, i.e., the most general scalar-tensor theory with second-order field equations. In doing so we generalize the previous models to have a new parameter (denoted by α) which results in controlling the evolution of the Hubble rate. The background dynamics is investigated to show that the generalized galilean genesis solution is an attractor, similarly to the original model. We also study the nature of primordial perturbations in the generalized galilean genesis scenario. In all the models described by our generalized genesis Lagrangian, amplification of tensor perturbations does not occur as opposed to what happens in quasi-de Sitter inflation. We show that the spectral index of curvature perturbations is determined solely from the parameter α and does not depend on the other details of the model. In contrast to the original model, a nearly scale-invariant spectrum of curvature perturbations is obtained for a specific choice of α. PACS numbers: 98.80.Cq, 04.50.Kd 1 The NEC can be violated stability at least within linear perturbation analysis. However, at nonlinear order, it is not clear whether there are no instabilities [10].

We propose a novel branch of the Galilean Genesis scenario as an alternative to inflation, in which the universe starts expanding from Minkowski in the asymptotic past with a gross violation of the null energy condition (NEC). This variant, described by several functions and parameters within the Horndeski scalar-tensor theory, shares the same background dynamics with the existing Genesis models, but the nature of primordial quantum fluctuations is quite distinct. In some cases, tensor perturbations grow on superhorizon scales. The tensor power spectrum can be red, blue, or scale invariant, depending on the model, while scalar perturbations are nearly scale invariant. This is in sharp contrast to typical NEC-violating cosmologies, in which a blue tensor tilt is generated. Though the primordial tensor and scalar spectra are both nearly scale invariant as in the inflationary scenario, the consistency relation in our variant of Galilean Genesis is non-standard.

We derive the cosmological matching conditions for the homogeneous and isotropic background and for linear perturbations in Horndeski's most general second-order scalar-tensor theory. In general relativity, the matching is done in such a way that the extrinsic curvature is continuous across the transition hypersurface. This procedure is generalized so as to incorporate the mixing of scalar and gravity kinetic terms in the field equations of Horndeski's theory. Our matching conditions have a wide range of applications including the galilean genesis and the bounce scenarios, in which stable, null energy condition violating solutions play a central role. We demonstrate how our matching conditions are used in the galilean genesis scenario. In doing so, we extend the previous genesis models and provide a unified description of the theory admitting the solution that starts expanding from the Minkowski spacetime.PACS numbers: 98.80.Cq

Galilean genesis is an alternative to inflation, in which the universe starts expanding from Minkowski with the stable violation of the null energy condition. In this paper, we discuss how the early universe is reheated through the gravitational particle production at the transition from the genesis phase to the subsequent phase where the kinetic energy of the scalar field is dominant. We then study the consequences of gravitational reheating after Galilean genesis on the spectrum of primordial gravitational waves. The resultant spectrum is strongly blue, and at high frequencies Ωgw ∝ f 3 in terms of the energy density per unit logarithmic frequency. Though this cannot be detected in existing detectors, the amplitude can be as large as Ωgw ∼ 10 −12 at f ∼ 100 MHz, providing a future test of the genesis scenario. The analysis is performed within the framework of generalized Galilean genesis based on the Horndeski theory, which enables us to derive generic formulas.