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Register a new userInstabilities in Mimetic Matter Perturbations
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We study cosmological perturbations in mimetic matter scenario with a general higher derivative function. We calculate the quadratic action and show that both the kinetic term and the gradient term have the wrong sings. We perform the analysis in both comoving and Newtonian gauges and confirm that the Hamiltonians and the associated instabilities are consistent with each other in both gauges. The existence of instabilities is independent of the specific form of higher derivative function which generates gradients for mimetic field perturbations. It is verified that the ghost instability in mimetic perturbations is not associated with the higher derivative instabilities such as the Ostrogradsky ghost.
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We investigate cosmological perturbations of scalar-tensor theories in Palatini formalism. First we introduce an action where the Ricci scalar is conformally coupled to a function of a scalar field and its kinetic term and there is also a k-essence term consisting of the scalar and its kinetic term. This action has three frames that are equivalent to one another: the original Jordan frame, the Einstein frame where the metric is redefined, and the Riemann frame where the connection is redefined. For the first time in the literature, we calculate the quadratic action and the sound speed of scalar and tensor perturbations in three different frames and show explicitly that they coincide. Furthermore, we show that for such action the sound speed of gravitational waves is unity. Thus, this model serves as dark energy as well as an inflaton even though the presence of the dependence of the kinetic term of a scalar field in the non-minimal coupling, different from the case in metric formalism. We then proceed to construct the L3 action called Galileon terms in Palatini formalism and compute its perturbations. We found that there are essentially 10 different(inequivalent) definitions in Palatini formalism for a given Galileon term in metric formalism. We also see that,in general, the L3 terms have a ghost due to Ostrogradsky instability and the sound speed of gravitational waves could potentially deviate from unity, in sharp contrast with the case of metric formalism. Interestingly, once we eliminate such a ghost, the sound speed of gravitational waves also becomes unity. Thus, the ghost-free L3 terms in Palatini formalism can still serve as dark energy as well as an inflaton, like the case in metric formalism.
In a recent paper arXiv:0910.2230, Khoury and Steinhardt proposed a way to generate adiabatic cosmological perturbations with a nearly flat spectrum in a contracting Universe. To produce these perturbations they used a regime in which the equation of state exponentially rapidly changed during a short time interval. Leaving aside the singularity problem and the difficult question about the possibility to transmit these perturbations from a contracting Universe to the expanding phase, we will show that the methods used in arXiv:0910.2230 are inapplicable for the description of the cosmological evolution and of the process of generation of perturbations in this scenario.
We study linear cosmological perturbations in the ``healthy extension of Horava-Lifshitz gravity which has recently been analyzed cite{BPS2}. We find that there are two degrees of freedom for scalar metric fluctuations, but that one of them decouples in the infrared limit. Also, for appropriate choices of the parameters defining the Lagrangian, the extra mode can be made well-behaved even in the ultraviolet.
Extending our previous work on the robustness of inflation to perturbations in the scalar field, we investigate the effects of perturbations in the transverse traceless part of the extrinsic curvature on the evolution of an inhomogeneous inflaton field. Focusing on small field models, we show that these additional metric inhomogeneities initially reduce the total number of e-folds as the amplitude increases, but that the reduction saturates and even reverses above a certain amplitude. We present an argument that this is due to the presence of a large initial Hubble friction when metric perturbations are large.
We study the quantum mechanical evolution of the tensor perturbations during inflation with non-linear tensor interactions. We first obtain the Lindblad terms generated by non-linear interactions by tracing out unobservable sub-horizon modes. Then we calculate explicitly the reduced density matrix for the super-horizon modes, and show that the probability of maintaining the unitarity of the squeezed state decreases in time. The decreased probability is transferred to other elements of the reduced density matrix including off-diagonal ones, so the evolution of the reduced density matrix describes the quantum-to-classical transition of the tensor perturbations. This is different from the classicality accomplished by the squeezed state, the suppression of the non-commutative effect, which is originated from the quadratic, linear interaction, and also maintains the unitarity. The quantum-to-classical transition occurs within 5 - 10 e-folds, faster than the curvature perturbation.
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