Vacuum energy remains the simplest model of dark energy which could drive the accelerated expansion of the Universe without necessarily introducing any new degrees of freedom. Inhomogeneous vacuum energy is necessarily interacting in general relativity. Although the four-velocity of vacuum energy is undefined, an interacting vacuum has an energy transfer and the vacuum energy defines a particular foliation of spacetime with spatially homogeneous vacuum energy in cosmological solutions. It is possible to give a consistent description of vacuum dynamics and in particular the relativistic equations of motion for inhomogeneous perturbations given a covariant prescription for the vacuum energy, or equivalently the energy transfer four-vector, and we construct gauge-invariant vacuum perturbations. We show that any dark energy cosmology can be decomposed into an interacting vacuum+matter cosmology whose inhomogeneous perturbations obey simple first-order equations.

Any unified dark matter cosmology can be decomposed into dark matter interacting with vacuum energy, without introducing any additional degrees of freedom. We present observational constraints on an interacting vacuum plus dark energy corresponding to a generalised Chaplygin gas cosmology. We consider two distinct models for the interaction leading to either a barotropic equation of state or dark matter that follows geodesics, corresponding to a rest-frame sound speed equal to the adiabatic sound speed or zero sound speed, respectively. For the barotropic model, the most stringent constraint on α comes from the combination of CMB+SNIa+LSS(m) gives α < 1.44 × 10 −5 at the 95% confidence level, which indicates that the barotropic model must be extremely close to the ΛCDM cosmology. For the case where the dark matter follows geodesics, perturbations have zero sound speed, and CMB+SNIa+gISW then gives the much weaker constraint −0.1522 < α < 0.2556 at the 95% confidence level.

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In this work we extend the perturbation theory for modified gravity (MG) in two main aspects. First, the construction of matter overdensities from Lagrangian displacement fields is shown to hold in a general framework, allowing us to find Standard Perturbation Theory (SPT) kernels from known Lagrangian Perturbation Theory (LPT) kernels. We then develop a theory of biased tracers for generalized cosmologies, extending already existing formalisms for ΛCDM. We present the correlation function in Convolution-LPT and the power spectrum in SPT for ΛCDM, f (R) Hu-Sawicky, and DGP braneworld models. Our formalism can be applied to many generalized cosmologies and to facilitate it, we are making public a code to compute these statistics. We further study the relaxation of bias with the use of a simple model and of excursion set theory, showing that in general the bias parameters have smaller values in MG than in General Relativity.

We study a unification model for dark energy, dark matter, and inflation with a single scalar field with non canonical kinetic term. In this model the kinetic term of the Lagrangian accounts for the dark matter and dark energy, and at early epochs a quadratic potential accounts for slow roll inflation. The present work is an extension to the work by Bose and Majumdar [Phys. Rev. D 79, 103517 (2009).] with a more general kinetic term that was proposed by Chimento in Phys. Rev. D 69, 123517 (2004). We demonstrate that the model is viable at the background and linear perturbation levels.

We study tachyon inflation within the large-N formalism, which takes a prescription for the small Hubble flow slow-roll parameter ϵ1 as a function of the large number of e-folds N. This leads to a classification of models through their behaviour at large N. In addition to the perturbative N class, we introduce the polynomial and exponential classes for the ϵ1 parameter. With this formalism we reconstruct a large number of potentials used previously in the literature for tachyon inflation. We also obtain new families of potentials from the polynomial class. We characterize the realizations of tachyon inflation by computing the usual cosmological observables up to second order in the Hubble flow slow-roll parameters. This allows us to look at observable differences between tachyon and canonical single field inflation. The analysis of observables in light of the Planck 2015 data shows the viability of some of these models, mostly for certain realization of the polynomial and exponential classes.

Vacuum energy is a simple model for dark energy driving an accelerated expansion of the universe. If the vacuum energy is inhomogeneous in spacetime then it must be interacting. We present the general equations for a spacetime-dependent vacuum energy in cosmology, including inhomogeneous perturbations. We show how any dark energy cosmology can be described by an interacting vac-uum+matter. Different models for the interaction can lead to different behaviour (e.g., sound speed for dark energy perturbations) and hence could be distinguished by cosmological observations. As an example we present the cosmic microwave microwave background anisotropies and the matter power spectrum for two different versions of a generalised Chaplygin gas cosmology.

We analyze the phase space of a particular unified model of dark matter, dark energy, and inflation that we recently studied in [Phys. Rev. D 83, 063502 (2011)] whose Lagrangian is of the form L(X,phi) = F(X) - V(phi). We show that this model possesses a large set of initial conditions consistent with a successful cosmological model in which an inflationary phase is possible, followed by a matter era to end with dark energy domination. In order to understand the success of the model, we study the general features that unified dark matter (UDM) models should comply and then we analyze some particular models and find their constrictions.Comment: 9 pages, 1 figure, v2 clarified discussions and formulae to match the accepted version to appear in the proceedings of "IX Taller DGFM-SMF