I present some recent result in loop quantum cosmology with inverse-volume quantum corrections. The full set of inflationary observables is derived from the perturbed Einstein equations and experimental bounds are placed upon the size of quantum corrections, using WMAP7 data.

A cosmological first order phase transition can lead to many interesting phenomena, such as electroweak baryogenesis or the production of a stochastic background of gravitational waves. The phase transition proceeds through the nucleation and subsequent expansion of bubbles, and the understanding of the dynamics of their expansion is very relevant for the study of these phenomena.

After a brief review of purely gravitational aspects of the AdS3/CFT2 correspondence, a similar analysis is performed for asymptotically flat spacetimes at null infinity in 3 and 4 dimensions. In the spirit of two dimensional conformal field theory, it is shown that the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions can be taken to be the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra.

We consider a multi-scalar-tensor model of gravity in which the action contains higher-order derivatives of the scalar fields without introducing extra propagating degrees of freedom. In the context of an inflationary era, we study the background evolution of this model as well as the linear and non-linear properties of the cosmological fluctuations it generates. Orthogonal non-Gaussianities are shown to arise for the first time in a concrete model and new shapes of non-Gaussianities are identified.

The study of CMB primordial non-Gaussianities provides a powerful way to put constraints on a large range of inflationary models. After a quick review of the main non-Gaussian features arising from different scenarios of inflation, I will introduce a general technique to study such signatures based on a modal expansion of the primordial CMB bispectrum (i.e. the 3-point function of the CMB multipoles). I will finally present some results obtained from the application of this technique to WMAP data for a variety of models and conclude with some forecasts for Planck.

Current Standard Model of elementary particles nicely describes (nearly) all phenomena observed in the laboratories. On cosmological scales the situation is much worse -- reliable experimental observations do not fit into the Standard Model. In the beginning the Universe had a period of inflationary expansion, now it is filled with Dark Matter and has baryon asymmetry. All these require explanation beyond the Standard Model.

We argue that observations of neutron stars and white dwarfs can impose constraints on dark matter candidates even with very small elastic and/or inelastic cross section, and small or even zero self-annihilation cross section, thus probing regions of parameters which are inaccessible for direct searches.

I will discuss the thermodynamic and hydrodynamic properties of 5d dilaton-gravity models, holographically dual to pure gauge theories which exhibit confinement and asymptotic freedom at zero temperature. This class of Einstein-dilaton gravities display a first order Hawking-Page deconfinement phase transition. Thermodynamic quantities are computed for a specific model and shown to be in good agreement with lattice results.

We study a cosmological set-up in which inflation is preceded by a bounce. In this way, the primordial singularity, one of the major shortcomings of inflation, is replaced by a (finite-size) scale factor reversal phase, before which the universe undergoes a phase of contraction. Our starting point is the bouncing background cosmology investigated previously by Falciano et al. [Phys. Rev. D 77, 083513 (2008)], which we complete by a detailed study of the transfer of cosmological perturbations through the bounce.

Motivated by the fact that cosmological perturbations of inflationary quantum origin were born Gaussian, the search for non-Gaussianities in the cosmic microwave background (CMB) anisotropies is considered as the privileged probe of non-linear physics in the early universe. Cosmic strings are active sources of gravitational perturbations and incessantly produce non-Gaussian distortions in the CMB.