Abstract:
One of the so-called viable modified gravities is analyzed. This kind of gravity theories are characterized by a well behavior at local scales, where General Relativity is recovered, while the modified terms become important at the cosmological level, where the late-time accelerating era is reproduced, and even the inflationary phase. In the present work, the future cosmological evolution for one of these models is studied. A transition to the phantom phase is observed. Furthermore, the scalar-tensor equivalence of f(R) gravity is also considered, which provides important information concerning this kind of models.

Abstract:
We consider the de Sitter cosmology deformed by the presence of a thermal bath of radiation and/or time-dependent moduli fields. Depending on the parameters, either a first or second order phase transition can occur. In the first case, an instanton allows a double analytic continuation. It induces a probability to enter the inflationary evolution by tunnel effect from another cosmological solution. The latter starts with a big bang and, in the case the transition does not occur, ends with a big crunch. A temperature duality exchanges the two cosmological branches. In the limit where the pure de Sitter universe is recovered, the tunnel effect reduces to a "creation from nothing", due to the vanishing of the big bang branch. However, the latter may be viable in some range of the deformation parameter. In the second case, there is a smooth evolution from a big bang to the inflationary phase.

Abstract:
Inflation models ending in a first order phase transition produce gravitational waves (GW) via bubble collisions of the true vacuum phase. We demonstrate that these bubble collisions can leave an observable signature in Advanced LIGO, an upcoming ground-based GW experiment. These GW are dependent on two parameters of the inflationary model: $\varepsilon$ represents the energy difference between the false vacuum and the true vacuum of the inflaton potential, and $\chi$ measures how fast the phase transition ends ($\chi \sim$ the number of e-folds during the actual phase transition). Advanced LIGO will be able to test the validity of single-phase transition models within the parameter space $10^7 \rm{GeV}\lesssim \varepsilon^{1/4} \lesssim 10^{10} \rm{GeV}$ and $0.19 \lesssim \chi \lesssim 1$. If inflation occurred through a first order phase transition, then Advanced LIGO could be the first to discover high frequency GW from inflation.

Abstract:
We study the non-linear dynamics of an inflationary phase transition in a quartically self coupled inflaton model within the framework of a de Sitter background. Large N and Hartree non-perturbative approximations combined with non-equilibrium field theory methods are used to study the self-consistent time evolution including backreaction effects. We find that when the system cools down from an initial temperature T_i > T_c to below T_c with the initial value of the zero mode of the inflaton phi(0) << m lambda^{-1/4}, the dynamics is determined by the growth of long-wavelength quantum fluctuations. For phi(0) >> m lambda^{-1/4} the dynamics is determined by the evolution of the classical zero mode. In the regime where spinodal quantum fluctuations give the most important contribution to the non-equilibrium dynamics, we find that they modify the equation of state providing a graceful exit from the inflationary stage. Inflation ends through this new mechanism at a time scale t_s >= [H/m^2]ln[lambda^{-1}] which for H >= m and very weak coupling allows over one hundred e-folds during the de Sitter phase. Spatially correlated domains grow to be of horizon-size and quantum fluctuations ``freeze-out'' for times t> t_s.

Abstract:
We have measured the magnetic hysteresis loops and the magnetic relaxation for $Bi_2Sr_2CaCu_2O_{8+\delta}$ (Bi-2212) single crystals which exhibit the second magnetization peak effect. Although no second peak effect is observed below 20 K in the measurement with fast field sweeping rate, it is found that the second peak effect will appear again after long time relaxation or in a measurement with very slow field sweeping rate at 16 K. It is anticipated that the peak effect will appear at very low temperatures (approaching zero K) when the relaxation time is long enough. We attribute this phenomenon to the profile of the interior magnetic field and conclude that the phase transition line of Bragg glass to vortex glass has no ending point at low temperatures.

Abstract:
We discuss the effects of cosmic phase transition on the spectrum of primordial gravitational waves generated during inflation. The energy density of the scalar condensation responsible for the phase transition may become sizable at the epoch of phase transition, which significantly affects the evolution of the universe. As a result, the amplitudes of the gravitational waves at high frequency modes are suppressed. Thus the gravitational wave spectrum can be a probe of phase transition in the early universe.

Abstract:
New exact inflationary solutions are presented in the scalar field theory, minimally coupled to gravity, with a potential term. No use is made of the slow rollover approximation. The scale factors are completely nonsingular and the transition to the deccelerating phase is smooth. Moreover, in one of these models, asymptotically one has transition to the matter dominated Universe.

Abstract:
We investigate the nucleation of circular cosmic strings in models of generalized inflationary universes with an accelerating scale factor. We consider toy cosmological models of a smooth inflationary exit and transition into a flat Minkowski spacetime. Our results establish that an inflationary expanding phase is necessary but not sufficient for quantum nucleation of circular cosmic strings to occur.

Abstract:
We compute the spectral index for scalar perturbations generated in a primordial inflationary model. In this model, the transition of the inflationary phase to the radiative era is achieved through the decay of the cosmological term leading a second order phase transition and the characteristics of the model allow to implement a set of initial conditions where the perturbations display a thermal spectrum when they emerge from the horizon. The obtained value for the spectral index is equal to 2, a result that depends very weakly on the various parameters of the model and on the initial conditions used.

Abstract:
The recent CMB data from Planck and BICEP2 observations have opened a new window for inflationary cosmology. In this Essay we compare three Starobinsky-like inflationary scenarios: (i) the original Starobinsky proposal; (ii) a family of dynamically broken SUGRA models; and (iii) a class of "decaying" vacuum $\Lambda(H)$ cosmologies. We then focus on the $\Lambda(H)$ variant, which spans the complete cosmic history of the universe from an early inflationary stage, followed by the "graceful exit" into the standard radiation regime, the matter epoch and, finally, the late-time accelerated expansion. Computing the effective potential we find that the "running" $\Lambda(H)$ models also provide a prediction for the tensor-to-scalar ratio of the CMB spectrum, $r \simeq 0.16$, which is compatible to within $1\sigma$ with the value $r=0.20^{+0.07}_{-0.05}$ recently measured by the BICEP2 collaboration.