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We examine the behavior of the standard-model electroweak phase transition in the early Universe. We argue that close to the critical temperature it is possible to estimate the {\it effective} infrared corrections to the 1-loop potential using well known $\varepsilon$-expansion results from the theory of critical phenomena in 3 spatial dimensions. The theory with the $\varepsilon$-corrected potential exhibits much larger fluctuations in the spatial correlations of the order parameter, considerably weakening the strength of the transition., Comment: 26 pages

Boson stars are gravitationally bound, spherically symmetric equilibrium configurations of cold, free, or interacting complex scalar fields \ensuremath{\varphi}. As these equilibrium configurations naturally present local anisotropy, it is sensible to expect departures from the well-known stability criteria for fluid stars. With this in mind, I investigate the dynamical instability of boson stars against charge-conserving, small radial perturbations. Following the method developed by Chandrasekhar, a variational base for determining the eigenfrequencies of the perturbations is found. This approach allows one to find numerically an upper bound for the central density where dynamical instability occurs. As applications of the formalism, I study the stability of equilibrium configurations obtained both for the free and for the self-interacting [with V(\ensuremath{\varphi})=(\ensuremath{\lambda}/4)\ensuremath{\Vert}\ensuremath{\varphi}${\ensuremath{\Vert}}^{4}$] massive scalar field \ensuremath{\varphi}. Instabilities are found to occur not for the critical central density as in fluid stars but for central densities considerably higher. The departure from the results for fluid stars is sensitive to the coupling \ensuremath{\lambda}; the higher the value of \ensuremath{\lambda}, the more the stability properties of boson stars approach those of a fluid star. These results are linked to the fractional anisotropy at the radius of the configuration.

The cosmological consequences of spontaneous breaking of an approximate discrete symmetry are studied. The breaking leads to formation of proto-domains of false and true vacuum separated by domain walls of thickness determined by the mass scale of the model. The cosmological evolution of the walls is extremely sensitive to the magnitude of the biasing; several scenarios are possible, depending on the interplay between the surface tension on the walls and the volume pressure from the biasing. Walls may disappear almost immediately after they form, or may live long enough to dominate the energy density of the Universe and cause power-law inflation. Limits are obtained on the biasing that characterizes each possible scenario.

We study possible cosmological solutions to a higher-dimensional model of gravity with a three-form taking values in the physical space, and show that it is possible to integrate Einstein's equations exactly for flat physical and internal spaces. We then present a detailed analysis of the possible trajectories in the phase plane of the Hubble factors and find the allowed regions for a physically acceptable cosmology. These turn out to be rather small.

Nontopological solitons are stable field configurations which may be formed in a primordial phase transition. We study their cosmic evolution and examine the possibility that such objects could contribute significantly to the energy density of the Universe. As the Universe cools, initially all but the largest lumps evaporate into free particles; those which survive may subsequently enter a brief accretion phase before they "freeze out" at a final size. Although the minimum critical charges which survive depend on particle masses and couplings, we develop an analysis which applies to a wide class of models. In most cases, solitons of moderate size survive the evaporation process only if there is a significant charge asymmetry or if they form at a temperature well below their binding energy per charge.

Boson stars are gravitationally bound states of complex scalar fields. In general, as a solution of the Einstein-Klein-Gordon system, the scalar field can be expanded as a sum over modes given by the product of radial functions and spherical harmonics. We show that if the configuration is not in its ground state, the excited modes will decay to the ground state through emission of scalar and gravitational radiation. Using a Newtonian approximation, we obtain the power radiated in gravitational waves and the frequency of the gravitons emitted in the decay, in the case where most of the star is already in its ground state. The process is similar to the spontaneous emission of a photon in atoms, hence the name gravitational atoms.''