We present a comprehensive, nonperturbative analytical method to investigate the dynamics of time-dependent oscillating scalar field configurations. The method is applied to oscillons in a ${\varphi }^4$ Klein-Gordon model in two and three spatial dimensions, yielding high accuracy results in the characterization of all aspects of the complex oscillon dynamics. In particular, we show how oscillons can be interpreted as long-lived perturbations about an attractor in field configuration space. By investigating their radiation rate as they approach the attractor, we obtain an accurate estimate of their lifetimes in $d=3$ and explain why they seem to be perturbatively stable in $d=2$, where $d$ is the number of spatial dimensions.

The breaking of an approximate discrete symmetry, the final stages of a first order phase transition, or a postinflationary biased probability distribution for scalar fields are possible cosmological scenarios characterized by the presence of unstable domain wall networks. Combining analytical and numerical techniques, we show that the nonspherical collapse of these domains can be a powerful source of gravitational waves. We compute their contribution to the stochastic background of gravitational radiation and explore their observability by present and future gravitational wave detectors.

We propose a measure of order in the context of nonequilibrium field theory and argue that this measure, which we call relative configurational entropy (RCE), may be used to quantify the emergence of coherent low-entropy configurations, such as time-dependent or time-independent topological and nontopological spatially extended structures. As an illustration, we investigate the nonequilibrium dynamics of spontaneous symmetry breaking in three spatial dimensions. In particular, we focus on a model where a real scalar field, prepared initially in a symmetric thermal state, is quenched to a broken-symmetric state. For a certain range of initial temperatures, spatially localized, long-lived structures known as oscillons emerge in synchrony and remain until the field reaches equilibrium again. We show that the RCE correlates with the number density of oscillons, thus offering a quantitative measure of the emergence of nonperturbative spatiotemporal patterns that can be generalized to a variety of physical systems.

We investigate the nonlinear dynamics of hybrid inflation models, which are characterized by two real scalar fields interacting quadratically. We start by solving numerically the coupled Klein-Gordon equations in static Minkowski spacetime, searching for possible coherent structures. We find long-lived, localized configurations, which we identify as a new kind of oscillon. We demonstrate that these two-field oscillons allow for “excited” states with much longer lifetimes than those found in previous studies of single-field oscillons. We then solve the coupled field equations in an expanding Friedmann-Robertson-Walker spacetime, finding that as the field responsible for inflating the Universe rolls down to oscillate about its minimum, it triggers the formation of long-lived two-field oscillons, which can contribute up to 20% of the total energy density of the Universe. We show that these oscillons emerge for a wide range of parameters consistent with WMAP 7-year data. These objects contain total energy of about $25\times {10}^{20}\mathrm{GeV}$, localized in a region of approximate radius $6\times {10}^{-26}\mathrm{cm}$. We argue that these structures could have played a key role during the reheating of the Universe.

We develop an analytical procedure to compute all relevant physical properties of scalar field oscillons in models with quartic polynomial potentials: energy, radius, frequency, core amplitude, and lifetime. We compare our predictions to numerical simulations of models with symmetric and asymmetric double-well potentials in three spatial dimensions, obtaining excellent agreement. We also explain why oscillons have not been seen to decay in two spatial dimensions.

We obtain bounds on the stability of various self-gravitating astrophysical objects using a new measure of shape complexity known as configurational entropy. We apply the method to Newtonian polytropes, neutron stars with an Oppenheimer-Volkoff equation of state, and to self-gravitating configurations of complex scalar field (boson stars) with different self couplings, showing that the critical stability region of these stellar configurations obtained from traditional perturbation methods correlates well with critical points of the configurational entropy with accuracy of a few percent or better.