We study the contribution to the primordial curvature perturbation on observational scales generated by the reheating field in massless preheating. To do so we use lattice simulations and a recent extension to the $delta N$ formalism. The work demons
trates the functionality of these techniques for calculating the observational signatures of models in which non-perturbative reheating involves a light scalar field.
We revisit the question of how to calculate correlations of the curvature perturbation, $zeta$, using the $delta N$ formalism when one cannot employ a truncated Taylor expansion of $N$. This problem arises when one uses lattice simulations to probe t
he effects of isocurvature modes on models of reheating. Working in real space, we use an expansion in the cross-correlation between fields at different positions, and present simple expressions for observables such as the power spectrum and the reduced bispectrum, $f_{rm NL}$. These take the same form as those of the usual $delta N$ expressions, but with the derivatives of $N$ replaced by non-perturbative $delta N$ coefficients. We test the validity of this expansion and argue that our expressions are particularly well suited for use with simulations.
We study how topological defects manifest themselves in the equal-time two-point field correlator. We consider a scalar field with Z_2 symmetry in 1, 2 and 3 spatial dimensions, allowing for kinks, domain lines and domain walls, respectively. Using n
umerical lattice simulations, we find that in any number of dimensions, the correlator in momentum space is to a very good approximation the product of two factors, one describing the spatial distribution of the defects and the other describing the defect shape. When the defects are produced by the Kibble mechanism, the former has a universal form as a function of k/n, which we determine numerically. This signature makes it possible to determine the kink density from the field correlator without having to resort to the Gaussian approximation. This is essential when studying field dynamics with methods relying only on correlators (Schwinger-Dyson, 2PI).
It has been conjectured that the phase transition in the Ginzburg-Landau theory is dual to the XY model transition. We study numerically a particular limit of the GL theory where this duality becomes exact, clarifying some of the problems encountered
in standard GL theory simulations. This may also explain the failure of the superconductor experiments to observe the XY model scaling.
