We study the effects of perturbative reheating on the evolution of the curvature perturbation ζ, in two-field inflation models. We use numerical methods to explore the sensitivity of fNL, n ζ and r to the reheating process, and present simple qualitative arguments to explain our results. In general, if a large non-Gaussian signal exists at the start of reheating, it will remain non-zero at the end of reheating. Unless all isocurvature modes have completely decayed before the start of reheating, we find that the non-linearity parameter, fNL, can be sensitive to the reheating timescale, and that this dependence is most appreciable for 'runaway' inflationary potentials that only have a minimum in one direction. For potentials with a minimum in both directions, fNL can also be sensitive to reheating if a mild hierarchy exists between the decay rates of each field. Within the class of models studied, we find that the spectral index n ζ , is fairly insensitive to large changes in the field decay rates, indicating that n ζ is a more robust inflationary observable, unlike the non-linearity parameter fNL. Our results imply that the statistics of ζ, especially fNL, can only be reliably used to discriminate between models of two-field inflation if the physics of reheating are properly accounted for.

Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing properties of quantum walks compared with their classical counterparts have been well-studied on regular structures and also shown to be sensitive to defects and imperfections in the lattice. As a simple example of a disordered system, we consider percolation lattices, in which edges or sites are randomly missing, interrupting the progress of the quantum walk. We use numerical simulation to study the properties of coined quantum walks on these percolation lattices in one and two dimensions. In one dimension (the line) we introduce a simple notion of quantum tunneling and determine how this affects the properties of the quantum walk as it spreads. On two-dimensional percolation lattices, we show how the spreading rate varies from linear in the number of steps down to zero, as the percolation probability decreases towards the critical point. This provides an example of fractional scaling in quantum walk dynamics.

We study the impacts of reheating temperature on the inflationary predictions of the spectral index and tensor-to-scalar ratio. Assuming sinusoidal oscillations and that reheating process is very fast, the reheating temperature can be constrained for sinusoidal oscillation within a factor of 10 -100 or even better with the prospect of future observations. Beyond this, we find that the predictions can also be insensitive to the reheating temperature in certain models, including Higgs inflation.

We study the evolution of the non-linear curvature perturbation during perturbative reheating, and hence how observables evolve to their final values which we may compare against observations. Our study includes the evolution of the two trispectrum parameters, gNL and τNL, as well as the scale dependence of both fNL and τNL. In general the evolution is significant and must be taken into account, which means that models of multifield inflation cannot be compared to observations without specifying how the subsequent reheating takes place. If the trispectrum is large at the end of inflation, it normally remains large at the end of reheating. In the classes of models we study, it remains very hard to generate τNL f 2 NL , regardless of the decay rates of the fields. Similarly, for the classes of models in which gNL τNL during slow-roll inflation, we find the relation typically remains valid during reheating. Therefore it is possible to observationally test such classes of models without specifying the parameters of reheating, even though the individual observables are sensitive to the details of reheating. It is hard to generate an observably large gNL however. The runnings, n f NL and nτ NL , tend to satisfy a consistency relation nτ NL = (3/2)n f NL regardless of the reheating timescale, but are in general too small to be observed for the class of models considered.

We explore the correlations between primordial non-Gaussianity and isocurvature perturbation. We sketch the generic relation between the bispectrum of the curvature perturbation and the cross-correlation power spectrum in the presence of explicit couplings between the inflaton and another light field which gives rise to isocurvature perturbation. Using a concrete model of a Peccei-Quinn type field with generic gravitational couplings, we illustrate explicitly how the primordial bispectrum correlates with the cross-correlation power spectrum. Assuming the resulting f NL ∼ O(1), we find that the form of the correlation depends mostly upon the inflation model but only weakly on the axion parameters, even though f NL itself does depend heavily on the axion parameters.