We discuss correlations among spectral observables as a new tool for differentiating between models for the primordial perturbation. We show that if generated in the isocurvature sector, a running of the scalar spectral index is correlated with the s
tatistical properties of non-Gaussianities. In particular, we find a large running will inevitably be accompanied by a large running of $f_{rm NL}$ and enhanced $g_{rm NL}$, with $g_{rm NL}gg f_{rm NL}^2$. If the tensor to scalar ratio is large, a large negative running must turn positive on smaller scales. Interestingly, the characteristic scale of the transition could potentially distinguish between the inflaton and isocurvature fields.
We explore inflation via the effective potential of the minimal Wess-Zumino model, considering both the real and imaginary components of the complex field. Using transport techniques, we calculate the full allowed range of $n_s$, $r$ and $f_{rm NL}$
for different choices of the single free parameter, $v$, and present the probability distribution of these signatures given a simple choice for the prior distribution of initial conditions. Our work provides a case study of multi-field inflation in a simple but realistic setting, with important lessons that are likely to apply more generally. For example, we find that there are initial conditions consistent with observations of $n_s$ and $r$ for values of $v$ that would be excluded if only evolutions in the real field direction were to be considered, and that these may yield enhanced values of $f_{rm NL}$. Moreover, we find that initial conditions fixed at high energy density, where the potential is close to quartic in form, can still lead to evolutions in a concave region of the potential during the observable number of e-folds, as preferred by present data. The Wess-Zumino model therefore provides an illustration that multi-field dynamics must be taken into account when seeking to understand fully the phenomenology of such models of inflation.
This proceedings contribution provides a brief update on the transport approach to calculating the statistics of perturbations produced during inflation. It is based in particular on work in collaboration with Gemma Anderson and David Seery.
We extend the `moment transport method for calculating the statistics of inflationary perturbations to the quantum phase of evolution on sub-horizon scales. The quantum transport equations form a set of coupled ordinary differential equations for the
evolution of quantum correlation functions during inflation, which are valid on sub- and super-horizon scales, and reduce to the known classical transport equations after horizon crossing. The classical and quantum equations follow directly from the field equations of cosmological perturbation theory. In this paper, we focus on how the evolution equations arise, and explore how transport methods relate to other approaches, and in particular how formal integral solutions to the transport equations connect to those of the In-In formalism.
We calculate the conditions required to produce a large local trispectrum during two-field slow-roll inflation. This is done by extending and simplifying the heatmap approach developed by Byrnes et al. The conditions required to generate a large tris
pectrum are broadly the same as those that can produce a large bispectrum. We derive a simple relation between tauNL and fNL for models with separable potentials, and furthermore show that gNL and tauNL can be related in specific circumstances. Additionally, we interpret the heatmaps dynamically, showing how they can be used as qualitative tools to understand the evolution of non-Gaussianity during inflation. We also show how fNL, tauNL and gNL are sourced by generic shapes in the inflationary potential, namely ridges, valleys and inflection points.
We investigate the behaviour of tensor fluctuations in Loop Quantum Cosmology, focusing on a class of scaling solutions which admit a near scale-invariant scalar field power spectrum. We obtain the spectral index of the gravitational field perturbati
ons, and find a strong blue tilt in the power spectrum with $n_t approx 2$. The amplitude of tensor modes are, therefore, suppressed by many orders of magnitude on large scales compared to those predicted by the standard inflationary scenario where $n_t approx 0$.
