We consider the steepest rate at which the power spectrum from single field inflation can grow, with the aim of providing a simple explanation for the $k^4$ growth found recently. With this explanation in hand we show that a slightly steeper $k^5 (lo
g k )^2$ growth is in fact possible. Moreover, we argue that the power spectrum after a steep growth cannot immediately decay, but must remain large for the $k$ modes which exit during a $sim2$ e-fold period. We also briefly consider how a strong growth can affect the spectral index of longer wavelengths preceding the growth, and show that even the conversion of isocurvature modes likely cannot lead to a stronger growth. These results have implications for the formation of primordial black holes, and other phenomena which require a large amplitude of power spectrum at short scales.
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 extend the transport framework for numerically evaluating the power spectrum and bispectrum in multi-field inflation to the case of a curved field-space metric. This method naturally accounts for all sub- and super-horizon tree level effects, incl
uding those induced by the curvature of the field-space. We present an open source implementation of our equations in an extension of the publicly available PyTransport code. Finally we illustrate how our technique is applied to examples of inflationary models with a non-trivial field-space metric.
PyTransport constitutes a straightforward code written in C++ together with Python scripts which automatically edit, compile and run the C++ code as a Python module. It has been written for Unix-like systems (OS X and Linux). Primarily the module emp
loys the transport approach to inflationary cosmology to calculate the tree-level power-spectrum and bispectrum of user specified models of multi-field inflation, accounting for all sub and super-horizon effects. The transport method we utilise means only coupled differential equations need to be solved, and the implementation presented here combines the speed of C++ with the functionality and convenience of Python. This document details the code and illustrates how to use it with a worked example. It has been updated to be a companion to the second version of the code, PyTransport 2.0, which includes functionality to deal with models of inflation with a curved field space metric.
We present a complete framework for numerical calculation of the power spectrum and bispectrum in canonical inflation with an arbitrary number of light or heavy fields. Our method includes all relevant effects at tree-level in the loop expansion, inc
luding (i) interference between growing and decaying modes near horizon exit; (ii) correlation and coupling between species near horizon exit and on superhorizon scales; (iii) contributions from mass terms; and (iv) all contributions from coupling to gravity. We track the evolution of each correlation function from the vacuum state through horizon exit and the superhorizon regime, with no need to match quantum and classical parts of the calculation; when integrated, our approach corresponds exactly with the tree-level Schwinger or in-in formulation of quantum field theory. In this paper we give the equations necessary to evolve all two- and three-point correlation functions together with suitable initial conditions. The final formalism is suitable to compute the amplitude, shape, and scale dependence of the bispectrum in models with |fNL| of order unity or less, which are a target for future galaxy surveys such as Euclid, DESI and LSST. As an illustration we apply our framework to a number of examples, obtaining quantitatively accurate predictions for their bispectra for the first time. Two accompanying reports describe publicly-available software packages that implement the method.
We study the behaviour of linear perturbations in multifield coupled quintessence models. Using gauge invariant linear cosmological perturbation theory we provide the full set of governing equations for this class of models, and solve the system nume
rically. We apply the numerical code to generate growth functions for various examples, and compare these both to the standard $Lambda$CDM model and to current and future observational bounds. Finally, we examine the applicability of the small scale approximation, often used to calculate growth functions in quintessence models, in light of upcoming experiments such as SKA and Euclid. We find the deviation of the full equation results for large k modes from the approximation exceeds the experimental uncertainty for these future surveys. The numerical code, PYESSENCE, written in Python will be publicly available.
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.
The observational signatures of multi-field inflation will generally evolve as the Universe reheats. We introduce a general analytic formalism for tracking this evolution through perturbative reheating, applicable to two field models with arbitrary s
eparable potentials. The various transitions, including the onset of scalar field oscillations and the reheating of each field, can happen in different orders and on arbitrary hypersurfaces. The effective equations of state of the oscillating fields are also arbitrary. Nevertheless, our results are surprisingly simple. Our formalism encapsulates and generalises a huge range of previous calculations including two-field inflation, spectator models, the inhomogeneous end of inflation scenario and numerous generalised curvaton scenarios.
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.
