The bispectrum of single-field inflationary trajectories in which the speed of sound of the inflationary trajectories $c_s$ is constant but not equal to the speed of light $c=1$ is explored. The trajectories are generated as random realisations of th
e Hubble Slow-Roll (HSR) hierarchy and the bispectra are calculated using numerical techniques that extends previous work. This method allows for out-of-slow-roll models with non-trivial time dependence and arbitrarily low $c_s$. The ensembles obtained using this method yield distributions for the shape and scale-dependence of the bispectrum and their relations with the standard inflationary parameters such as scalar spectral tilt $n_s$ and tensor-to-scalar ratio $r$. The distributions demonstrate the squeezed-limit consistency relations for arbitrary single-field inflationary models.
The simplest interpretation of the Bicep2 result is that the scalar primordial power spectrum is slightly suppressed at large scales. These models result in a large tensor-to-scalar ratio $r$. In this work we show that the type of inflationary trajec
tory favoured by Bicep2 also leads to a larger non-Gaussian signal at large scales, roughly an order of magnitude larger than a standard slow-roll trajectory.
The recent BICEP2 detection of, what is claimed to be primordial $B$-modes, opens up the possibility of constraining not only the energy scale of inflation but also the detailed acceleration history that occurred during inflation. In turn this can be
used to determine the shape of the inflaton potential $V(phi)$ for the first time - if a single, scalar inflaton is assumed to be driving the acceleration. We carry out a Monte Carlo exploration of inflationary trajectories given the current data. Using this method we obtain a posterior distribution of possible acceleration profiles $epsilon(N)$ as a function of $e$-fold $N$ and derived posterior distributions of the primordial power spectrum $P(k)$ and potential $V(phi)$. We find that the BICEP2 result, in combination with Planck measurements of total intensity Cosmic Microwave Background (CMB) anisotropies, induces a significant feature in the scalar primordial spectrum at scales $ksim 10^{-3}$ Mpc$^{-1}$. This is in agreement with a previous detection of a suppression in the scalar power.
We use the Hamilton--Jacobi formalism to constrain the space of possible single field, inflationary Hubble flow trajectories when compared to the WMAP and Planck satellites Cosmic Microwave Background (CMB) results. This method yields posteriors on t
he space of Hubble Slow Roll (HSR) parameters that uniquely determine the history of the Hubble parameter during the inflating epoch. The trajectories are used to numerically determine the observable primordial power spectrum and bispectra that can then be compared to observations. Our analysis is used to infer the most likely shape of the inflaton potential $V(phi)$ and also yields a prediction for, $f_{rm NL}$, the dimensionless amplitude of the non-Gaussian bispectrum.
We carry out a numerical calculation of the bispectrum in generalised trajectories of canonical, single--field inflation. The trajectories are generated in the Hamilton-Jacobi (HJ) formalism based on Hubble Slow Roll (HSR) parameters. The calculation
allows generally shape and scale dependent bispectra, or dimensionless $f_{NL}$, in the out-of-slow-roll regime. The distributions of $f_{NL}$ for various shapes and HSR proposals are shown as an example of how this procedure can be used within the context of Monte Carlo exploration of inflationary trajectories. We also show how allowing out-of-slow-roll behaviour can lead to a bispectrum that is relatively large for equilateral shapes.
