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Planck and WMAP constraints on generalised Hubble flow inflationary trajectories

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 the 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 $V(ϕ)$ and also yields a prediction for, $f_{\rm NL}$, the dimensionless amplitude of the non-Gaussian bispectrum.