Monte Carlo reconstruction of the inflationary potential

I review various aspects of techniques for reconstructing the potential of the inflaton field from observations, with special emphasis on difficulties which might arise. While my view is that if inflation is to prove viable then most likely it will be one of the simplest models, it is important to consider the impact should we need to move to a more complicated model-building realm.

We present and discuss a new approach increasing by orders of magnitude the speed of performing Bayesian inference and parameter estimation within the framework of slow-roll inflation. The method relies on the determination of an effective likelihood for inflation which is a function of the primordial amplitude of the scalar perturbations complemented with the necessary number of the so-called Hubble flow functions to reach the desired accuracy. Starting from any cosmological...

These lecture notes have been written for a short introductory course on the status of inflation after Planck and BICEP2, given at the Xth Modave School of Mathematical Physics. The first objective is to give an overview of the theory of inflation: motivations, homogeneous scalar field dynamics, slow-roll approximation, linear theory of cosmological perturbations, classification of single field potentials and their observable predictions. This includes a pedagogical derivatio...

Inflation is now an accepted paradigm in standard cosmology, with its predictions consistent with observations of the cosmic microwave background. It lacks, however, a firm physical theory, with many possible theoretical origins beyond the simplest, canonical, slow-roll inflation, including Dirac-Born-Infeld inflation and k-inflation. We discuss how a hierarchy of Hubble flow parameters, extended to include the evolution of the inflationary sound speed, can be applied to comp...

We make a more general determination of the inflationary observables in the standard 4-D and 5-D single-field inflationary scenarios, by the exact reconstruction of the dynamics of the inflation potential during the observable inflation with minimal number of assumptions: the computation does not assume the slow-roll approximation and is valid in all regimes if the field is monotonically rolling down its potential. Making use of the {\em Hamilton-Jacobi} formalism developed f...

We study the constraints on the inflationary parameter space derived from the 3 year WMAP dataset using ``slow roll reconstruction'', using the SDSS galaxy power spectrum to gain further leverage where appropriate. This approach inserts the inflationary slow roll parameters directly into a Monte Carlo Markov chain estimate of the cosmological parameters, and uses the inflationary flow hierarchy to compute the parameters' scale-dependence. We work with the first three paramete...

We place observational constraints on slow-variation single-field inflationary models by carrying out the cosmological Monte Carlo simulation with the recent data of Planck combined with the WMAP large-angle polarization, baryon acoustic oscillations, and ACT/SPT temperature data. Our analysis covers a wide variety of models with second-order equations of motion-- including potential-driven slow-roll inflation, non-minimally coupled models, running kinetic couplings, Brans-Di...

If primordial scalar and tensor perturbation spectra can be inferred from observations of the cosmic background radiation and large-scale structure, then one might hope to reconstruct a unique single-field inflaton potential capable of generating the observed spectra. In this paper we examine conditions under which such a potential can be reliably reconstructed. For it to be possible at all, the spectra must be well fit by a Taylor series expansion. A complete reconstruction ...

We extract parameters relevant for distinguishing among single-field inflation models from the Wilkinson Microwave Anisotropy Probe (WMAP) data set, and from a combination of the WMAP data and seven other Cosmic Microwave Background (CMB) experiments. We use only CMB data and perform a likelihood analysis over a grid of models including the full error covariance matrix. We find that a model with a scale-invariant scalar power spectrum ($n=1$), no tensor contribution, and no r...

We consider approaches to cosmological parameter estimation in the inflationary cosmology, focussing on the required accuracy of the initial power spectra. Parametrizing the spectra, for example by power-laws, is well suited to testing the inflationary paradigm but will only correctly estimate cosmological parameters if the parametrization is sufficiently accurate, and we investigate conditions under which this is achieved both for present data and for upcoming satellite data...