Monte Carlo reconstruction of the inflationary potential

In this paper my prime objective is to analyze the constraints on a sub-Planckian excursion of a single inflaton field within Effective Field Theory framework in a model independent fashion. For a generic single field inflationary potential, using the various parameterization of the primordial power spectrum I have derived the most general expression for the field excursion in terms of various inflationary observables, applying the observational constraints obtained from rece...

Scalar field cosmological inflation has a first integral relating the Hubble function and the lagrangian of the scalar field(s), which is known under the names of "Hamilton-Jacobi approach" or "superpotential equation". Here we exploit the simplicity of this superpotential equation and use it as an alternative but equivalent cosmological evolution equation during inflation, replacing the Friedman-Robertson-Walker (FRW) equations. It turns out that all inflationary observables...

We describe a method of obtaining the inflationary potential from observations which does not use the slow-roll approximation. Rather, the microwave anisotropy spectrum is obtained directly from a parametrized potential numerically, with no approximation beyond linear perturbation theory. This permits unbiased estimation of the parameters describing the potential, as well as providing the full error covariance matrix. We illustrate the typical uncertainties obtained using the...

We extract parameters relevant for distinguishing among single-field inflation models from the Wilkinson Microwave Anisotropy Probe (WMAP) three-year data set, and also from WMAP in combination with the Sloan Digital Sky Survey (SDSS) galaxy power spectrum. Our analysis leads to the following conclusions: 1) the Harrison--Zel'dovich model is consistent with both data sets at a 95% confidence level; 2) there is no strong evidence for running of the spectral index of scalar per...

This paper describes a general program for deriving the action of single field inflation models with nonstandard kinetic energy terms using CMBR power spectrum data. This method assumes that an action depends on a set of undetermined functions, each of which is a function of either the inflaton wave function or its time derivative. The scalar, tensor and non-gaussianity of the curvature perturbation spectrum are used to derive a set of reconstruction equations whose solution ...

We discuss the theoretical framework behind reconstruction of a generic class of inflationary potentials for canonical single-field slow-roll inflation in a model-independent fashion. The Non-Bunch Davies (NBD) initial condition is an essential choice to determine the structure of potential and to accommodate the blue-tilted tensor power spectrum feature recently observed in NANOGrav. Using the reconstruction technique we found the favoured parameter space which supports blue...

We propose a general inverse formula for extracting inflationary parameters from the observed power spectrum of cosmological perturbations. Under the general slow-roll scheme, which helps to probe the properties of inflation in a model independent way, we invert the leading order, single field, power spectrum formula. We also give some physically interesting examples to demonstrate its wide applicability and illuminate its properties.

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 ...

While inflation gives an appealing explanation of observed cosmological data, there are a wide range of different inflation models, providing differing predictions for the initial perturbations. Typically models are motivated either by fundamental physics considerations or by simplicity. An alternative is to generate large numbers of models via a random generation process, such as the flow equations approach. The flow equations approach is known to predict a definite structur...

By using the relations between the slow-roll parameters and the power spectrum for the single field slow-roll inflation, we derive the scalar spectral tilt $n_s$ and the tensor to scalar ratio $r$ for the constant slow-roll inflation and obtain the constraint on the slow-roll parameter $\eta$ from the Planck 2015 results. The inflationary potential for the constant slow-roll inflation is then reconstructed in the framework of both general relativity and scalar-tensor theory o...