arXiv subjects

Sebastian Dorn

Publications and source records attributed to Sebastian Dorn.

22 records · Page 2Linked to original sources

arXiv2014

Generic inference of inflation models by local non-Gaussianity

The presence of multiple fields during inflation might seed a detectable amount of non-Gaussianity in the curvature perturbations, which in turn becomes observable in present data sets like the cosmic microwave background (CMB) or the large scale structure (LSS). Within this proceeding we present a fully analytic method to infer inflationary parameters from observations by exploiting higher-order statistics of the curvature perturbations. To keep this analyticity, and thereby to dispense with numerically expensive sampling techniques, a saddle-point approximation is introduced whose precision has been validated for a numerical toy example. Applied to real data, this approach might enable to discriminate among the still viable models of inflation.

astro-ph.CO↗

arXiv2014

Generic inference of inflation models by non-Gaussianity and primordial power spectrum reconstruction

We present a generic inference method for inflation models from observational data by the usage of higher-order statistics of the curvature perturbation on uniform density hypersurfaces. This method is based on the calculation of the posterior for the primordial non-Gaussianity parameters $f_\text{NL}$ and $g_\text{NL}$, which in general depend on specific parameters of inflation and reheating models, and enables to discriminate among the still viable inflation models. To keep analyticity as far as possible to dispense with numerically expensive sampling techniques a saddle-point approximation is introduced, whose precision is validated for a numerical toy example. The mathematical formulation is done in a generic way so that the approach remains applicable to cosmic microwave background data as well as to large scale structure data. Additionally, we review a few currently interesting inflation models and present numerical toy examples thereof in two and three dimensions to demonstrate the efficiency of the higher-order statistics method. A second quantity of interest is the primordial power spectrum. Here, we present two Bayesian methods to infer it from observational data, the so called critical filter and an extension thereof with smoothness prior, both allowing for a non-parametric spectrum reconstruction. These methods are able to reconstruct the spectra of the observed perturbations and the primordial ones of curvature perturbation even in case of non-Gaussianity and partial sky coverage. We argue that observables like $T-$ and $B-$modes permit to measure both spectra. This also allows to infer the level of non-Gaussianity generated since inflation.

astro-ph.CO↗

arXiv2013

Fast and precise way to calculate the posterior for the local non-Gaussianity parameter $f_\text{nl}$ from cosmic microwave background observations

We present an approximate calculation of the full Bayesian posterior probability distribution for the local non-Gaussianity parameter $f_{\text{nl}}$ from observations of cosmic microwave background anisotropies within the framework of information field theory. The approximation that we introduce allows us to dispense with numerically expensive sampling techniques. We use a novel posterior validation method (DIP test) in cosmology to test the precision of our method. It transfers inaccuracies of the calculated posterior into deviations from a uniform distribution for a specially constructed test quantity. For this procedure we study toy cases that use one- and two-dimensional flat skies, as well as the full spherical sky. We find that we are able to calculate the posterior precisely under a flat-sky approximation, albeit not in the spherical case. We argue that this is most likely due to an insufficient precision of the used numerical implementation of the spherical harmonic transform, which might affect other non-Gaussianity estimators as well. Furthermore, we present how a nonlinear reconstruction of the primordial gravitational potential on the full spherical sky can be obtained in principle. Using the flat-sky approximation, we find deviations for the posterior of $f_{\text{nl}}$ from a Gaussian shape that become more significant for larger values of the underlying true $f_{\text{nl}}$. We also perform a comparison to the well-known estimator of Komatsu et al. [Astrophys. J. 634, 14 (2005)] and finally derive the posterior for the local non-Gaussianity parameter $g_{\text{nl}}$ as an example of how to extend the introduced formalism to higher orders of non-Gaussianity.

astro-ph.CO↗

arXiv2013

Diagnostics for insufficiencies of posterior calculations in Bayesian signal inference

We present an error-diagnostic validation method for posterior distributions in Bayesian signal inference, an advancement of a previous work. It transfers deviations from the correct posterior into characteristic deviations from a uniform distribution of a quantity constructed for this purpose. We show that this method is able to reveal and discriminate several kinds of numerical and approximation errors, as well as their impact on the posterior distribution. For this we present four typical analytical examples of posteriors with incorrect variance, skewness, position of the maximum, or normalization. We show further how this test can be applied to multidimensional signals.

astro-ph.IM↗