Cosmological Parameter Estimation: Method

CMB anisotropy data could put powerful constraints on theories of the evolution of our Universe. Using the observations of the large number of CMB experiments, many studies have put constraints on cosmological parameters assuming different frameworks. Assuming for example inflationary paradigm, one can compute the confidence intervals on the different components of the energy densities, or the age of the Universe, inferred by the current set of CMB observations. The aim of this note is to present some of the available methods to derive the cosmological parameters with their confidence intervals from the CMB data, as well as some practical issues to investigate large number of parameters

Efficient Cosmological Parameter Estimation from Microwave Background Anisotropies

We revisit the issue of cosmological parameter estimation in light of current and upcoming high-precision measurements of the cosmic microwave background power spectrum. Physical quantities which determine the power spectrum are reviewed, and their connection to familiar cosmological parameters is explicated. We present a set of physical parameters, analytic functions of the usual cosmological parameters, upon which the microwave background power spectrum depends linearly (or with some other simple dependence) over a wide range of parameter values. With such a set of parameters, microwave background power spectra can be estimated with high accuracy and negligible computational effort, vastly increasing the efficiency of cosmological parameter error determination. The techniques presented here allow calculation of microwave background power spectra $10^5$ times faster than comparably accurate direct codes (after precomputing a handful of power spectra). We discuss various issues of parameter estimation, including parameter degeneracies, numerical precision, mapping between physical and cosmological parameters, and systematic errors, and illustrate these considerations with an idealized model of the MAP experiment.Comment: 22 pages, 12 figure

Testing cosmological models and understanding cosmological parameter determinations with metaparameters

Cosmological parameters affect observables in physically distinct ways. For example, the baryon density, omega_b, affects the ionization history and also the pressure of the pre-recombination fluid. To investigate the relative importance of different physical effects to the determination of omega_b, and to test the cosmological model, we artificially split omega_b into two `metaparameters': omega_{be} which controls the ionization history and omega_{bp} which plays the role of omega_b for everything else. In our demonstration of the technique we find omega_b = .0229 +/- .0012 (with no parameter splitting), omega_{bp} = .0238 +/- .0021, omega_{be}= .0150 +/- .0034 and omega_{bp}-omega_{be} = .0088 +/- .0039.Comment: 5 pages, submitted to Ap

Thick Domain Walls in AdS Black Hole Spacetimes

Equations of motion for a real self-gravitating scalar field in the background of a black hole with negative cosmological constant were solved numerically. We obtain a sequence of static axisymmetric solutions representing thick domain wall cosmological black hole systems, depending on the mass of black hole, cosmological parameter and the parameter binding black hole mass with the width of the domain wall. For the case of extremal cosmological black hole the expulsion of scalar field from the black hole strongly depends on it.Comment: 20 pages, 19 figures, accepted for publication in Phys. Rev.

Gravitational waves during inflation in presence of a decaying cosmological parameter from a 5D vacuum theory of gravity

We study gravitational waves generated during the inflationary epoch in presence of a decaying cosmological parameter on a 5D geometrical background which is Riemann flat. Two examples are considered, one with a constant cosmological parameter and the second with a decreasing one.Comment: accepted in Phys. Lett.

Precise cosmological parameter estimation using CosmoRec

We use the new cosmological recombination code, CosmoRec, for parameter estimation in the context of (future) precise measurements of the CMB temperature and polarization anisotropies. We address the question of how previously neglected physical processes in the recombination model of Recfast affect the determination of key cosmological parameters, for the first time performing a model-by-model computation of the recombination problem. In particular we ask how the biases depend on different combinations of parameters, e.g. when varying the helium abundance or the effective number of neutrino species in addition to the standard six parameters. We also forecast how important the recombination corrections are for a combined Planck, ACTPol and SPTpol data analysis. Furthermore, we ask which recombination corrections are really crucial for CMB parameter estimation, and whether an approach based on a redshift-dependent correction function to Recfast is sufficient in this context.Comment: 12 pages, 7 figures, submitted to MNRA

Cosmological parameter inference with Bayesian statistics

Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In this paper, we review some fundamental concepts to understand Bayesian statistics and then introduce MCMC algorithms and samplers that allow us to perform the parameter inference procedure. We also introduce a general description of the standard cosmological model, known as the $\Lambda$CDM model, along with several alternatives, and current datasets coming from astrophysical and cosmological observations. Finally, with the tools acquired, we use an MCMC algorithm implemented in python to test several cosmological models and find out the combination of parameters that best describes the Universe.Comment: 30 pages, 17 figures, 5 tables; accepted for publication in Universe; references adde

C_l interpolation for cosmological parameter estimation

I will briefly present my work on cosmological parameters estimation. Classical methods for parameters estimation involve the exploration of the parameter space on a precalculated grid of cosmological models. Here we try to estimate the cosmological parameters by using a minimization method associated with the interpolation of the C_l spectrum. We first use a simple multidimensional linear interpolation, and show the flaws of this method. We then introduce a new interpolation method, based on a physical description of the location of the acoustic peaks in the power spectrumComment: Proceeding XV rencontres de Blois, june 2003. 4 page

Bounding the Hubble flow in terms of the w parameter

The last decade has seen increasing efforts to circumscribe and bound the cosmological Hubble flow in terms of model-independent constraints on the cosmological fluid - such as, for instance, the classical energy conditions of general relativity. Quite a bit can certainly be said in this regard, but much more refined bounds can be obtained by placing more precise constraints (either theoretical or observational) on the cosmological fluid. In particular, the use of the w-parameter (w=p/rho) has become increasingly common as a surrogate for trying to say something about the cosmological equation of state. Herein we explore the extent to which a constraint on the w-parameter leads to useful and nontrivial constraints on the Hubble flow, in terms of constraints on density rho(z), Hubble parameter H(z), density parameter Omega(z), cosmological distances d(z), and lookback time T(z). In contrast to other partial results in the literature, we carry out the computations for arbitrary values of the space curvature k in [-1,0,+1], equivalently for arbitrary Omega_0 <= 1.Comment: 15 page