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

Physical effects of the Immirzi parameter

The Immirzi parameter is a constant appearing in the general relativity action used as a starting point for the loop quantization of gravity. The parameter is commonly believed not to show up in the equations of motion, because it appears in front of a term in the action that vanishes on shell. We show that in the presence of fermions, instead, the Immirzi term in the action does not vanish on shell, and the Immirzi parameter does appear in the equations of motion. It determines the coupling constant of a four-fermion interaction. Therefore the Immirzi parameter leads to effects that are observable in principle, even independently from nonperturbative quantum gravity.Comment: 3 pages. Substantial revision from the first versio

An equation of state for purely kinetic k-essence inspired by cosmic topological defects

We investigate the physical properties of a purely kinetic k-essence model with an equation of state motivated in superconducting membranes. We compute the equation of state parameter $w$ and discuss its physical evolution via a nonlinear equation of state. Using the adiabatic speed of sound and energy density, we restrict the range of parameters of the model in order to have an acceptable physical behavior. Furthermore, we analyze the evolution of the luminosity distance $d_{L}$ with redshift $z$ by comparing (normalizing) it with the $\Lambda$CDM model. Since the equation of state parameter is $z$-dependent the evolution of the luminosity distance is also analyzed using the Alcock-Paczy\'{n}ski test.Comment: 19 pages, 13 figures, typos corrected and references adde

Continuous replica-symmetry breaking in mean-field spin-glass models: Perturbation expansion without the replica trick

The full mean-field solution of spin glass models with a continuous order-parameter function is not directly available and approximate schemes must be used to assess its properties. The averaged physical quantities are to be represented via the replica trick and the limit to zero number of replicas is to be performed for each of them. To avoid this we introduce a perturbation expansion for a mean-field free-energy functional with a continuous order-parameter function without the need to refer to the replica trick. The expansion can be used to calculate all physical quantities in all mean-field spin-glass models and at all temperatures, including zero temperature. The small expansion parameter is a difference between the continuous order-parameter function and the corresponding order parameter from the solution with one level of replica-symmetry breaking. The first correction beyond the approximation with one level of replica-symmetry breaking is explicitly evaluated in the glassy phase of the Sherrington-Kirkpatrick model.Comment: 13 pages, 7 figure

Positive Equation-of-state Parameter in the Accelerating Dilaton Cosmology

In a semiclassically quantized two-dimensional cosmological model, it can be shown that the parameter of the equation of state for the accelerating universe can be positive due to the negative energy density and the negative pressure, which is a little different from the conventional wisdom that the parameter is negative with the positivity of the energy density. Furthermore, we show that the full parameter composed of the classical and the quantum-mechanical contributions is positive and finite even though the partial state parameter from the quantum-mechanical contribution is not positive definite, which means that the state parameter is not perturbatively additive in this model.Comment: 9 pages, 4 figures; to appear in the Journal of Korean Physical Societ

Some Exact Results on the Ultrametric Overlap Distribution in Mean Field Spin Glass Models (I)

The mean field spin glass model is analyzed by a combination of mathematically rigororous methods and a powerful Ansatz. The method exploited is general, and can be applied to others disordered mean field models such as, e.g., neural networks. It is well known that the probability measure of overlaps among replicas carries the whole physical content of these models. A functional order parameter of Parisi type is introduced by rigorous methods, according to previous works by F. Guerra. By the Ansatz that the functional order parameter is the correct order parameter of the model, we explicitly find the full overlap distribution. The physical interpretation of the functional order parameter is obtained, and ultrametricity of overlaps is derived as a natural consequence of a branching diffusion process. It is shown by explicit construction that ultrametricity of the 3-replicas overlap distribution together with the Ghirlanda-Guerra relations determines the distribution of overlaps among s replicas, for any s, in terms of the one-overlap distribution.Comment: 17 pages, submitted to Euro. Phys. Jou. B Direc

LRS Bianchi type-I cosmological model with constant deceleration parameter in f(R,T)f(R,T) gravity

A spatially homogeneous anisotropic LRS Bianchi type-I cosmological model is studied in $f(R,T)$ gravity with a special form of Hubble's parameter, which leads to constant deceleration parameter. The parameters involved in the considered form of Hubble parameter can be tuned to match, our models with the $\Lambda$CDM model. With the present observed value of the deceleration parameter, we have discussed physical and kinematical properties of a specific model. Moreover, we have discussed the cosmological distances for our model.Comment: Published versio