Precise Estimation of Cosmological Parameters Using a More Accurate Likelihood Function

The estimation of cosmological parameters from a given data set requires a construction of a likelihood function which, in general, has a complicated functional form. We adopt a Gaussian copula and constructed a copula likelihood function for the convergence power spectrum from a weak lensing survey. We show that the parameter estimation based on the Gaussian likelihood erroneously introduces a systematic shift in the confidence region, in particular for a parameter of the dark energy equation of state w. Thus, the copula likelihood should be used in future cosmological observations.Comment: 5 pages, 3 figures. Maches version published by the Physical Review Letter

Constraints on the Evolution of the Primordial Magnetic Field from the Small-Scale Cosmic Microwave Background Angular Anisotropy

Recent observations of the cosmic microwave background (CMB) have extended the measured power spectrum to higher multipoles $l\gtrsim$1000, and there appears to be possible evidence for excess power on small angular scales. The primordial magnetic field (PMF) can strongly affect the CMB power spectrum and the formation of large scale structure. In this paper, we calculate the CMB temperature anisotropies generated by including a power-law magnetic field at the photon last-scattering surface (PLSS). We then deduce an upper limit on the PMF based on our theoretical analysis of the power excess on small angular scales. We have taken into account several important effects such as the modified matter sound speed in the presence of a magnetic field. An upper limit to the field strength of $|B_\lambda|\lesssim$ 4.7 nG at the present scale of 1 Mpc is deduced. This is obtained by comparing the calculated theoretical result including the Sunyaev-Zeldovich (SZ) effect with recent observed data on the small-scale CMB anisotropies from the $Wilkinson Microwave Anisotropy Probe$ (WMAP), the Cosmic Background Imager (CBI), and the Arcminute Cosmology Bolometer Array Receiver (ACBAR). We discuss several possible mechanisms for the generation and evolution of the PMF.Comment: 27 pages, 4 figures, accepted to ApJ April 10, 200

Constraining the Primordial Magnetic Field from Cosmic Microwave Background Anisotropies at Higher Multipoles

The cosmological magnetic field is one of the important physical quantities which affect strongly the cosmic microwave background (CMB) power spectrum. Recent CMB observations have been extended to higher multipoles $l\gtrsim$1000, and they resultantly exhibit an excess power than the standard model prediction in cosmological theory which best fits the Wilkinson Microwave Anisotropy Probe (WMAP) data at lower multipoles $l\lesssim$900. We calculate the CMB temperature anisotropies generated by the power-law magnetic field at the last scattering surface (LSS) in order to remove the tension between theory and observation at higher multipoles and also place an upper limit on primordial magnetic field. In our present calculation we take account of the effect of ionization ratio exactly without approximation. This effect is very crucial to precisely estimate the effect of the magnetic field on CMB power spectrum. We consider both effects of the scalar and vector modes of magnetic field on the CMB anisotropies, where current data are known to be insensitive to the tensor mode which we ignore in the present study. In order to constrain the primordial magnetic field, we evaluate likelihood function of the WMAP data in a wide range of parameters of the magnetic field strength $|\mathbf{B}|_\lambda$ and the power-law spectral index $n$, along with six cosmological parameters in flat Universe models, using the technique of the Markov Chain Monte Carlo(MCMC) method. We find that the upper limit at $2\sigma$ C.L. turns out to be $|\mathbf{B}_\lambda|\lesssim 3.9$nG at 1 Mpc for any $n_B$ values, which is obtained by comparing the calculated result including the Sunyaev-Zeldovich(SZ) effect with recent WMAP data of the CMB anisotropies.Comment: 10 pages, 1 figures, 1 table, accepted to ApJ Letter April 13, 200

Effects of a primordial magnetic field with log-normal distribution on the cosmic microwave background

We study the effect of primordial magnetic fields (PMFs) on the anisotropies of the cosmic microwave background (CMB). We assume the spectrum of PMFs is described by log-normal distribution which has a characteristic scale, rather than power-law spectrum. This scale is expected to reflect the generation mechanisms and our analysis is complementary to previous studies with power-law spectrum. We calculate power spectra of energy density and Lorentz force of the log-normal PMFs, and then calculate CMB temperature and polarization angular power spectra from scalar, vector, and tensor modes of perturbations generated from such PMFs. By comparing these spectra with WMAP7, QUaD, CBI, Boomerang, and ACBAR data sets, we find that the current CMB data set places the strongest constraint at $k\simeq 10^{-2.5}$ Mpc$^{-1}$ with the upper limit $B\lesssim 3$ nG.Comment: 14 pages, 6 figure