Professor Pedro Ferreira

Abstract:

We consider the most general parametrization of flat topologically compact universes, complementing the work of Scannapieco, Levin and Silk to include non-trivial shapes. We find that modifications in shape of the fundamental domain will lead to distinct signatures in the anisotropy of the cosmic microwave radiation. We make a preliminary assessment of the effect on three statistics: the angular power spectrum, the distribution of identified ``circles'' on the surface of last scattering and the correlation function of antipodal points.

Abstract:

We use a frequentist statistical approach to set confidence intervals on the values of cosmological parameters using the MAXIMA-1 and COBE measurements of the angular power spectrum of the cosmic microwave background. We define a $\Delta \chi^{2}$ statistic, simulate the measurements of MAXIMA-1 and COBE, determine the probability distribution of the statistic, and use it and the data to set confidence intervals on several cosmological parameters. We compare the frequentist confidence intervals to Bayesian credible regions. The frequentist and Bayesian approaches give best estimates for the parameters that agree within 15%, and confidence interval-widths that agree within 30%. The results also suggest that a frequentist analysis gives slightly broader confidence intervals than a Bayesian analysis. The frequentist analysis gives values of \Omega=0.89{+0.26\atop -0.19}, \Omega_{\rm B}h^2=0.026{+0.020\atop -0.011} and n=1.02{+0.31\atop -0.10}, and the Bayesian analysis gives values of \Omega=0.98{+0.14\atop -0.19}, \Omega_{\rm B}h^2=0.0.029{+0.015\atop-0.010}, and $n=1.18{+0.10\atop -0.23}$, all at the 95% confidence level.

Abstract:

We use a frequentist statistical approach to set confidence intervals on the values of cosmological parameters using the MAXIMA-1 and COBE measurements of the angular power spectrum of the cosmic microwave background. We define a Δχ² statistic, simulate the measurements of MAXIMA-1 and COBE, determine the probability distribution of the statistic, and use it and the data to set confidence intervals on several cosmological parameters. We compare the frequentist confidence intervals with Bayesian credible regions. The frequentist and Bayesian approaches give best estimates for the parameters that agree within 15 per cent, and confidence interval widths that agree to within 30 per cent. The results also suggest that a frequentist analysis gives slightly broader confidence intervals than a Bayesian analysis. The frequentist analysis gives values of Ω = 0.89^+0.26-0.19, ΩB h² = 0.026^+0.020-0.011 and n = 1.02^+0.31-0.10 and the Bayesian analysis gives values of Ω = 0.98^+0.14-0.19, ΩB h² = 0.029^+0.015-0.010 and n = 1.18^+0.10-0.23, all at the 95 per cent confidence level.

Abstract:

The measurement of the cosmic microwave background taken during the MAXIMA-1 flight was used to estimate the bispectrum of cosmological perturbations. An estimator for the bispectrum was proposed that appropriated in the flat sky approximation and was applied to the MAXIMA-1 data. This measurement placed constraints on models of the inflation and the bispectrum analysis of the data showed the consistency of the data with Gaussianity.

Abstract:

We use the measurement of the cosmic microwave background taken during the MAXIMA-1 flight to estimate the bispectrum of cosmological perturbations. We propose an estimator for the bispectrum that is appropriate in the flat sky approximation, apply it to the MAXIMA-1 data, and evaluate errors using bootstrap methods. We compare the estimated value with what would be expected if the sky signal were Gaussian and find that it is indeed consistent, with a chi(2) per degree of freedom of approximately unity. This measurement places constraints on models of inflation.