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Register a new userFrequentist Estimation of Cosmological Parameters from the MAXIMA-1 Cosmic Microwave Background Anisotropy Data
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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{+0.26atop -0.19}, Omega_{rm B}h^2=0.026{+0.020atop -0.011} and n=1.02{+0.31atop -0.10}, and the Bayesian analysis gives values of Omega=0.98{+0.14atop -0.19}, Omega_{rm B}h^2=0.0.029{+0.015atop-0.010}, and $n=1.18{+0.10atop -0.23}$, all at the 95% confidence level.
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We extend the analysis of the MAXIMA-1 cosmic microwave background (CMB) data to smaller angular scales. MAXIMA, a bolometric balloon experiment, mapped a 124 deg$^2$ region of the sky with 10arcmin resolution at frequencies of 150, 240 and 410 GHz during its first flight. The original analysis, which covered the multipole range $36 leq ell leq 785$, is extended to $ell = 1235$ using data from three 150 GHz photometers in the fully cross-linked central 60 deg$^2$ of the map. The main improvement over the original analysis is the use of 3arcmin square pixels in the calculation of the map. The new analysis is consistent with the original for $ell < 785$. For $ell > 785$, where inflationary models predict a third acoustic peak, the new analysis shows power with an amplitude of $56 pm 7$ microk at $ell simeq 850$ in excess to the average power of $42 pm 3$ microk in the range $441 < ell < 785$.
We discuss the cosmological implications of the new constraints on the power spectrum of the Cosmic Microwave Background Anisotropy derived from a new high resolution analysis of the MAXIMA-1 measurement (Lee et al. 2001). The power spectrum shows excess power at $ell sim 860$ over the average level of power at $411 leell le 785.$ This excess is statistically significant on the 95% confidence level. Such a feature is consistent with the presence of a third acoustic peak, which is a generic prediction of inflation-based models. The height and the position of the excess power match the predictions of a family of inflationary models with cosmological parameters that are fixed to fit the CMB data previously provided by BOOMERANG-LDB and MAXIMA-1 experiments (e.g., Jaffe et al.2001). Our results, therefore, lend support for inflationary models and more generally for the dominance of coherent perturbations in the structure formation of the Universe. At the same time, they seem to disfavor a large variety of the non-standard (but still inflation-based) models that have been proposed to improve the quality of fits to the CMB data and consistency with other cosmological observables. Within standard inflationary models, our results combined with the COBE-DMR data give best fit values and 95% confidence limits for the baryon density, $Omega_b h^2simeq 0.033{pm 0.013}$, and the total density, $Omega=0.9{+0.18atop -0.16}$. The primordial spectrum slope ($n_s$) and the optical depth to the last scattering surface ($tau_c$) are found to be degenerate and to obey the relation $n_s simeq 0.46 tau_c + (0.99 pm 0.14)$, for $tau_c le 0.5$ (all 95% c.l.).
We describe the Millimeter wave Anisotropy eXperiment IMaging Array (MAXIMA), a balloon-borne experiment designed to measure the temperature anisotropy of the Cosmic Microwave Background (CMB) on angular scales of 10 to 5 degrees . MAXIMA mapped the CMB using 16 bolometric detectors in spectral bands centered at 150 GHz, 240 GHz, and 410 GHz, with 10 resolution at all frequencies. The combined receiver sensitivity to CMB anisotropy was ~40 microK/rt(sec). Systematic parasitic contributions were minimized by using four uncorrelated spatial modulations, thorough crosslinking, multiple independent CMB observations, heavily baffled optics, and strong spectral discrimination. Pointing reconstruction was accurate to 1, and absolute calibration was better than 4%. Two MAXIMA flights with more than 8.5 hours of CMB observations have mapped a total of 300 deg^2 of the sky in regions of negligible known foreground emission. MAXIMA results have been released in previous publications. MAXIMA maps, power spectra and correlation matrices are publicly available at http://cosmology.berkeley.edu/maxima
We cross-correlate the cosmic microwave background temperature anisotropy maps from the WMAP, MAXIMA-I, and MAXIMA-II experiments. We use the cross-spectrum, which is the spherical harmonic transform of the angular two-point correlation function, to quantify the correlation as a function of angular scale. We find that the three possible pairs of cross-spectra are in close agreement with each other and with the power spectra of the individual maps. The probability that there is no correlation between the maps is smaller than 1 * 10^(-8). We also calculate power spectra for maps made of differences between pairs of maps, and show that they are consistent with no signal. The results conclusively show that the three experiments not only display the same statistical properties of the CMB anisotropy, but also detect the same features wherever the observed sky areas overlap. We conclude that the contribution of systematic errors to these maps is negligible and that MAXIMA and WMAP have accurately mapped the cosmic microwave background anisotropy.
We set new constraints on a seven-dimensional space of cosmological parameters within the class of inflationary adiabatic models. We use the angular power spectrum of the cosmic microwave background measured over a wide range of ell in the first flight of the MAXIMA balloon-borne experiment (MAXIMA-1) and the low ell results from COBE/DMR. We find constraints on the total energy density of the universe, Omega=1.0^{+0.15}_{-0.30}, the physical density of baryons, Omega_{b}h^2=0.03 +/- 0.01, the physical density of cold dark matter, Omega_{cdm}h^2=0.2^{+0.2}_{-0.1}$, and the spectral index of primordial scalar fluctuations, n_s=1.08+/-0.1, all at the 95% confidence level. By combining our results with measurements of high-redshift supernovae we constrain the value of the cosmological constant and the fractional amount of pressureless matter in the universe to 0.45<Omega_Lambda<0.75 and 0.25<Omega_{m}<0.50, at the 95% confidence level. Our results are consistent with a flat universe and the shape parameter deduced from large scale structure, and in marginal agreement with the baryon density from big bang nucleosynthesis.
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