Frequentist Estimation of Cosmological Parameters from the MAXIMA-1 Cosmic Microwave Background Anisotropy Data

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.Comment: 10 pages, 9 Postscript figures, changes made to reflect published versio

The EBEX Experiment

EBEX is a balloon-borne polarimeter designed to measure the intensity and polarization of the cosmic microwave background radiation. The measurements would probe the inflationary epoch that took place shortly after the big bang and would significantly improve constraints on the values of several cosmological parameters. EBEX is unique in its broad frequency coverage and in its ability to provide critical information about the level of polarized Galactic foregrounds which will be necessary for all future CMB polarization experiments. EBEX consists of a 1.5 m Dragone-type telescope that provides a resolution of less than 8 arcminutes over four focal planes each of 4 degree diffraction limited field of view at frequencies up to 450 GHz. The experiment is designed to accommodate 330 transition edge bolometric detectors per focal plane, for a total of up to 1320 detectors. EBEX will operate with frequency bands centered at 150, 250, 350, and 450 GHz. Polarimetry is achieved with a rotating achromatic half-wave plate. EBEX is currently in the design and construction phase, and first light is scheduled for 2008.Comment: 13 pages, 10 figures. Figure 1 is changed from the one which appeared in the Proceedings of the SPI

MAX 4 and MAX 5 CMB anisotropy measurement constraints on open and flat-Lambda CDM cosmogonies

We account for experimental and observational uncertainties in likelihood analyses of cosmic microwave background (CMB) anisotropy data from the MAX 4 and MAX 5 experiments. These analyses use CMB anisotropy spectra predicted in open and spatially-flat Lambda cold dark matter cosmogonies. Amongst the models considered, the combined MAX data set is most consistent with the CMB anisotropy shape in Omega_0 ~ 0.1-0.2 open models and less so with that in old (t_0 >~ 15 - 16 Gyr, i.e., low h), high baryon density (Omega_B >~ 0.0175/h^2), low density (Omega_0 ~ 0.2 - 0.4), flat-Lambda models. The MAX data alone do not rule out any of the models we consider at the 2-sigma level. Model normalizations deduced from the combined MAX data are consistent with those drawn from the UCSB South Pole 1994 data, except for the flat bandpower model where MAX favours a higher normalization. The combined MAX data normalization for open models with Omega_0 ~ 0.1-0.2 is higher than the upper 2-sigma value of the DMR normalization. The combined MAX data normalization for old (low h), high baryon density, low-density flat-Lambda models is below the lower 2-sigma value of the DMR normalization. Open models with Omega_0 ~ 0.4-0.5 are not far from the shape most favoured by the MAX data, and for these models the MAX and DMR normalizations overlap. The MAX and DMR normalizations also overlap for Omega_0 = 1 and some higher h, lower Omega_B, low-density flat-Lambda models.Comment: Latex, 37 pages, uses aasms4 styl

Supernovae Ia Constraints on a Time-Variable Cosmological "Constant"

The energy density of a scalar field $\phi$ with potential $V(\phi) \propto \phi^{-\alpha}$, $\alpha > 0$, behaves like a time-variable cosmological constant that could contribute significantly to the present energy density. Predictions of this spatially-flat model are compared to recent Type Ia supernovae apparent magnitude versus redshift data. A large region of model parameter space is consistent with current observations. (These constraints are based on the exact scalar field model equations of motion, not on the widely used time-independent equation of state fluid approximation equations of motion.) We examine the consequences of also incorporating constraints from recent measurements of the Hubble parameter and the age of the universe in the constant and time-variable cosmological constant models. We also study the effect of using a non-informative prior for the density parameter.Comment: Accepted for publication in Ap

MAXIPOL: Cosmic Microwave Background Polarimetry Using a Rotating Half-Wave Plate

We discuss MAXIPOL, a bolometric balloon-borne experiment designed to measure the E-mode polarization of the cosmic microwave background radiation (CMB). MAXIPOL is the first bolometric CMB experiment to observe the sky using rapid polarization modulation. To build MAXIPOL, the CMB temperature anisotropy experiment MAXIMA was retrofitted with a rotating half-wave plate and a stationary analyzer. We describe the instrument, the observations, the calibration and the reduction of data collected with twelve polarimeters operating at 140 GHz and with a FWHM beam size of 10 arcmin. We present maps of the Q and U Stokes parameters of an 8 deg^2 region of the sky near the star Beta Ursae Minoris. The power spectra computed from these maps give weak evidence for an EE signal. The maximum-likelihood amplitude of l(l+1)C^{EE}_{l}/(2 pi) is 55_{-45}^{+51} uK^2 (68%), and the likelihood function is asymmetric and skewed positive such that with a uniform prior the probability that the amplitude is positive is 96%. This result is consistent with the expected concordance LCDM amplitude of 14 uK^2. The maximum likelihood amplitudes for l(l+1)C^{BB}_{l}/(2 pi) and $\ell(\ell+1)C^{EB}_{\ell}/2\pi$ are -31_{-19}^{+31} and 18_{-34}^{+27} uK^2 (68%), respectively, which are consistent with zero. All of the results are for one bin in the range 151 < l < 693. Tests revealed no residual systematic errors in the time or map domain. A comprehensive discussion of the analysis of the data is presented in a companion paper.Comment: 19 pages, 11 figures, 2 tables, submitted to Ap

Determining Foreground Contamination in CMB Observations: Diffuse Galactic Emission in the MAXIMA-I Field

Observations of the CMB can be contaminated by diffuse foreground emission from sources such as Galactic dust and synchrotron radiation. In these cases, the morphology of the contaminating source is known from observations at different frequencies, but not its amplitude at the frequency of interest for the CMB. We develop a technique for accounting for the effects of such emission in this case, and for simultaneously estimating the foreground amplitude in the CMB observations. We apply the technique to CMB data from the MAXIMA-1 experiment, using maps of Galactic dust emission from combinations of IRAS and DIRBE observations, as well as compilations of Galactic synchrotron emission observations. The spectrum of the dust emission over the 150--450 GHz observed by MAXIMA is consistent with preferred models but the effect on CMB power spectrum observations is negligible.Comment: 19 pages, 8 figures, accepted for publication in the Astrophysical Journal. Monor changes to match the published versio

Estimate of the Cosmological Bispectrum from the MAXIMA-1 Cosmic Microwave Background Map

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.Comment: 5 pages, 2 figures. New version to match paper accepted for publication in Phys. Rev. Lett. Non-diagonal terms included leading to new limits on f_N

Dark energy perturbations and cosmic coincidence

While there is plentiful evidence in all fronts of experimental cosmology for the existence of a non-vanishing dark energy (DE) density \rho_D in the Universe, we are still far away from having a fundamental understanding of its ultimate nature and of its current value, not even of the puzzling fact that \rho_D is so close to the matter energy density \rho_M at the present time (i.e. the so-called "cosmic coincidence" problem). The resolution of some of these cosmic conundrums suggests that the DE must have some (mild) dynamical behavior at the present time. In this paper, we examine some general properties of the simultaneous set of matter and DE perturbations (\delta\rho_M, \delta\rho_D) for a multicomponent DE fluid. Next we put these properties to the test within the context of a non-trivial model of dynamical DE (the LXCDM model) which has been previously studied in the literature. By requiring that the coupled system of perturbation equations for \delta\rho_M and \delta\rho_D has a smooth solution throughout the entire cosmological evolution, that the matter power spectrum is consistent with the data on structure formation and that the "coincidence ratio" r=\rho_D/\rho_M stays bounded and not unnaturally high, we are able to determine a well-defined region of the parameter space where the model can solve the cosmic coincidence problem in full compatibility with all known cosmological data.Comment: Typos correcte

Making Maps Of The Cosmic Microwave Background: The MAXIMA Example

This work describes Cosmic Microwave Background (CMB) data analysis algorithms and their implementations, developed to produce a pixelized map of the sky and a corresponding pixel-pixel noise correlation matrix from time ordered data for a CMB mapping experiment. We discuss in turn algorithms for estimating noise properties from the time ordered data, techniques for manipulating the time ordered data, and a number of variants of the maximum likelihood map-making procedure. We pay particular attention to issues pertinent to real CMB data, and present ways of incorporating them within the framework of maximum likelihood map-making. Making a map of the sky is shown to be not only an intermediate step rendering an image of the sky, but also an important diagnostic stage, when tests for and/or removal of systematic effects can efficiently be performed. The case under study is the MAXIMA data set. However, the methods discussed are expected to be applicable to the analysis of other current and forthcoming CMB experiments.Comment: Replaced to match the published version, only minor change

Multiple Methods for Estimating the Bispectrum of the Cosmic Microwave Background with Application to the MAXIMA Data

We describe different methods for estimating the bispectrum of Cosmic Microwave Background data. In particular we construct a minimum variance estimator for the flat-sky limit and compare results with previously-studied frequentist methods. Application to the MAXIMA dataset shows consistency with primordial Gaussianity. Weak quadratic non-Gaussianity is characterised by a tunable parameter $f_{NL}$, corresponding to non-Gaussianity at a level $\sim 10^{-5}f_{NL}$ (ratio of non-Gaussian to Gaussian terms), and we find limits of $|f_{NL}|<950$ for the minimum-variance estimator and $|f_{NL}|<1650$ for the usual frequentist estimator. These are the tightest limits on primordial non-Gaussianity which include the full effects of the radiation transfer function.Comment: 24 pages, 13 figure