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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}, 24 pages, 13 figures

We propose a new formalism to handle asymmetric beams in the data analysis of cosmic microwave background anisotropy experiments. For any beam shape, the formalism finds the optimal circularly symmetric equivalent and is thus easily adaptable to existing data analysis methods. We demonstrate certain key points by using a simulated highly elliptic beam, and the beams and data of the MAXIMA-1 experiment, where the asymmetry is mild. In particular, we show that in both cases the formalism does not bias the angular power spectrum estimates. We analyze the limitations of the formalism and find that it is well suited for most practical situations., 41 pages, 13 figures; ApJS in press

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., Replaced to match the published version, only minor changes

Recent results from BOOMERANG-98 and MAXIMA-1, taken together with COBE DMR, provide consistent and high signal-to-noise measurements of the cosmic microwave background power spectrum at spherical harmonic multipole bands over 2

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 $411 \le\ell \le 785.$ 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, $\Omega_b h^2\simeq 0.033{\pm 0.013}$, and the total density, $\Omega=0.9{+0.18\atop -0.16}$. 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.).

The MAXIMA cosmic microwave background anisotropy experiment had a significant impact on cosmology. Results from the program have played a significant role in determining the geometry of the universe, given strong supporting evidence to inflation, and, in combination with other astrophysical data, showed that the universe is filled with dark matter and energy. We present a subset of the internal consistency checks that were carried out on the MAXIMA-1 data prior to their release, which demonstrate that systematics errors were much smaller than statistical errors. We also discuss the MAXIMA-2 flight and data, compare the maps of MAXIMA-1 and -2 in areas where they overlap and show that the two independent experiments confirm each other. All of these results demonstrate that MAXIMA mapped the cosmic microwave background anisotropy with high accuracy, to be published in C.R. Physique, 2003, (Academie des Science), 14 pages, figures embedded, a version with high quality figures is available from http://cosmology.berkeley.edu/maxima/comp_publications.html

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 $\ell(\ell+1)C^{EB}_{\ell}/2��$ 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., 19 pages, 11 figures, 2 tables, submitted to ApJ

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 present results from and the analysis of data from MAXIPOL, a balloon-borne experiment designed to measure the polarization in the Cosmic Microwave Background (CMB). MAXIPOL is the first CMB experiment to obtain results using a rotating half-wave plate as a rapid polarization modulator. We report results from observations of a sky area of 8 deg^2 with 10-arcmin resolution, providing information up to l~700. We use a maximum-likelihood method to estimate maps of the Q and U Stokes parameters from the demodulated time streams, and then both Bayesian and frequentist approaches to compute the EE, EB, and BB power spectra. Detailed formalisms of the analyses are given. A variety of tests show no evidence for systematic errors. The Bayesian analysis gives weak evidence for an EE signal. The EE power is 55^{+51}_{-45} \mu K^2 at the 68% confidence level for l=151-693. Its likelihood function is asymmetric and skewed positive such that with a uniform prior the probability of a positive EE power is 96%. The powers of EB and BB signals at the 68% confidence level are 18^{+27}_{-34} \mu K^2 and -31^{+31}_{-19} \mu K^2 respectively and thus consistent with zero. The upper limit of the BB-mode at the 95% confidence level is 9.5 \mu K. Results from the frequentist approach are in agreement within statistical errors. These results are consistent with the current concordance LCDM model., Comment: 12 pages, 10 figures, 5 tables; ApJ published

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, 22 pages, 22 figures, 13 tables. Submitted to ApJ. More information and figures are available for download at http://cosmology.berkeley.edu/maxima/

MAXIMA is a balloon-borne platform for measuring the anisotropy of the Cosmic Microwave Background (CMB). It has measured the CMB power spectrum with a ten-arcminute FWHM beam, corresponding to a detection of the power spectrum out to spherical harmonic multipole l~1000. The spectrum is consistent with a flat Universe with a nearly scale-invariant initial spectrum of adiabatic density fluctuations. Moreover, the MAXIMA data are free from any notable non-Gaussian contamination and from foreground dust emission. In the same region, the WMAP experiment observes the same structure as that observed by MAXIMA, as evinced by analysis of both maps and power spectra. The next step in the evolution of the MAXIMA program is MAXIPOL, which will observe the polarization of the CMB with comparable resolution and high sensitivity over a small patch of the sky., To appear in New Astronomy Reviews, Proceedings of the CMBNET Meeting, 20-21 February, 2003, Oxford, UK

We discuss MAXIPOL, a bolometric balloon-borne experiment designed to measure the E-mode polarization anisotropy of the cosmic microwave background radiation (CMB) on angular scales of 10 arcmin to 2 degrees. MAXIPOL is the first CMB experiment to collect data with a polarimeter that utilizes a rotating half-wave plate and fixed wire-grid polarizer. We present the instrument design, elaborate on the polarimeter strategy and show the instrument performance during flight with some time domain data. Our primary data set was collected during a 26 hour turnaround flight that was launched from the National Scientific Ballooning Facility in Ft. Sumner, New Mexico in May 2003. During this flight five regions of the sky were mapped. Data analysis is in progress., Comment: 8 pages, 6 figures; To be published in "The Cosmic Microwave Background and its Polarization", New Astronomy Reviews, (eds. S. Hanany and K.A. Olive)

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 version

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_NL

Gaussianity of the cosmological perturbations is one of the key predictions of standard inflation, but it is violated by other models of structure formation such as cosmic defects. We present the first test of the Gaussianity of the cosmic microwave background (CMB) on subdegree angular scales, where deviations from Gaussianity are most likely to occur. We apply the methods of moments, cumulants, the Kolmogorov test, the chi (2) test, and Minkowski functionals in eigen, real, Wiener-filtered, and signal-whitened spaces, to the MAXIMA-1 CMB anisotropy data. We find that the data, which probe angular scales between 10 arcmin and 5 deg, are consistent with Gaussianity. These results show consistency with the standard inflation and place constraints on the existence of cosmic defects.

MAXIMA is a balloon-based bolometric experiment to measure the temperature anisotropy of the CMB over spatial frequency range 36 ≤ l ≤ 1235. The MAXIMA-1 flight produced a 124 square degree temperature anisot0ropy map with a beam diameter of 10 arcmin. These data have been used to produce a power spectrum which is in excellent agreement with data from BOOMERANG and DASI, but covers a wider range of angular scales. The MAXIMA power spectrum is consistent with the prediction of Lambda CDM models and has been used to constrain cosmological models. The MAXIMA experiment is described and an outline is given of the contents and significance of papers written by the MAXIMA team. MAXIMA is being modified to measure the polarization anisotropy of the CMB. A brief description of this MAXIPOL experiment is also given.

We discuss the status of the data obtained from the first two flights of the MAXIMA balloon-borne experiment. MAXIMA is sensitive to CMB fluctuations on angular scales from 10 arcmin to 5 degrees. The instrument uses a 16 element bolometric array with 3 frequency bands centered at 150, 240, and 410 GHz. An angular power spectrum of the CMB anisotropy has been obtained from the data of the first flight, MAXIMA-1, which shows a peak at l∼220 of 78±6 μK and an amplitude varying between 40 μK and 50 μK from 400

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 10\arcmin 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 3\arcmin 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 present a map and an angular power spectrum of the anisotropy of the cosmic microwave background (CMB) from the first flight of MAXIMA. MAXIMA is a balloon-borne experiment with an array of 16 bolometric photometers operated at 100 mK. MAXIMA observed a 124 square degrees region of the sky with 10 arcminute resolution at frequencies of 150, 240 and 410 GHz. The data were calibrated using in-flight measurements of the CMB dipole anisotropy. A map of the CMB anisotropy was produced from three 150 and one 240 GHz photometer without need for foreground subtractions. Analysis of this CMB map yields a power spectrum for the CMB anisotropy over the range 36 < l < 785. The spectrum shows a peak with an amplitude of 78 +/- 6 micro-Kelvin at l ~ 220 and an amplitude varying between ~40 micro-Kelvin and ~50 micro-Kelvin for 400 < l < 785.

We describe the MAXIMA experiment, a balloon-borne measurement designed to map temperature anisotropy in the Cosmic Microwave Background (CMB) over a wide range of angular scales (multipole range 80 < l < 800). The experiment consists of a 1.3 m diameter off-axis Gregorian telescope and a receiver with a 16 element array of bolometers cooled to 100 mK. The frequency bands are centered at 150, 240, and 410 GHz. The 10' FWHM beam sizes are well matched to the scale of acoustic peaks expected in the angular power spectrum of the CMB. The first flight of the experiment in its full configuration was launched in August 1998. A 122 sq-deg map of the sky was made near the Draco constellation during the 7 hour flight in a region of extremely low galactic dust contamination. This map covers 0.3% of the sky and has 3200 independent beamsize pixels. We describe the MAXIMA instrument and its performance during the recent flight., To appear in proceedings of `3K Cosmology', ed. F Melchiorri, Conference held Oct 5-10 1998, Rome, 13 pages LaTeX (using aipproc2.sty & aipproc2.cls), Postscript with higher resolution graphics available at http://cfpa.berkeley.edu/group/cmb/gen.html

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, Comment: 4 pages, 4 figures. Reflects version published on ApJ Letters. Includes erratum (1 page, 2 figures) as published on ApJ Letters