Emory F. Bunn

The Wiener filtered COBE DMR data and predictions for the Tenerife experiment

We apply a Wiener filter to the two-year COBE DMR data. The resulting sky map has significantly reduced noise levels compared to the raw data: the most prominent hot and cold spots are significant at the 4-sigma level. Furthermore, the entire covariance matrix of the errors in the filtered sky map is known, and it is therefore possible to make constrained realizations of the microwave sky with the correct a posteriori probability distribution. The filtered DMR sky map is used to make predictions for the Tenerife experiment. Two prominent features are predicted in a region of the sky not yet analyzed by the Tenerife group. The presence of these features is a robust prediction of the standard cosmological paradigm; if these features are not observed, some of our fundamental assumptions must be incorrect.

How Anisotropic is Our Universe

Large-scale cosmic microwave background anisotropies in homogeneous, globally anisotropic cosmologies are investigated. We perform a statistical analysis in which the 4-yr data from the Cosmic Background Explorer satellite is searched for the specific anisotropy patterns predicted by these models and thereby set definitive upper limits on the amount of shear, ({sigma}/{ital H}){sub 0}, and vorticity, ({omega}/{ital H}){sub 0}, which are orders of magnitude stronger than previous constraints. We find that primordial anisotropy should have been fine tuned to be less than 10{sup {minus}3} of its natural value in the Planck era. {copyright} {ital 1996 The American Physical Society.}

Four-year COBE normalization of inflationary cosmologies

We supply fitting formulas enabling the normalization of slow-roll inflation models to the four-year COBE data. We fully include the effect of the gravitational wave modes, including the predicted relation of the amplitude of these modes to that of the density perturbations. We provide the normalization of the matter power spectrum, which can be directly used for large-scale structure studies. The normalization for tilted spectra is a special case. We also provide fitting functions for the inflationary energy scale of COBE-normalized models and discuss the validity of approximating the spectra by power laws. In an Appendix, we extend our analysis to include models with a cosmological constant, both with and without gravitational waves. {copyright} {ital 1996 The American Physical Society.}

Cosmological-Constant Cold Dark Matter Models and the COBE Two-Year Sky maps

We compare the two-year COBE DMR sky maps with the predictions of cosmological-constant cold dark matter models. Using a Bayesian analysis, we find that the most likely value of the cosmological constant in such a model is Lambda = 0. The data set an upper limit on Lambda of 0.78 (0.85) at 90% confidence, and 0.86 (0.92) at 95% confidence with (without) the quadrupole anisotropy.

QUBIC: The QU Bolometric Interferometer For Cosmology

The primordial B-mode polarisation of the Cosmic Microwave Background is the imprints of the gravitational wave background generated by inflation. Observing the B-mode is up to now the most direct way to constrain the physics of the primordial Universe, especially inflation. To detect these B-modes, high sensitivity is required as well as an exquisite control of systematics effects. To comply with these requirements, we propose a new instrument called QUBIC (Q and U Bolometric Interferometer for Cosmology) based on bolometric interferometry. The control of systematics is obtained with a close-packed interferometer while bolometers cooled to very low temperature allow for high sensitivity. We present the architecture of this new instrument, the status of the project and the self-calibration technique which allows accurate measurement of the instrumental systematic effects.

The kinematic origin of the cosmological redshift

A common belief about big-bang cosmology is that the cosmological redshift cannot be properly viewed as a Doppler shift (that is, as evidence for a recession velocity) but must be viewed in terms of the stretching of space. We argue that, contrary to this view, the most natural interpretation of the redshift is as a Doppler shift, or rather as the accumulation of many infinitesimal Doppler shifts. The stretching-of-space interpretation obscures a central idea of relativity, namely that it is always valid to choose a coordinate system that is locally Minkowskian. We show that an observed frequency shift in any spacetime can be interpreted either as a kinematic (Doppler) shift or a gravitational shift by imagining a suitable family of observers along the photon’s path. In the context of the expanding universe, the kinematic interpretation corresponds to a family of comoving observers and hence is more natural.

The meaning of Einstein’s equation

This is a brief introduction to general relativity, designed for both students and teachers of the subject. While there are many excellent expositions of general relativity, few adequately explain the geometrical meaning of the basic equation of the theory: Einstein’s equation. Here we give a simple formulation of this equation in terms of the motion of freely falling test particles. We also sketch some of the consequences of this formulation and explain how it is equivalent to the usual one in terms of tensors. Finally, we include an annotated bibliography of books, articles, and websites suitable for the student of relativity.

The COBE normalization of CMB anisotropies

With the advent of the COBE detection of fluctuations in the Cosmic Microwave Background radiation, the study of inhomogeneous cosmology has entered a new phase. It is now possible to accurately normalize fluctuations on the largest observable scales, in the linear regime. In this paper we present a model-independent method of normalizing theories to the full COBE data. This technique allows an extremely wide range of theories to be accurately normalized to COBE in a very simple and fast way. We give the best fitting normalization and relative peak likelihoods for a range of spectral shapes, and discuss the normalization for several popular theories. Additionally we present both Bayesian and frequentist measures of the goodness of fit of a representative range of theories to the COBE data.

The COBE normalization for standard cold dark matter

The Cosmic Background Explorer Satellite (COBE) detection of microwave anisotropies provides the best way of fixing the amplitude of cosmological fluctuations on the largest scales. This normalization is usually given for an n = 1 spectrum, including only the anisotropy caused by the Sachs-Wolfe effect. This is certainly not a good approximation for a model containing any reasonable amount of baryonic matter. In fact, even tilted Sachs-Wolfe spectra are not a good fit to models like cold dark matter (CDM). Here, we normalize standard CDM (sCDM) to the two-year COBE data and quote the best amplitude in terms of the conventionally used measures of power. We also give normalizations for some specific variants of this standard model, and we indicate how the normalization depends on the assumed values on n, Omega(sub B) and H(sub 0). For sCDM we find the mean value of Q = 19.9 +/- 1.5 micro-K, corresponding to sigma(sub 8) = 1.34 +/- 0.10, with the normalization at large scales being B = (8.16 +/- 1.04) x 10(exp 5)(Mpc/h)(exp 4), and other numbers given in the table. The measured rms temperature fluctuation smoothed on 10 deg is a little low relative to this normalization. This is mainly due to the low quadrupole in the data: when the quadrupole is removed, the measured value of sigma(10 deg) is quite consistent with the best-fitting the mean value of Q. The use of the mean value of Q should be preferred over sigma(10 deg), when its value can be determined for a particular theory, since it makes full use of the data.

Wiener filtering of the COBE Differential Microwave Radiometer data

We derive an optimal linear filter to suppress the noise from the COBE DMR sky maps for a given power spectrum. We then apply the filter to the first-year DMR data, after removing pixels within