COBE DMR Research Articles

How the CMB Anisotropy Pattern Could Be a Map of Gravitational Entropy

The rationale for Flat Space Cosmology (FSC) calculations of gravitational entropy in the form ofis presented. These calculations indicate a tight correlation with the COBE DMR measurement showing CMB RMS temperature variations of 18 micro Kelvins. The COBE dT/T anisotropy ratio of 0.66 × 10−5 falls within the FSC gravitational entropy range calculated for the beginning and ending conditions of the recombination/decoupling epoch. Thus, the FSC model incorporating gravity as an emergent property of entropy suggests that the CMB temperature anisotropy pattern could simply be a map of gravitational entropy, as opposed to a magnified “quantum fluctuation” event at a finite beginning of time.

Constraints on the Tensor Mode from Large Scale Structure Observations

Observational data on the large scale structure (LSS) of the Universe are used to establish an upper limit for the amplitude of the tensor mode marginalized over all other cosmological parameters within the class of adiabatic inflationary models. It is shown that the upper 1σ limit for the contribution of a tensor mode to the COBE DMR data is T/S < 1.

The WMAP data and results

The Wilkinson Microwave Anisotropy Probe (WMAP) science team has released results from the first year of operation at the Earth–Sun L 2 Lagrange point. The maps are consistent with previous observations but have much better sensitivity and angular resolution than the COBE DMR maps, and much better calibration accuracy and sky coverage than ground-based and balloon-borne experiments. The angular power spectra from these ground-based and balloon-borne experiments are consistent within their systematic and statistical uncertainties with the WMAP results. WMAP detected the large angular-scale correlation between the temperature and polarization anisotropies of the CMB caused by electron scattering since the Universe became reionized after the “Dark Ages”, giving a value for the electron scattering optical depth of 0.17 ± 0.04. The simplest ΛCDM model with n=1 and Ω tot =1 fixed provides an adequate fit to the WMAP data and gives parameters which are consistent with determinations of the Hubble constant and observations of the accelerating Universe using supernovae. The time-ordered data, maps, and power spectra from WMAP can be found at http://lambda.gsfc.nasa.gov along with 13 papers by the WMAP science team describing the results in detail.

Suppressing the lower multipoles in the CMB anisotropies

The Cosmic Microwave Background (CMB) anisotropy power on the largestangular scales observed both by WMAP and COBE DMR appears to be lowerthan the one predicted by the standard model of cosmology with almostscale free primordial perturbations arising from a period of inflation. One can either interpretthis as a manifestation of cosmic variance or as a physical effectthat requires an explanation. We discuss various mechanisms that couldbe responsible for the suppression of such low ℓmultipoles. Features in the late time evolution of metric fluctuationsmay do this via the integral Sachs–Wolfe effect. Another possibilityis a suppression of power at large scales in the primordial spectruminduced by a fast rolling stage in the evolution of the inflaton fieldat the beginning of the last 65 e-folds of inflation. We illustratethis effect in a simple model of inflation and fit the resulting CMBspectrum to the observed temperature–temperature (TT) powerspectrum. We find that the WMAP observations suggest a cutoff atkc = 4.9+1.3−1.6 × 10−4 Mpc−1 at 68% confidence,but only an upper limit of kc < 7.4 × 10−4 Mpc−1 at95%. Thus, although it improves the fit of the data, the presence ofa cutoff in power spectrum is only required at a level close to2σ. This is obtained with a prior which corresponds to equaldistribution w.r.t. kc. We discuss how other choices (such as an equaldistribution w.r.t. lnkc, which is natural in the context ofinflation) can affect the statistical interpretation.

COBE—DMR constraints on the non-linear coupling parameter: a wavelet based method

Non-linearity introduced in slow-roll inflation will produce weakly non-Gaussian cosmic microwave background (CMB) temperature fluctuations. We have simulated non-Gaussian large-scale CMB maps (including COBE—DMR constraints) introducing an additional quadratic term in the gravitational potential. The amount of non-linearity is controlled by the so-called non-linear coupling parameter fnl. An analysis based on the Spherical Mexican Hat wavelet was applied to these and to the COBE—DMR maps. Skewness values obtained at several scales were combined into a Fisher discriminant. Comparison of the Fisher discriminant distributions obtained for different non-linear coupling parameters with the COBE—DMR values sets a constraint of |fnl| < 1100 at the 68 per cent confidence level. This new constraint is tighter than the one previously obtained by using the bispectrum by Komatsu et al.

Constraints on Cosmological Parameters from the Lyα Forest Power Spectrum andCOBEDMR

We combine COBE DMR measurements of cosmic microwave background (CMB) anisotropy with a recent measurement of the mass power spectrum at redshift z = 2.5 from Lyα forest data to derive constraints on cosmological parameters and test the inflationary cold dark matter (CDM) scenario of structure formation. By treating the inflationary spectral index n as a free parameter, we are able to find successful fits to the COBE and Lyα forest constraints in Ωm = 1 models with and without massive neutrinos and in low-Ωm models with and without a cosmological constant. Within each class of model, the combination of COBE and the Lyα forest P(k) constrains a parameter combination of the form ΩmhαnβΩ, with different indices for each case. This new constraint breaks some of the degeneracies in cosmological parameter determinations from other measurements of large-scale structure and CMB anisotropy. The Lyα forest P(k) provides the first measurement of the slope of the linear mass power spectrum on ~Mpc scales, ν = -2.25 ± 0.18, and it confirms a basic prediction of the inflationary CDM scenario: an approximately scale invariant spectrum of primeval fluctuations (n ≈ 1) modulated by a transfer function that bends P(k) toward kn-4 on small scales. Considering additional observational data, we find that COBE-normalized, Ωm = 1 models that match the Lyα forest P(k) do not match the observed masses of rich galaxy clusters, and that low-Ωm models with a cosmological constant provide the best overall fit to the available data, even without the direct evidence for cosmic acceleration from Type Ia supernovae. With our fiducial parameter choices, the flat, low-Ωm models that match COBE and the Lyα forest P(k) also match recent measurements of small-scale CMB anisotropy. Modest improvements in the Lyα forest P(k) measurement could greatly restrict the allowable region of parameter space for CDM models, constrain the contribution of tensor fluctuations to CMB anisotropy, and achieve a more stringent test of the current consensus model of structure formation.

Gaussianity of Degree‐Scale Cosmic Microwave Background Anisotropy Observations

We present results from a first test of the Gaussianity of degree-scale cosmic microwave background (CMB) anisotropy. We investigate Gaussianity of the CMB anisotropy by studying the topology of CMB anisotropy maps from the QMAP and Saskatoon experiments. We also study the QMASK map, a combination map of the QMAP and Saskatoon data. We measure the genus from noise-suppressed Wiener-filtered maps at an angular scale of about 1.5 degrees. To test the Gaussianity of the observed anisotropy, we compare these results to those derived from a collection of simulated maps for each experiment in a Gaussian spatially-flat cosmological constant dominated cold dark matter model. The genus-threshold level relations of the QMAP and Saskatoon maps are consistent with Gaussianity. While the combination QMASK map has a mildly non-Gaussian genus curve which is not a consequence of known foreground contamination, this result is not statistically significant at the 2 sigma level. These results extend previous upper limits on the non-Gaussianity of the large angular scale (> 10 degrees) CMB anisotropy (measured by the COBE DMR experiment) down to degree angular scales.

Cosmological parameters from complementary observations of the Universe

We use observational data on the large scale structure (LSS) of the Universe measured over a wide range of scales from sub-galactic up to horizon scale and on the cosmic microwave background anisotropies to determine cosmological parameters within the class of adiabatic inflationary models. We show that a mixed dark matter model with cosmological constant ($\Lambda$MDM model) and parameters $\Omega_m=0.37^{+0.25}_{-0.15}$, $\Omega_{\Lambda}=0.69^{+0.15}_{-0.20}$, $\Omega_{\nu}=0.03^{+0.07}_{-0.03}$, $N_{\nu}=1$, $\Omega_b=0.037^{+0.033}_{-0.018}$, $n_s=1.02^{+0.09}_{-0.10}$, $h=0.71^{+0.22}_{-0.19}$, $b_{cl}=2.4^{+0.7}_{-0.7}$ (1$\sigma$ confidence limits) matches observational data on LSS, the nucleosynthesis constraint, direct measurements of Hubble constant, the high redshift supernova type Ia results and the recent measurements of the location and amplitude of the first acoustic peak in the CMB anisotropy power spectrum. The best model is $\Lambda$ dominated (65% of the total energy density) and has slightly positive curvature, $\Omega=1.06$. The clustered matter consists in 8% massive neutrinos, 10% baryons and 82% cold dark matter (CDM). The upper 2$\sigma$ limit on the neutrino content can be expressed in the form $\Omega_{\nu}h^2/N_{\nu}^{0.64}\le0.042$ or, via the neutrino mass, $m_{\nu}\le4.0$eV. The upper 1(2)$\sigma$ limit for the contribution of a tensor mode to the COBE DMR data is T/S$<1(1.5)$. Furthermore, it is shown that the LSS observations together with the Boomerang (+MAXIMA-1) data on the first acoustic peak rule out zero-$\Lambda$ models at more than $2\sigma$ confidence limit.

Cosmology from MAXIMA-1, BOOMERANG, and COBE DMR cosmic microwave background observations.

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<l less similar to 800. Analysis of the combined data yields 68% (95%) confidence limits on the total density, Omega(tot) approximately 1.11+/-0.07 (+0.13)(-0.12), the baryon density, Omega(b)h(2) approximately 0.032(+0.005)(-0.004) (+0.009)(-0.008), and the scalar spectral tilt, n(s) approximately 1.01(+0.09)(-0.07) (+0.17)(-0.14). These data are consistent with inflationary initial conditions for structure formation. Taken together with other cosmological observations, they imply the existence of both nonbaryonic dark matter and dark energy in the Universe.

Bumpy power spectra and ΔT/T

With the recent publication of the measurements of the radiation angular power spectrum from the BOOMERanG-98 Antarctic flight [1], it has become apparent that the currently favoured spatially-flat cold dark matter model (matter density parameter Ω m = 0.3, flatness being restored by a cosmological constant Ω Λ = 0.7, Hubble parameter h = 0.65, baryon density parameter Ω b h 2 = 0.02) no longer provides a good fit to the data. We describe a phenomenological approach to resurrecting this paradigm. We consider a primordial power spectrum which incorporates a bump, arbitrarily placed at k b, and characterized by a Gaussian in log k of standard deviation σ b and amplitude A b, that is superimposed on to a scale-invariant power spectrum. We generate a range of theoretical models that include a bump at scales consistent with cosmic microwave background and large-scale structure observations, and perform a simple χ 2 test to compare our models with the COBE DMR data and the recently published BOOMERanG-98 and MAXIMA-1 data [2]. Unlike models that include a high baryon content, our models predict a low third acoustic peak. We find that low ℓ observations (20 < ℓ < 200) are a critical discriminant of the bumps because the transfer function has a sharp cutoff on the high ℓ side of the first acoustic peak. We show that the concordance cosmology can be resurrected using our phenomenological approach and our best-fitting model is in agreement with the PSCz observations. A more detailed account of this work has been submitted to Monthly Notices of the Royal Astronomical Society for publication [3].

Testing the Gaussianity of the COBE DMR data with spherical wavelets

Testing the Gaussianity of the COBE DMR data with spherical wavelets

Testing the Gaussianity of the COBE DMR data with spherical wavelets

We investigate the Gaussianity of the 4-year COBE-DMR data (in HEALPix pixelisation) using an analysis based on spherical Haar wavelets. We use all the pixels lying outside the Galactic cut and compute the skewness, kurtosis and scale-scale correlation spectra for the wavelet coefficients at each scale. We also take into account the sensitivity of the method to the orientation of the input signal. We find a detection of non-Gaussianity at $> 99$ per cent level in just one of our statistics. Taking into account the total number of statistics computed, we estimate that the probability of obtaining such a detection by chance for an underlying Gaussian field is 0.69. Therefore, we conclude that the spherical wavelet technique shows no strong evidence of non-Gaussianity in the COBE-DMR data.

CMB anisotropy experiments

Anisotropies in the cosmic microwave background (CMB) encode information about the evolution and development of the universe. Quality observations of CMB anisotropies can provide a very strong test of cosmological models and provide high precision determination of major cosmological parameters. This paper provides a review of the COBE DMR results, the current status of the measurements of the CMB anisotropy power spectrum and then focuses current and future programs including both suborbit al observations and the two selected satellite missions: the NASA MidEX mission MAP and the ESA M3 mission Max Planck Surveyor. This review includes both a description of the experimental programs and the expected quality level of results.

A preferred-direction statistic for sky maps

Large patterns could exist on the microwave sky as a result of various non-standard possibilities for the large-scale Universe—rotation or shear, non-trivial topology, and single topological defects are specific examples. All-sky (or nearly all-sky) CMB data sets allow us, uniquely, to constrain such exotica, and it is therefore worthwhile to explore a wide range of statistical tests. We describe one such statistic here, which is based on determining gradients and is useful for assessing the level of ‘preferred directionality’ or ‘stripiness’ in the map. This method is more general than other techniques for picking out specific patterns on the sky, and it also has the advantage of being easily calculable for the mega-pixel maps which will soon be available. For the purposes of illustration, we apply this statistic to the four-year COBE DMR data. For future CMB maps, we expect this to be a useful statistical test of the large-scale structure of the Universe. In principle, the same statistic could also be applied to sky maps at other wavelengths, to CMB polarization maps, and to catalogues of discrete objects. It may also be useful as a means of checking for residual directionality (e.g. from Galactic or ecliptic signals) in maps.

COBE and global topology: an example of the application of the identified circles principle

The significance to which the cosmic microwave background (CMB) observations by the satellite COBE can be used to refute a specific observationally based hypothesis for the global topology (3-manifold) of the Universe is investigated, by a new method of applying the principle of matched circle pairs. Moreover, it is shown that this can be done without assuming Gaussian distributions for the density perturbation spectrum. The Universe is assumed to correspond to a flat Friedmann-Lemaître model with a zero value of the cosmological constant. The 3-manifold is hypothesized to be a 2-torus in two directions, with a third axis larger than the horizon diameter. The positions and lengths of the axes are determined by the relative positions of the galaxy clusters Coma, RX J1347.5-1145 and CL 09104+4109, assumed to be multiple topological images of a single, physical cluster. If the following two assumptions are valid: (i) that the error estimates in the COBE DMR data are accurate estimates of the total random plus systematic error; and (ii) that the temperature fluctuations are dominated by the naïve Sachs-Wolfe effect; then the distribution of the temperature differences between multiply imaged pixels is significantly wider than the uncertainty in the differences, and the candidate is rejected at the 94 per cent level. This result is valid for either the ‘subtracted’ or ‘combined’ Analysed Science Data Sets, for either 10° or 20° smoothing, and is slightly strengthened if suspected contaminated regions from the galactic centre and the Ophiuchus and Orion complexes are removed.

COBE constraints on inflation models with a massive nonminimal scalar field

We derive power spectra of the scalar- and tensor-type structures generated in an inflation model based on a massive nonminimally coupled scalar field with the strong coupling assumption. We make analyses in both the original frame and the conformally transformed Einstein frame. We derive contributions of both structures to the anisotropy of the cosmic microwave background radiation, and compare the contributions with the four-year COBE DMR data. The previous study showed that a sufficient amount of inflation requires a small coupling parameter. In such a case the spectra become near Zeldovich spectra, and the gravitational wave contribution becomes negligible compared with the scalar-type contribution which is testable in future CMBR experiments.

Is the Cosmic Microwave Background Really Non-Gaussian?

Two recent papers have claimed detection of non-Gaussian features in the COBE DMR sky maps of the cosmic microwave background. We confirm these results, but argue that Gaussianity is still not convincingly ruled out. Since a score of non-Gaussianity tests have now been published, one might expect some mildly significant results even by chance. Moreover, in the case of one measure which yields a detection, a bispectrum statistic, we find that if the non-Gaussian feature is real, it may well be due to detector noise rather than a non-Gaussian sky signal, since a signal-to-noise analysis localizes it to angular scales smaller than the beam. We study its spatial origin in case it is nonetheless due to a sky signal (eg, a cosmic string wake or flat-spectrum foreground contaminant). It appears highly localized in the direction b=39.5, l=257, since removing a mere 5 pixels inside a single COBE beam area centered there makes the effect statistically insignificant. We also test Guassianity with an eigenmode analysis which allows a sky map to be treated as a random number generator. A battery of tests of this generator all yield results consistent with Gaussianity.

Partition function based analysis of cosmic microwave background maps

We present an alternative method to analyse cosmic microwave background (CMB) maps. We base our analysis on the study of the partition function. This function is used to examine the CMB maps, making use of the different information embedded at different scales and moments. Using the partition function in a likelihood analysis in two dimensions (Qrms-PS, n), we find the best-fitting model to the best data available at present (the COBE–DMR 4 years data set). By means of this analysis we find a maximum in the likelihood function for n=1.8-0.65+0.35 and Qrms-PS = 10-2.5+3μ K (95 per cent confidence level) in agreement with the results of other similar analyses [Smoot et al. (1 yr), Bennet et al. (4 yr)]. Also making use of the partition function we perform a multifractal analysis and study the possible fractal nature of the CMB sky. We find that the measure used in the analysis is not a fractal. Finally, we use the partition function for testing the statistical distribution of the COBE—DMR data set. We conclude that no evidence of non-Gaussianity can be found by means of this method.

The Tenerife Cosmic Microwave Background Maps: Observations and First Analysis

The results of the Tenerife cosmic microwave background (CMB) experiments are presented. These observations cover 5000 and 6500 deg2 on the sky at 10 and 15 GHz, respectively, centered on decl. ~ +35°. The experiments are sensitive to multipoles l = 10-30 that correspond to the Sachs-Wolfe plateau of the CMB power spectra. The sensitivity values of the data are ~31 and ~12 μK at 10 and 15 GHz, respectively, in a beam-size region (5° × 5°). The data at 15 GHz show clear detection of structure at high Galactic latitude; the results at 10 GHz are compatible with these, but at lower significance. A likelihood analysis of the 10 and 15 GHz data at high Galactic latitude, assuming a flat CMB band power spectrum, gives a signal ΔTl = 30 μK (68% C.L.). Including the possible contaminating effect due to the diffuse Galactic component, the CMB signal is ΔTl = 30 μK. These values are stable against the Galactic cut chosen. Assuming a Harrison-Zeldovich spectrum for the primordial fluctuations, the above values imply an expected quadrupole Qrms-ps = 20 μK, which agrees with previous results from these experiments, and which are compatible with the COBE DMR data in the case of the standard inflationary cold dark matter models.

Current Status of the Cosmic Microwave Background Radiation

My goal is to summarize our understanding of the cosmic microwave background radiation (CMBR) at this interesting moment after the detection of fluctuations in the background and before the next generation of satellite experiments. I begin by listing recent reviews and papers on the spectrum of the CMBR. I then sketch the current theoretical description of the power spectrum of fluctuations in the CMBR. Astronomical foregrounds and the nature of secondary fluctuations are treated next. Then I turn to observations, with special emphasis on the final results of the COBE–DMR experiment, on the growing evidence for ΔT/T = 2–3 × 10−5 fluctuations at degree scales, and on what they tell us about cosmological parameters.