Fluctuations in the cosmic microwave background

The search for fluctuations in the Cosmic Microwave Background (CMB) is one of the most important topics in modern cosmology, since their detection would reveal a great many details about the early universe and, in particular, the nature of the primordial density perturbations giving rise to the galaxies and clusters of galaxies seen in the universe today. However, the search for such anisotropies is not trivial- none have been detected as yet - largely as a consequence of the fact that all radiative astrophysical sources can give rise to anisotropic foregrounds which confuse the search for genuine cosmological signals. In this thesis, a detailed study is made of the contribution of such foregrounds to searches for CMB fluctuations. After Chapter 1 summarises the theoretical and observational status of the subject, Chapters 2, 3 and 4 consider the foreground resulting from the Galaxy. It is found that frequencies in excess of 20 GHz are required to reduce the Galactic Synchrotron Radiation to a level where genuine anisotropies might be detected (the synchrotron emission is almost certainly responsible for a previously claimed detection), and that dust emission, especially if very cold dust exists which is unseen and possibly untraced by the dust responsible for the emission seen in the IRAS 100µm passband, can seriously constrain high frequency searches. In Chapter 4 a model is derived for the overall Galactic foreground including a separation of the thermal and non-thermal radio emission in the Galactic plane. Comparison with observations at 10 and 15 GHz suggests that the model is ~ 10%- 20% accurate on average at these frequencies, and maps of the predicted emission at the COBE frequencies 31.5, 53, and 90 GHz are provided. .4. search is made for a frequency window and sky region which minimises the Galactic contribution to the fluctuation measurements: highly sensitive, high resolution searches should be designed with these values in mind. Chapter 5 investigates the anisotropies resulting from discrete extragalactic sources, in particular, the far-infrared emission from dust in spiral galaxies and the integrated radio emission due to radio galaxies, QSOs etc. A frequency window of ~ 30 - 100 GHz is found to minimise both Galactic and extragalactic foreground anisotropies. Chapter 6 considers several cosmological models which could generate the recently observed large-scale structure in the galaxy- distribution: these are constrained by CMB anisotropy limits. It is concluded that genuine cosmological variations in the CMB temperature are now close to detection if the observed galaxy- structures are real. Chapter 7 indicates some future projects which should help in the detection and interpretation of CMB fluctuations

COBE-DMR-normalised Open Inflation, CDM Cosmogony

Fourier analysis on a cut sky of the two-year COBE DMR 53 and 90 GHz sky maps (in galactic coordinates) is used to determine the normalisation of an open inflation model based on the cold dark matter scenario. The normalised model is compared to measures of large-scale structure in the universe. Although the DMR data alone does not provide sufficient discriminative power to prefer a particular value of the mass density parameter, the open model appears to be reasonably consistent with observations when Omega_0 ~ 0.3 - 0.4 and merits further study.Comment: uuencoded file containing 6 postscript files (11 pgs text, 4 figures, 1 table

Report on 3 and 4-point correlation statistics in the COBE DMR anisotrophy maps

As part of the work performed under NASA contract # NAS5-32648, we have computed the 3-point and 4-point correlation functions of the COBE-DNIR 2-year and 4-year anisotropy maps. The motivation for this study was to search for evidence of non-Gaussian statistical fluctuations in the temperature maps: skewness or asymmetry in the case of the 3-point function, kurtosis in the case of the 4-point function. Such behavior would have very significant implications for our understanding of the processes of galaxy formation, because our current models of galaxy formation predict that non-Gaussian features should not be present in the DMR maps. The results of our work showed that the 3-point correlation function is consistent with zero and that the 4-point function is not a very sensitive probe of non-Gaussian behavior in the COBE-DMR data. Our computation and analysis of 3-point correlations in the 2-year DMR maps was published in the Astrophysical Journal Letters, volume 446, page L67, 1995. Our computation and analysis of 3-point correlations in the 4-year DMR maps will be published, together with some additional tests, in the June 10, 1996 issue of the Astrophysical Journal Letters. Copies of both of these papers are attached as an appendix to this report

Report on 3- and 4-Point Correlation Statistics in COBE DMR Anisotropy Maps

As part of the work performed under this contract, we have computed the 3- and 4-point correlation functions of the COBE-DMR 2-year and 4-year anisotropy maps. The results of our work showed that the 3-point correlation function is consistent with zero and that the 4-point function is not a very sensitive probe of non-Gaussian behavior in the COBE-DMR data

CMB Anisotropy in COBE-DMR-Normalized Flat Λ\Lambda CDM Cosmogony

We compute the cosmic microwave background (CMB) anisotropy in a low-density, flat, cosmological constant, cold dark matter model which is normalized to the two-year COBE DMR sky map. Although conclusions regarding model viability must remain tentative until systematic effects are better understood, there are mild indications that these models have more intermediate scale power than is indicated by presently available CMB anisotropy observational data, with old ($t_0 \geq 15-16$Gyr), high baryon density ($\Omega_B \geq 0.0175 h^{-2}$), low density ($\Omega_0 \sim 0.2-0.4$) models doing the worst.Comment: 9 pages including 2 figures, one 5 pages table: two uuencoded postscript file

Searching for non-Gaussianity in the VSA data

We have tested Very Small Array (VSA) observations of three regions of sky for the presence of non-Gaussianity, using high-order cumulants, Minkowski functionals, a wavelet-based test and a Bayesian joint power spectrum/non-Gaussianity analysis. We find the data from two regions to be consistent with Gaussianity. In the third region, we obtain a 96.7% detection of non-Gaussianity using the wavelet test. We perform simulations to characterise the tests, and conclude that this is consistent with expected residual point source contamination. There is therefore no evidence that this detection is of cosmological origin. Our simulations show that the tests would be sensitive to any residual point sources above the data's source subtraction level of 20 mJy. The tests are also sensitive to cosmic string networks at an rms fluctuation level of $105 \mu K$ (i.e. equivalent to the best-fit observed value). They are not sensitive to string-induced fluctuations if an equal rms of Gaussian CDM fluctuations is added, thereby reducing the fluctuations due to the strings network to $74 \mu K$ rms . We especially highlight the usefulness of non-Gaussianity testing in eliminating systematic effects from our data.Comment: Minor corrections; accepted for publication to MNRA

High sensitivity measurements of the CMB power spectrum with the extended Very Small Array

We present deep Ka-band ($\nu \approx 33$ GHz) observations of the CMB made with the extended Very Small Array (VSA). This configuration produces a naturally weighted synthesized FWHM beamwidth of $\sim 11$ arcmin which covers an $\ell$-range of 300 to 1500. On these scales, foreground extragalactic sources can be a major source of contamination to the CMB anisotropy. This problem has been alleviated by identifying sources at 15 GHz with the Ryle Telescope and then monitoring these sources at 33 GHz using a single baseline interferometer co-located with the VSA. Sources with flux densities \gtsim 20 mJy at 33 GHz are subtracted from the data. In addition, we calculate a statistical correction for the small residual contribution from weaker sources that are below the detection limit of the survey. The CMB power spectrum corrected for Galactic foregrounds and extragalactic point sources is presented. A total $\ell$-range of 150-1500 is achieved by combining the complete extended array data with earlier VSA data in a compact configuration. Our resolution of $\Delta \ell \approx 60$ allows the first 3 acoustic peaks to be clearly delineated. The is achieved by using mosaiced observations in 7 regions covering a total area of 82 sq. degrees. There is good agreement with WMAP data up to $\ell=700$ where WMAP data run out of resolution. For higher $\ell$-values out to $\ell = 1500$, the agreement in power spectrum amplitudes with other experiments is also very good despite differences in frequency and observing technique.Comment: 16 pages. Accepted in MNRAS (minor revisions

Bayesian joint estimation of non-Gaussianity and the power spectrum

We propose a rigorous, non-perturbative, Bayesian framework which enables one jointly to test Gaussianity and estimate the power spectrum of CMB anisotropies. It makes use of the Hilbert space of an harmonic oscillator to set up an exact likelihood function, dependent on the power spectrum and on a set of parameters $\alpha_i$, which are zero for Gaussian processes. The latter can be expressed as series of cumulants; indeed they perturbatively reduce to cumulants. However they have the advantage that their variation is essentially unconstrained. Any truncation(i.e.: finite set of $\alpha_i$) therefore still produces a proper distribution - something which cannot be said of the only other such tool on offer, the Edgeworth expansion. We apply our method to Very Small Array (VSA) simulations based on signal Gaussianity, showing that our algorithm is indeed not biased.Comment: 11pages, 4 figures, submitted to MNRA