Mapping the large-scale anisotropy in the WMAP data

Pramana, 2004

The breakdown of statistical homogeneity and isotropy of cosmic perturbations is a generic feature of ultra large scale structure of the cosmos, in particular, of non trivial cosmic topology. The statistical isotropy (SI) of the Cosmic Microwave Background temperature fluctuations (CMB anisotropy) is sensitive to this breakdown on the largest scales comparable to, and even beyond the cosmic horizon. We propose a set of measures, κ ℓ (ℓ = 1, 2, 3, . . .) which for non-zero values indicate and quantify statistical isotropy violations in a CMB map. We numerically compute the predicted κ ℓ spectra for CMB anisotropy in flat torus universe models. Characteristic signature of different models in the κ ℓ spectrum are noted.

Nuclear Physics B - Proceedings Supplements, 1994

New Astronomy Reviews, 2006

The statistical expectation values of the temperature fluctuations and polarization of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy (SI) of the CMB maps recently measured by the Wilkinson Microwave Anisotropy Probe (WMAP) using the bipolar spherical harmonic formalism proposed in Hajian & Souradeep 2003 for CMB temperature anisotropy and extended to CMB polarization in Basak, Hajian & Souradeep 2006. The Bipolar Power Spectrum (BiPS) had been measured for the full sky CMB anisotropy maps of the first year WMAP data and now for the recently released three years of WMAP data. We also introduce and measure directional sensitive reduced Bipolar coefficients on the three year WMAP ILC map. Consistent with our published results from first year WMAP data we have no evidence for violation of statistical isotropy on large angular scales. Preliminary analysis of the recently released first WMAP polarization maps, however, indicate significant violation of SI even when the foreground contaminated regions are masked out. Further work is required to confirm a possible cosmic origin and rule out the (more likely) origin in observational artifact such as foreground residuals at high galactic latitude.

The Astrophysical Journal, 2004

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.

2003

The breakdown of statistical homogeneity and isotropy of cosmic perturbations is a generic feature of ultra large scale structure of the cosmos, in particular, of non trivial cosmic topology. The statistical isotropy (SI) of the Cosmic Microwave Background temperature fluctuations (CMB anisotropy) is sensitive to this breakdown on the largest scales comparable to, and even beyond the cosmic horizon. We study a set of measures, κ ℓ (ℓ = 1, 2, 3, . . .) which for non-zero values indicate and quantify statistical isotropy violations in a CMB map. The main goal here is to interpret the κ ℓ spectrum and relate it to characteristic patterns in the correlation function of CMB anisotropy arising from cosmic topology. We numerically compute the predicted κ ℓ spectrum for CMB anisotropy in flat torus universe models. The essential features are captured in the leading order approximation to the correlation function where κ ℓ can be calculated analytically. The κ ℓ spectrum is shown to reflect the number, importance and relative orientation of principal directions in the CMB correlation dictated by the shape of the Dirichlet domain (DD) of the compact space and its size relative to cosmic horizon. Hence, besides detecting cosmic topology, κ ℓ can discriminate between different topology of the universe complementing ongoing search for cosmic topology in CMB anisotropy data.

This paper focuses on cosmological constraints derived from analysis of WMAP data alone. A simple ΛCDM cosmological model fits the five-year WMAP temperature and polarization data. The basic parameters of the model are consistent with the three-year data and now better constrained: Ω b h 2 = 0.02273 ± 0.00062, Ω c h 2 = 0.1099 ± 0.0062, Ω Λ = 0.742 ± 0.030, n s = 0.963 +0.014 −0.015 , τ = 0.087 ± 0.017, and σ 8 = 0.796 ± 0.036, with h = 0.719 +0.026 −0.027 . With five years of polarization data, we have measured the optical depth to reionization, τ > 0, at 5σ significance. The redshift of an instantaneous reionization is constrained to be z reion = 11.0 ± 1.4 with 68% confidence. The 2σ lower limit is z reion > 8.2, and the 3σ limit is z reion > 6.7. This excludes a sudden reionization of the universe at z = 6 at more than 3.5σ significance, suggesting that reionization was an extended process. Using two methods for polarized foreground cleaning we get consistent estimates for the optical depth, indicating an error due to foreground treatment of τ ∼ 0.01. This cosmological model also fits small-scale CMB data, and a range of astronomical 1 WMAP is the result of a partnership between Princeton University and NASA's Goddard Space Flight Center. Scientific guidance is provided by the WMAP Science Team.

The Astrophysical Journal, 2003

We analyze the Cosmic Microwave Background (CMB) anisotropy data from the independent COBE FIRAS and DMR observations. We extract the frequency spectrum of the FIRAS signal that has the spatial distribution seen by DMR and show that it is consistent with CMB temperature fluctuations in the radiation well into the Wien region of the spectrum. Conversely, we form a map of the Planckian component of the sky temperature from FIRAS and show that it correlates with the DMR anisotropy map. The rms fluctuations at angular scales of 7 • are 48±14 µK for the FIRAS data vs 35±2 µK for the DMR data and 31±6 µK for the combination (1 σ uncertainties). The consistency of these data, from very different instruments with very different observing strategies, provide compelling support for the interpretation that the signal seen by DMR is, in fact, temperature anisotropy of cosmological origin. The data also limit rms fluctuations in the Compton y parameter, observable via the Sunyaev-Zel'dovich effect, to ∆y < 3 × 10 −6 (95% CL) on 7 • angular scales.

The Astrophysical Journal, 1997

We study the anisotropy of the cosmic microwave background (CMB) in cold and mixed dark matter (CDM and MDM) models, with non scale-invariant primordial power spectra (i.e. n = 1) and a late, sudden reionization of the intergalactic medium at redshift z rh . We test these models against recent detections of CMB anisotropy at large and intermediate angular scales. We find that current CMB anisotropy measurements cannot discriminate between CDM and MDM models. Our likelihood analysis indicates that models with blue power spectra (n ≃ 1.2) and a reionization at z rh ∼ 20 are most consistent with the anisotropy data considered here. Without reionization our analysis gives 1.0 ≤ n ≤ 1.26 (95% C.L.) for Ω b = 0.05.

The Astrophysical Journal, 2004

We report on the results from two independent but complementary statistical analyses of the WMAP first-year data, based on the power spectrum and N-point correlation functions. We focus on large and intermediate scales (larger than about 3 •) and compare the observed data against Monte Carlo ensembles with WMAP-like properties. In both analyses, we measure the amplitudes of the large-scale fluctuations on opposing hemispheres and study the ratio of the two amplitudes. The power-spectrum analysis shows that this ratio for WMAP, as measured along the axis of maximum asymmetry, is high at the 95%-99% level (depending on the particular multipole range included). The axis of maximum asymmetry of the WMAP data is weakly dependent on the multipole range under consideration but tends to lie close to the ecliptic axis. In the N-point correlation function analysis we focus on the northern and southern hemispheres defined in ecliptic coordinates, and we find that the ratio of the large-scale fluctuation amplitudes is high at the 98%-99% level. Furthermore, the results are stable with respect to choice of Galactic cut and also with respect to frequency band. A similar asymmetry is found in the COBE-DMR map, and the axis of maximum asymmetry is close to the one found in the WMAP data. Subject headings: cosmic microwave background-cosmology: observations-methods: statistical

Astrophysical Journal, 2001

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 $441 < \ell < 785$.