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Item Primordial power spectrum from WMAP(2011-07-05) Shafieloo, Arman; Souradeep, TarunThe observed angular power spectrum of the cosmic microwave background temperature anisotropy, Cl, is a convolution of a cosmological radiative transport kernel with an assumed primordial power spectrum of inhomogeneities. Exquisite measurements of Cl over a wide range of multipoles from the Wilkinson Microwave Anisotropy Probe (WMAP) has opened up the possibility to deconvolve the primordial power spectrum for a given set of cosmological parameters (base model). We implement an improved (error sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from WMAP assuming the concordance cosmological model. The most prominent feature of the recovered P(k) is a sharp, infrared cutoff on the horizon scale. The resultant Cl spectrum using the recovered spectrum has a likelihood far better than a scale invariant, or, “best fit” scale free spectra (ΔlnL≈25 with respect to Harrison Zeldovich, and, ΔlnL≈11 with respect to power law with ns=0.95). The recovered P(k) has a localized excess just above the cutoff which leads to great improvement of likelihood over the simple monotonic forms of model infrared cutoff spectra considered in the post WMAP literature. The recovered P(k), in particular, the form of infrared cutoff is robust to small changes in the cosmological parameters. We show that remarkably similar form of infrared cutoff is known to arise in very reasonable extensions and refinements of the predictions from simple inflationary scenarios. Our method can be extended to other cosmological observations such as the measured matter power spectrum and, in particular, the much awaited polarization spectrum from WMAP.Item Statistical isotropy of CMB anisotropy from WMAP(2005-02-01) Souradeep, Tarun; Hajian, AmirThe statistical expectation values of the temperature fluctuations of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy of the CMB anisotropy maps recently measured by the Wilkinson Microwave Anisotropy Probe (WMAP) using bipolar spherical harmonic power spectrum proposed in Hajian & Souradeep 2003. The Bipolar Power Spectrum (BiPS) is estimated for the full sky CMB anisotropy maps of the first year WMAP data. The method allows us to isolate regions in multipole space and study each region independently. This search shows no evidence for violation of statistical isotropy in the first-year WMAP data on angular scales larger than that corresponding to l ≈ 60 .Item Post-WMAP Assessment of Infrared cutoff in the Primordial Spectrum from Inflation(2005-08-01) Sinha, Rita; Souradeep, TarunThe recent Cosmic Microwave Background (CMB) measurements indicate that there is power deficiency of the CMB anisotropies at large scales compared with the ΛCDM model. We have investigated the possibility of explaining such effects by a class of primordial power spectra which have infrared cutoffs close to the horizon scale. The primordial power spectrum recovered by direct deconvolution of the observed CMB angular spectrum indicates that the data prefers a sharp infrared cutoff with a localized excess (bump) just above the cutoff. We have been motivated to assess plausible extensions of simplest inflationary scenarios which readily accommodate similar form of infrared cutoff. We carry out a complete Bayesian analysis of the parameter space using Markov Chain Monte Carlo technique with such a class of primordial power spectra. We show that primordial power spectrum that have features such as an infrared cutoff followed by a subsequent excess in power give better fit to the observed data compared to a nearly scale-invariant power law or power spectrum with just a monotonic infrared cutoff. However, there is substantial room for improvement in the match to data and calls for exploration of other mechanisms that may lead to infrared cutoff even closer to that recovered by direct deconvolution approach.Item Estimation of Primordial Spectrum with post-WMAP 3 year data(2007-07-14) Shafieloo, Arman; Souradeep, TarunIn this paper we implement an improved (error sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the WMAP 3 year data to determine the primordial power spectrum assuming different points in the cosmological parameter space for a flat ΛCDM cosmological model. We also present the preliminary results of the cosmological parameter estimation by assuming a free form of the primordial spectrum, for a reasonably large volume of the parameter space. The recovered spectrum for a considerably large number of the points in the cosmological parameter space has a likelihood far better than a ‘best fit’ power law spectrum up to ∆χ2 eff ≈ −30. We use Discrete Wavelet Transform (DWT) for smoothing the raw recovered spectrum from the binned data. The results obtained here reconfirm and sharpen the conclusion drawn from our previous analysis of the WMAP 1st year data. A sharp cut off around the horizon scale and a bump after the horizon scale seem to be a common feature for all of these reconstructed primordial spectra. We have shown that although the WMAP 3 year data prefers a lower value of matter density for a power law form of the primordial spectrum, for a free form of the spectrum, we can get a very good likelihood to the data for higher values of matter density. We have also shown that even a flat CDM model, allowing a free form of the primordial spectrum, can give a very high likelihood fit to the data. Theoretical interpretation of the results is open to the cosmology community. However, this work provides strong evidence that the data retains discriminatory power in the cosmological parameter space even when there is full freedom in choosing the primordial spectrum.Item CMB anisotropy power spectrum using linear combinations of WMAP maps(2007-06-25) Saha, Rajib; Souradeep, Tarun; Jain, Pankaj; et al.In recent years the goal of estimating different cosmological parameters precisely has set new challenges in the effort to accurately measure the angular power spectrum of CMB. This has required removal of foreground contamination as well as detector noise bias with reliability and precision. Recently, a novel model-independent method for the estimation of CMB angular power spectrum solely from multi-frequency observations has been proposed and implemented on the first yearWMAP data by Saha et al. 2006. All previous estimates of power spectrum of CMB are based upon foreground templates using data sets from different experiments. However our methodology demonstrates that CMB angular spectrum can be reliably estimated with precision from a self contained analysis of the WMAP data. In this work we provide a detailed description of this method. We also study and identify the biases present in our power spectrum estimate. We apply our methodoly to extract the power spectrum from the WMAP 1 year and 3 year data.Item Features in the primordial spectrum from WMAP: A wavelet analysis(2006-01-01) Shafieloo, Arman; Souradeep, Tarun; Manimaran, P.Precise measurements of the anisotropies in the cosmic microwave background enable us to do an accurate study on the form of the primordial power spectrum for a given set of cosmological parameters. In a previous paper [1], we implemented an improved (error sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the first year of WMAP data to determine the primordial power spectrum assuming a concordance cosmological model. This recovered spectrum has a likelihood far better than a scale invariant, or, ‘best fit’ scale free spectra (∆ln L ≈ 25 w.r.t. Harrison Zeldovich, and, ∆ln L ≈ 11 w.r.t. power law with ns = 0.95). In this paper we use Discrete Wavelet Transform (DWT) to decompose the local features of the recovered spectrum individually to study their effect and significance on the recovered angular power spectrum and hence the likelihood. We show that besides the infra-red cut off at the horizon scale, the associated features of the primordial power spectrum around the horizon have a significant effect on improving the likelihood. The strong features are localized at the horizon scale.Item Model Independent Foreground Power Spectrum Estimation using WMAP 5-year Data(2009-01-01) Ghosh, Tuhin; Saha, Rajib; Jain, Pankaj; et al.In this paper, we propose & implement on WMAP 5-year data, a model independent approach of foreground power spectrum estimation for multifrequency observations of CMB experiments. Recently a model independent approach of CMB power spectrum estimation was proposed by Saha et al. 2006. This methodology demonstrates that CMB power spectrum can be reliably estimated solely from WMAP data without assuming any template models for the foreground components. In the current paper, we extend this work to estimate the galactic foreground power spectrum using the WMAP 5 year maps following a self contained analysis. We apply the model independent method in harmonic basis to estimate the foreground power spectrum and frequency dependence of combined foregrounds. We also study the behaviour of synchrotron spectral index variation over different regions of the sky. We compare our results with those obtained from MEM foreground maps which are formed in pixel space. We find that relative to our model independent estimates MEM maps overestimates the foreground power close to galactic plane and underestimates it at high latitudes.Item Oscillation in the inflaton potential: Exact numerical analysis and comparison with the recent and forthcoming CMB datasets(2011-06-15) Aich, Moumita; Hazra, Dhiraj Kumar; Sriramkumar, L.; et al.Amongst the multitude of inflationary models currently available, models that lead to features in the primordial scalar spectrum are drawing increasing attention, since certain features have been found to provide a better fit to the CMB data than the conventional, nearly scale invariant, primordial spectrum. In this work, we carry out an exact numerical analysis of two models that lead to oscillations over all scales in the scalar power spectrum. We consider the model described by a quadratic potential which is superposed by a sinusoidal modulation and the recently popular axion monodromy model. Since the oscillations continue even onto smaller scales, in addition to the WMAP data, we also compare the models with the small scale data from ACT. Though, both the models, broadly, result in oscillations in the spectrum, interestingly, we find that, while the monodromy model leads to a considerably better fit to the data in comparison to the standard power law spectrum, the quadratic potential superposed with a sinusoidal modulation does not improve the fit to a similar extent. We also carry out forecasting of the parameters using simulated Planck data for both the models. We show that the Planck mock data performs better in constraining the model parameters as compared to the presently available CMB datasets.Item CMB Polarization and Temperature Power Spectra Estimation using Linear Combination of WMAP 5-year Maps(2009-03-01) Souradeep, Tarun; Jain, Pankaj; Saha, Rajib; et al.We estimate CMB polarization and temperature power spectra using WMAP 5-year foreground contaminated maps. The power spectrum is estimated by using a model independent method, which does not utilize directly the diffuse foreground templates nor the detec tor noise model. The method essentially consists of two steps, (i) removal of diffuse foregrounds contamination by making linear combination of individual maps in harmonic space and (ii) cross-correlation of foreground cleaned maps to minimize detector noise bias. For temperature power spectrum we also estimate and subtract residual unre- solved point source contamination in the cross-power spectrum using the point source model provided by the WMAP science team. Our 1TT, TE and EE power spectra are in good agreement with the published results of the WMAP science team. The error bars on the polarization power spectra, however, turn out to be smaller in comparison to what is obtained by the WMAP science team. We perform detailed numerical simulations to test for bias in our procedure. We find that the bias is small in all cases. A negative bias at low l in TT power spectrum has been pointed in an earlier publication. We find that the bias corrected quadrupole power (l(l + 1)Cl/2π) is 532 µK2, approximately 2.5 times the estimate (213.4 µK2) made by the WMAP team.Item Evolution of the CMB power spectrum across WMAP data releases: A nonparametric analysis(2011-07-04) Aghamousa, Amir; Arjunwadkar, Mihir; Souradeep, Tarun