2011 (IPP)
Permanent URI for this collectionhttp://localhost:4000/handle/11007/151
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Item Statistics of bipolar representation of CMB maps(2011-09-04) Joshi, Nidhi; Rotti, Aditya; Souradeep, TarunGaussianity of temperature fluctuations in the Cosmic Microwave Background(CMB) implies that the statistical properties of the temperature field can be completely characterized by its two point correlation function. The two point correlation function can be expanded in full generality in the bipolar spherical harmonic(BipoSH) basis. Looking for significant deviations from zero for Bipolar Spherical Harmonic(BipoSH) Coefficients derived from observed CMB maps forms the basis of the strategy used to detect isotropy violation. In order to quantify ”significant deviation” we need to understand the distributions of these coefficients. We analytically evaluate the moments and the distribution of the coefficients of expansion(ALM l1l2 ), using characteristic function approach. We show that for BipoSH coefficients with M = 0 an analytical form for the moments up to any arbitrary order can be derived. For the remaining BipoSH coefficients with M = 0, the moments derived using the characteristic function approach need to be supplemented with a correction term. The correction term is found to be important particularly at low multipoles. We provide a general prescription for calculating these corrections, however we restrict the explicit calculations only up to kurtosis. We confirm our results with measurements of BipoSH coefficients on numerically simulated statistically isotropic CMB maps.Item 'Standard' Cosmological model & beyond with CMB(2011-04-16) Souradeep, TarunObservational Cosmology has indeed made very rapid progress in the past decade. The ability to quantify the universe has largely improved due to observational constraints coming from structure formation Measurements of CMB anisotropy and, more recently, polarization have played a very important role. Besides precise determination of various parameters of the 'standard’ cosmological model, observations have also established some important basic tenets that underlie models of cosmology and structure formation in the universe – ‘acausally’ correlated initial perturbations in a flat, statistically isotropic universe, adiabatic nature of primordial density perturbations. These are consistent with the expectation of the paradigm of inflation and the generic prediction of the simplest realization of inflationary scenario in the early universe. Further, gravitational instability is the established mechanism for structure formation from these initial perturbations. The signature of primordial perturbations observed as the CMB anisotropy and polarization is the most compelling evidence for new, possibly fundamental, physics in the early universe. The community is now looking beyond the estimation of parameters of a working 'standard’ model of cosmology for subtle, characteristic signatures from early universe physics.Item Odd-parity bipolar spherical harmonics(2011-09-13) Book, Laura G.; Kamionkowski, Marc; Souradeep, TarunBipolar spherical harmonics (BiPoSHs) provide a general formalism for quantifying departures in the cosmic microwave background (CMB) from statistical isotropy (SI) and from Gaussianity. However, prior work has focused only on BiPoSHs with even parity. Here we show that there is another set of BiPoSHs with odd parity, and we explore their cosmological applications. We describe systematic artifacts in a CMB map that could be sought by measurement of these odd-parity BiPoSH modes. These BiPoSH modes may also be produced cosmologically through lensing by gravitational waves (GWs), among other sources. We derive expressions for the BiPoSH modes induced by the weak lensing of both scalar and tensor perturbations. Our estimate of the expected signal-to-noise with which we could measure the weak lensing of GWs from the correlation of two BiPoSH modes is respectable, indicating that such a measurement may be merited. We also investigate the possibility to detect parity-breaking physics, such as chiral GWs, by cross-correlating opposite parity BiPoSH modes with multipole moments of the CMB polarization. We nd that the expected signal-to-noise of such a detection is modest, with errors dominated by cosmic variance.Item Evolution of the CMB power spectrum across WMAP data releases: A nonparametric analysis(2011-07-04) Aghamousa, Amir; Arjunwadkar, Mihir; Souradeep, TarunItem Early universe with CMB polarization(2011-04-16) Souradeep, TarunThe Universe is the grandest conceivable scale on which the human mind can strive to understand nature. The amazing aspect of cosmology, the branch of science that attempts to understand the origin and evolution of the Universe, is that it is largely comprehensible by applying the same basic laws of physics that we use for other branches of physics. The observed cosmic microwave background (CMB) is understood by applying the basic laws of radiative processes and transfer, masterfully covered in the classic text by S. Chandrasekhar, in the cosmological context. In addition to the now widely acclaimed temperature anisotropy, there is also linear polarization information imprinted on the observed Cosmic Microwave background. CMB polarization already has addressed, and promises to do a lot more, to unravel the deepest fundamental queries about physics operating close to the origin of the Universe.Item Cosmological parameter estimation using particle swarm optimization (PSO)(2011-08-30) Prasad, Jayanti; Souradeep, TarunObtaining the set of cosmological parameters consistent with observational data is an important exercise in current cosmological research. It involves finding the global maximum of the likelihood function in the multi-dimensional parameter space. Currently sampling based methods, which are in general stochastic in nature, like Markov-Chain Monte Carlo(MCMC), are being commonly used for parameter estimation. The beauty of stochastic methods is that the computational cost grows, at the most, linearly in place of exponentially (as in grid based approaches) with the dimensionality of the search space. MCMC methods sample the full joint probability distribution (posterior) from which one and two dimensional probability distributions, best fit (average) values of parameters and then error bars can be computed. In the present work we demonstrate the application of another stochastic method, named Particle Swarm Optimization (PSO), that is widely used in the field of engineering and artificial intelligence, for cosmological parameter estimation from WMAP seven years data. We find that there is a good agreement between the values of the best fit parameters obtained from PSO and publicly available code COSMOMC. However, there is a slight disagreement between error bars mainly due to the fact that errors are computed differently in PSO. Apart from presenting the results of our exercise, we also discuss the merits of PSO and explain its usefulness in more extensive search in higher dimensional parameter space.Item Beyond the standard cosmological model with CMB(2011-06-02) Souradeep, TarunMeasurements of CMB anisotropy and, more recently, polarization have played a very important role in cosmology. Besides precise determination of various parameters of the ‘standard’ cosmological model, observations have also established some important basic tenets that underlie models of cosmology and structure formation in the universe – ‘acausally’ correlated, adiabatic, primordial perturbations in a flat, statistically isotropic universe. These are consistent with the expectation of the paradigm of inflation and the generic prediction of the simplest realization of inflationary scenario in the early universe. Further, gravitational instability is the established mechanism for structure formation from these initial perturbations. Primordial perturbations observed as the CMB anisotropy and polarization is the most compelling evidence for new, possibly fundamental, physics in the early universe. The community is now looking beyond the parameter estimation of the ‘standard’ model, for subtle, characteristic signatures of early universe physics.