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Amir Hajian

Publications and source records attributed to Amir Hajian.

66 records · Page 4Linked to original sources
arXiv2007

Analysis of the apparent lack of power in the cosmic microwave background anisotropy at large angular scales

We study the apparent lack of power on large angular scales in the WMAP data. We confirm that although there is no apparent lack of power at large angular scales for the full-sky maps, the lowest multipoles of the WMAP data happen to have the magnitudes and orientations, with respect to the Galactic plane, that are needed to make the large scale power in cut-sky maps surprisingly small. Our analysis shows that most of the large scale power of the observed CMB anisotropy maps comes from two regions around the Galactic plane (~9% of the sky). One of them is a cold spot within ~40 degrees of the Galactic center and the other one is a hot spot in the vicinity of the Gum Nebula. If the current full-sky map is correct, there is no clear deficit of power at large angular scales and the alignment of the l=2 and l=3 multipoles remains the primary intriguing feature in the full-sky maps. If the full-sky map is incorrect and a cut is required, then the apparent lack of power remains mysterious. Future missions such as Planck, with a wider frequency range and greater sensitivity, will permit a better modeling of the Galaxy and will shed further light on this issue.

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arXiv2006

Efficient Cosmological Parameter Estimation with Hamiltonian Monte Carlo

Traditional Markov Chain Monte Carlo methods suffer from low acceptance rate, slow mixing and low efficiency in high dimensions. Hamiltonian Monte Carlo resolves this issue by avoiding the random walk. Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) technique built upon the basic principle of Hamiltonian mechanics. Hamiltonian dynamics allows the chain to move along trajectories of constant energy, taking large jumps in the parameter space with relatively inexpensive computations. This new technique improves the acceptance rate by a factor of 4 and boosts up the efficiency by at least a factor of D in a D-dimensional parameter space. Therefor shorter chains will be needed for a reliable parameter estimation comparing to a traditional MCMC chain yielding the same performance. Besides that, the HMC is well suited for sampling from non-Gaussian and curved distributions which are very hard to sample from using the traditional MCMC methods. The method is very simple to code and can be easily plugged into standard parameter estimation codes such as CosmoMC. In this paper we demonstrate how the HMC can be efficiently used in cosmological parameter estimation.

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arXiv2006

Measuring Statistical Isotropy of CMB Anisotropy

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.

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arXiv2006

Testing Global Isotropy of Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Data: Temperature Analysis

We examine statistical isotropy of large scale anisotropies of the Internal Linear Combination (ILC) map, based on three year WMAP data. Our study reveals no significant deviation from statistical isotropy on large angular scales of 3-year ILC map. Comparing statistical isotropy of 3-year ILC map and 1-year ILC map, we find a significant improvement in 3-year ILC map which can be due to the gain model, improved ILC map processing and foreground minimization.

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arXiv2006

Statistical Isotropy of CMB Polarization Maps

We formulate statistical isotropy of CMB anisotropy maps in its most general form. We also present a fast and orientation independent statistical method to determine deviations from statistical isotropy in CMB polarization maps. Importance of having statistical tests of departures from SI for CMB polarization maps lies not only in interesting theoretical motivations but also in testing cleaned CMB polarization maps for observational artifacts such as residuals from polarized foreground emission. We propose a generalization of the Bipolar Power Spectrum (BiPS) to polarization maps. Application to the observed CMB polarization maps will be soon possible after the release of WMAP three year data. As a demonstration we show that for E-polarization this test can detect breakdown of statistical isotropy due to polarized synchrotron foreground.

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arXiv2005

Statistical isotropy of CMB anisotropy from WMAP

The 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.

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arXiv2004

The Cosmic Microwave Background Bipolar Power Spectrum: Basic Formalism and Applications

We study the statistical isotropy (SI) of temperature fluctuations of the CMB as distinct from Gaussianity. We present a detailed formalism of the bipolar power spectrum (BiPS) which was introduced as a fast method of measuring the statistical isotropy by Hajian & Souradeep 2003. The method exploits the existence of patterns in the real space correlations of the CMB temperature field. We discuss the applications of BiPS in constraining the topology of the universe and other theoretical scenarios of SI violation. Unlike the traditional methods of search for cosmic topology, this method is computationally fast. We also show that BiPS is potentially a good tool to detect the effect of observational artifacts in a CMB map such as non-circular beam, anisotropic noise, etc. Our method has been successfully applied to the Wilkinson Microwave Anisotropy Probe sky maps by Hajian et al. 2004, but no strong evidence of SI violation was found.

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arXiv2004

Statistical Isotropy of the Wilkinson Microwave Anisotropy Probe Data: A Bipolar Power Spectrum Analysis

The statistical expectation values of the temperature fluctuations of the Cosmic Microwave Background (CMB) are assumed to be preserved under rotations of the sky. We investigate the Statistical Isotropy (SI) of the CMB anisotropy maps recently measured by the Wilkinson Microwave Anisotropy Probe (WMAP) using Bipolar Power Spectrum (BiPS) proposed in [Hajian & Souradeep 2003]. The method can probe specific regions in multipole space using appropriate window functions. The BiPS is estimated for full sky CMB anisotropy maps based on the first year WMAP data using a range of window functions. The BiPS spectra computed for both full sky maps for all our window functions are consistent with zero, roughly within $2 σ$. The null BiPS results may be interpreted as an absence of strong violation of statistical isotropy in the first-year WMAP data on angular scales larger than that corresponding to $l\sim60$. However, pending a careful direct comparison, our results do not necessarily conflict with the specific SI related anomalies reported using other statistical tests.

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arXiv2003

Measuring Statistical isotropy of the CMB anisotropy

The statistical expectation values of the temperature fluctuations of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. This assumption of {\em statistical isotropy} (SI) of the CMB anisotropy should be observationally verified since detection of violation of SI could have profound implications for cosmology. We propose a set of measures, $κ_\ell$ ($\ell=1,2,3, ...$) for detecting violation of statistical isotropy in an observed CMB anisotropy sky map indicated by non zero $κ_\ell$. We define an estimator for the $κ_\ell$ spectrum and analytically compute its cosmic bias and cosmic variance. The results match those obtained by measuring $κ_\ell$ using simulated sky maps. Non-zero (bias corrected) $κ_\ell$ larger than the SI cosmic variance will imply violation of SI. The SI measure proposed in this paper is an appropriate statistics to investigate preliminary indication of SI violation in the recently released WMAP data.

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arXiv2003

Statistical Isotropy of CMB and Cosmic Topology

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 largest scales comparable to, and even beyond the cosmic horizon. We study a set of measures, $κ_\ell$ ($\ell=1,2,3, >...$) which for non-zero values indicate and quantify statistical isotropy violations in a CMB map. The main goal here is to interpret the $κ_\ell$ spectrum and relate it to characteristic patterns in the correlation function of CMB anisotropy arising from cosmic topology. We numerically compute the predicted $κ_\ell$ spectrum for CMB anisotropy in flat torus universe models. The essential features are captured in the leading order approximation to the correlation function where $κ_\ell$ can be calculated analytically. The $κ_\ell$ 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, $κ_\ell$ can discriminate between different topology of the universe complementing ongoing search for cosmic topology in CMB anisotropy data.

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arXiv2003

Statistical isotropy of the Cosmic Microwave Background

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, $κ_\ell$ ($\ell=1,2,3, ...$) which for non-zero values indicate and quantify statistical isotropy violations in a CMB map. We numerically compute the predicted $κ_\ell$ spectra for CMB anisotropy in flat torus universe models. Characteristic signature of different models in the $κ_\ell$ spectrum are noted.

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arXiv2002

Inhomogeneities in the Microwave Background Radiation interpreted within the framework of the Quasi-Steady State Cosmology

We calculate the expected angular power spectrum of the temperature fluctuations in the microwave background radiation (MBR) generated in the quasi-steady state cosmology (QSSC). The paper begins with a brief description of how the background is produced and thermalized in the QSSC. We then discuss within the framework of a simple model, the likely sources of fluctuations in the background due to astrophysical and cosmological causes. Power spectrum peaks at $l \approx 6-10$, 180-220 and 600-900 are shown to be related in this cosmology respectively to curvature effects at the last minimum of the scale factor, clusters and groups of galaxies. The effect of clusters is shown to be related to their distribution in space as indicated by a toy model of structure formation in the QSSC. We derive and parameterize the angular power spectrum using six parameters related to the sources of temperature fluctuations at three characteristic scales. We are able to obtain a satisfactory fit to the observational band power estimates of MBR temperature fluctuation spectrum. Moreover, the values of `best fit' parameters are consistent with the range of expected values.

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