Bipolar harmonic encoding of CMB correlation patterns

Joshi, Nidhi; Jhingan, Sanjay; Souradeep, T.; Hajian, Amir

doi:10.1103/physrevd.81.083012

Cited by 23 publications

(24 citation statements)

References 55 publications

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“…This anisotropy was characterized (as it is here also) in terms of an uncorrelated and unpolarized background of gravitational waves with a direction-dependent intensity parametrized in terms of spherical-harmonic expansion of the intensity. Here we re-derive anisotropy-detection tools using mathematical objects (bipolar spherical harmonics; BiPoSHs [32][33][34]) developed for analogous problems in the study of the cosmic microwave background. The analysis here provides some simplifications and insights and also intuitive estimates for the smallest detectable signals.…”

Section: Introductionmentioning

confidence: 99%

The search for statistical anisotropy in the gravitational-wave background with pulsar timing arrays

Hotinli¹,

Kamionkowski²,

Jaffe³

2019

TheOJA

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Pulsar-timing arrays (PTAs) are seeking gravitational waves from supermassive-black-hole binaries, and there are prospects to complement these searches with stellar-astrometry measurements. Theorists still disagree, however, as to whether the local gravitational-wave background will be statistically isotropic, as arises if it is the summed contributions from many SMBH binaries, or whether it exhibits the type of statistical anisotropy that arises if the local background is dominated by a handful (or even one) bright source. Here we derive, using bipolar spherical harmonics, the optimal PTA estimators for statistical anisotropy in the GW background and simple estimates of the detectability of this anisotropy. We provide results on the smallest detectable amplitude of a dipole anisotropy (and several other low-order multipole moments) and also the smallest detectable amplitude of a "beam" of gravitational waves. Results are presented as a function of the signal-tonoise with which the GW signal is detected and as a function of the number of pulsars (assuming uniform distribution on the sky and equal sensitivity per pulsar). We provide results first for measurements with a single time-domain window function and then show how the results are augmented with the inclusion of time-domain information. The approach here is intended to be conceptually straightforward and to complement the results of more detailed (but correspondingly less intuitive) modeling of the actual measurements.

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Section: Introductionmentioning

confidence: 99%

The search for statistical anisotropy in the gravitational-wave background with pulsar timing arrays

Hotinli¹,

Kamionkowski²,

Jaffe³

2019

TheOJA

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“…These coefficients are known as bipolar spherical harmonic (BipoSH) coefficients (Hajian and Souradeep, 2003;Joshi et al, 2010). As we shall see, the BipoSH coefficients provide a convenient way to organize the effects of the non-Gaussian modulation.…”

Section: B Non-gaussian Modulation Of Cmbmentioning

confidence: 99%

Anomalies in the Cosmic Microwave Background and Their Non-Gaussian Origin in Loop Quantum Cosmology

Agulló

Kranas

Vijayakumar

2021

Front. Astron. Space Sci.

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Anomalies in the cosmic microwave background (CMB) refer to features that have been observed, mostly at large angular scales, and which show some tension with the statistical predictions of the standard ΛCDM model. In this work, we focus our attention on power suppression, dipolar modulation, a preference for odd parity, and the tension in the lensing parameter AL. Though the statistical significance of each individual anomaly is inconclusive, collectively they are significant, and could indicate new physics beyond the ΛCDM model. In this article, we present a brief, but pedagogical introduction to CMB anomalies and propose a common origin in the context of loop quantum cosmology.

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“…Non-zero BipoSH coefficients with L > 0 capture SI violation [41]. The BipoSH coefficients can be categorized into two distinct classes, defined as even ( l 1 + l 2 + L is even) and odd (l 1 + l 2 + L is odd) parity BipoSH.…”

Section: Primer: Bipolar Spherical Harmonic (Biposh) Representationmentioning

confidence: 99%

Estimating statistical isotropy violation in CMB due to non-circular beam and complex scan in minutes

Pant

Das

Rotti

et al. 2016

J. Cosmol. Astropart. Phys.

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Abstract. Mild, unavoidable deviations from circular-symmetry of instrumental beams along with scan strategy can give rise to measurable Statistical Isotropy (SI) violation in Cosmic Microwave Background (CMB) experiments. If not accounted properly, this spurious signal can complicate the extraction of other SI violation signals (if any) in the data. However, estimation of this effect through exact numerical simulation is computationally intensive and time consuming. A generalized analytical formalism not only provides a quick way of estimating this signal, but also gives a detailed understanding connecting the leading beam anisotropy components to a measurable BipoSH characterisation of SI violation. In this paper, we provide an approximate generic analytical method for estimating the SI violation generated due to a non-circular (NC) beam and arbitrary scan strategy, in terms of the Bipolar Spherical Harmonic (BipoSH) spectra. Our analytical method can predict almost all the features introduced by a NC beam in a complex scan and thus reduces the need for extensive numerical simulation worth tens of thousands of CPU hours into minutes long calculations. As an illustrative example, we use WMAP beams and scanning strategy to demonstrate the easability, usability and efficiency of our method. We test all our analytical results against that from exact numerical simulations.

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Bipolar harmonic encoding of CMB correlation patterns

Cited by 23 publications

References 55 publications

The search for statistical anisotropy in the gravitational-wave background with pulsar timing arrays

The search for statistical anisotropy in the gravitational-wave background with pulsar timing arrays

Anomalies in the Cosmic Microwave Background and Their Non-Gaussian Origin in Loop Quantum Cosmology

Estimating statistical isotropy violation in CMB due to non-circular beam and complex scan in minutes

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