arXiv subjects

Aditya Rotti

Publications and source records attributed to Aditya Rotti.

36 records · Page 2Linked to original sources

arXiv2019

Measuring our velocity from fluctuations in number counts

Our velocity relative to the cosmic microwave background (CMB) generates a dipole from the CMB monopole, which was accurately measured by COBE. The relative velocity also modulates and aberrates the CMB fluctuations, generating a small signature of statistical isotropy violation in the covariance matrix. This signature was first measured by Planck 2013. Galaxy surveys are similarly affected by a Doppler boost. The dipole generated from the number count monopole has been extensively discussed, and measured (at very low accuracy) in the NVSS and TGSS radio continuum surveys. For the first time, we present an analysis of the Doppler imprint on the number count fluctuations, using the bipolar spherical harmonic formalism to quantify these effects. Next-generation wide-area surveys with a high redshift range are needed to detect the small Doppler signature in number count fluctuations. We show that radio continuum surveys with the SKA should enable a detection at $\gtrsim 3 σ$ in Phase 2, with marginal detection possible in Phase 1.

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arXiv2018

Can we neglect relativistic temperature corrections in the Planck thermal SZ analysis?

Measurements of the thermal Sunyaev-Zel'dovich (tSZ) effect have long been recognized as a powerful cosmological probe. Here we assess the importance of relativistic temperature corrections to the tSZ signal on the power spectrum analysis of the Planck Compton-$y$ map, developing a novel formalism to account for the associated effects. The amplitude of the tSZ power spectrum is found to be sensitive to the effective electron temperature, $\bar{T}_e$, of the cluster sample. Omitting the corresponding modifications leads to an underestimation of the $yy$-power spectrum amplitude. Relativistic corrections thus add to the error budget of tSZ power spectrum observables such as $σ_8$. This could help alleviate the tension between various cosmological probes, with the correction scaling as $Δσ_8/σ_8 \simeq 0.019\,[k\bar{T}_e\,/\,5\,{\rm keV}]$ for Planck. At the current level of precision, this implies a systematic shift by $\simeq 1σ$, which can also be interpreted as an overestimation of the hydrostatic mass bias by $Δb \simeq 0.046\,(1-b)\,[k\bar{T}_e\,/\,5\,{\rm keV}]$, bringing it into better agreement with hydrodynamical simulations. It is thus time to consider relativistic temperature corrections in the processing of current and future tSZ data.

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arXiv2018

Real-space computation of $E$/$B$-mode maps I: Formalism, Compact Kernels, and Polarized Filaments

We derive full-sky, real-space operators that convert between polarization Stokes Q/U parameters and the coordinate-independent scalar E/B modes that are widely used in Cosmic Microwave Background (CMB) and cosmic shear analysis. We also derive real space operators that decompose the measured Stokes parameters into those corresponding to E-modes and B-modes respectively, without ever evaluating the scalar fields themselves. For all these real space operators we show that the kernels split naturally into angular and radial parts and we show explicitly how the radial extent of these kernels depends on the targeted band-limit. The kernels can be interpreted either as a complex convolving beam or as a Green's function when they are expressed in terms of the forward or inverse rotation Euler angles. We show that an arbitrary radial function can produce E/B-like maps, provided it vanishes at the origin and the antipodal point. These maps are simply filtered versions of the standard E/B maps. We argue that it is possible compute E/B maps in real space with a compactly-supported kernel, an approach that can guarantee the avoidance of known foreground regions and could be employed in a massively-parallel scheme at high-resolution. We show that the spin raising and lowering operators $ð^2$/$\barð^2$ are special cases of these generalized radial functions, and present their band limited versions. The spatial structure of the real space operators provides great intuition for the E/B structure of polarized, filamentary galactic foregrounds. We predict a non-zero B-mode signature that is expected from polarized filaments in the sky. This paper is the first part in a series of papers that explore real-space computation of polarization modes and their applications.

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arXiv2016

CMB-S4 Science Book, First Edition

This book lays out the scientific goals to be addressed by the next-generation ground-based cosmic microwave background experiment, CMB-S4, envisioned to consist of dedicated telescopes at the South Pole, the high Chilean Atacama plateau and possibly a northern hemisphere site, all equipped with new superconducting cameras. CMB-S4 will dramatically advance cosmological studies by crossing critical thresholds in the search for the B-mode polarization signature of primordial gravitational waves, in the determination of the number and masses of the neutrinos, in the search for evidence of new light relics, in constraining the nature of dark energy, and in testing general relativity on large scales.

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arXiv2016

Isotropy-Violation Diagnostics for $B$-mode Polarization Foregrounds to the Cosmic Microwave Background

Isotropy-violation statistics can highlight polarized galactic foregrounds that contaminate primordial $B$-modes in the Cosmic Microwave Background (CMB). We propose a particular isotropy-violation test and apply it to polarized Planck 353 GHz data, constructing an map that indicates $B$-mode foreground dust power over the sky. We build our main isotropy test in harmonic space via the bipolar spherical harmonic basis, and our method helps us to identify the least-contaminated directions. By this measure, there are regions of low foreground in and around the BICEP field, near the South Galactic Pole, and in the Northern Galactic Hemisphere. There is also a possible foreground feature in the BICEP field. We compare our results to those based on the local power spectrum, which is computed on discs using a version of the method of Planck Int.~XXX (2016). The discs method is closely related to our isotropy-violation diagnostic. We pay special care to the treatment of noise, including chance correlations with the foregrounds. Currently we use our isotropy tool to assess the cleanest portions of the sky, but in the future such methods will allow isotropy-based null tests for foreground contamination in maps purported to measure primordial $B$-modes, particularly in cases of limited frequency coverage.

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arXiv2016

Constraining stochastic gravitational wave background from weak lensing of CMB B-modes

A stochastic gravitational wave background (SGWB) will affect the CMB anisotropies via weak lensing. Unlike weak lensing due to large scale structure which only deflects photon trajectories, a SGWB has an additional effect of rotating the polarization vector along the trajectory. We study the relative importance of these two effects, deflection \& rotation, specifically in the context of E-mode to B-mode power transfer caused by weak lensing due to SGWB. Using weak lensing distortion of the CMB as a probe, we derive constraints on the spectral energy density ($Ω_{GW}$) of the SGWB, sourced at different redshifts, without assuming any particular model for its origin. We present these bounds on $Ω_{GW}$ for different power-law models characterizing the SGWB, indicating the threshold above which observable imprints of SGWB must be present in CMB.

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arXiv2016

Statistical isotropy violation in WMAP CMB maps resulting from non-circular beams

Statistical isotropy (SI) of Cosmic Microwave Background (CMB) fluctuations is a key observational test to validate the cosmological principle underlying the standard model of cosmology. While a detection of SI violation would have immense cosmological ramification, it is important to recognise their possible origin in systematic effects of observations. WMAP seven year (WMAP-7) release claimed significant deviation from SI in the bipolar spherical harmonic (BipoSH) coefficients $A_{ll}^{20}$ and $A_{l-2l}^{20}$. Here we present the first explicit reproduction of the measurements reported in WMAP-7, confirming that beam systematics alone can completely account for the measured SI violation. The possibility of such a systematic origin was alluded to in WMAP-7 paper itself and other authors but not as explicitly so as to account for it accurately. We simulate CMB maps using the actual WMAP non-circular beams and scanning strategy. Our estimated BipoSH spectra from these maps match the WMAP-7 results very well. It is also evident that only a very careful and adequately detailed modelling, as carried out here, can conclusively establish that the entire signal arises from non-circular beam effect. This is important since cosmic SI violation signals are expected to be subtle and dismissing a large SI violation signal as observational artefact based on simplistic plausibility arguments run the serious risk of "throwing the baby out with the bathwater".

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arXiv2015

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

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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arXiv2015

Recovering hidden signals of statistical anisotropy from a masked or partial CMB sky

Any isotropy violating phenomena on cosmic microwave background (CMB) induces off-diagonal correlations in the two-point function. These correlations themselves can be used to estimate the underlying anisotropic signals. Masking due to residual foregrounds, or availability of partial sky due to survey limitation, are unavoidable circumstances in CMB studies. But, masking induces additional correlations, and thus complicates the recovery of such signals. In this work, we discuss a procedure based on bipolar spherical harmonic (BipoSH) formalism to comprehensively addresses any spurious correlations induced by masking and successfully recover hidden signals of anisotropy in observed CMB maps. This method is generic, and can be applied to recover a variety of isotropy violating phenomena. Here, we illustrate the procedure by recovering the subtle Doppler boost signal from simulated boosted CMB skies, which has become possible with the unprecedented full-sky sensitivity of PLANCK probe.

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arXiv2015

Weak lensing in non-statistically isotropic universes

The Bipolar Spherical Harmonics (BipoSH) form a natural basis to study the CMB two point correlation function in a non-statistically isotropic (non-SI) universe. The coefficients of expansion in this basis are a generalisation of the well known CMB angular power spectrum and contain complete information of the statistical properties of a non-SI but Gaussian random CMB sky. We use these coefficients to describe the weak lensing of CMB photons in a non-SI universe. Finally we show that the results reduce to the standard weak lensing results in the isotropic limit.

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arXiv2015

A novel approach to reconstructing signals of isotropy violation from a masked CMB sky

Statistical isotropy (SI) is one of the fundamental assumptions made in cosmological model building. This assumption is now being rigorously tested using the almost full sky measurements of the CMB anisotropies. A major hurdle in any such analysis is to handle the large biases induced due to the process of masking. We have developed a new method of analysis, using the bipolar spherical harmonic basis functions, in which we semi-analytically evaluate the modifications to SI violation induced by the mask. The method developed here is generic and can be potentially used to search for any arbitrary form of SI violation. We specifically demonstrate the working of this method by recovering the Doppler boost signal from a set of simulated, masked CMB skies.

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arXiv2014

Orthogonal BipoSH measures : Scrutinizing sources of isotropy violation

The two point correlation function of the CMB temperature anisotropies is generally assumed to be statistically isotropic (SI). Deviations from this assumption could be traced to physical or observational artefacts and systematic effects. Measurement of non-vanishing power in the BipoSH spectra is a standard statistical technique to search for isotropy violations. Although this is a neat tool allowing a blind search for SI violations in the CMB sky, it is not easy to discern the cause of isotropy violation using this measure. In this article, we propose a novel technique of constructing orthogonal BipoSH estimators, which can be used to discern between models of isotropy violation.

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arXiv2013

A comparison of CMB lensing efficiency of gravitational waves and large scale structure

We provide a detailed treatment and comparison of the weak lensing effects due to large-scale structure (LSS), or scalar density perturbations and those due to gravitational waves(GW) or tensor perturbations, on the temperature and polarization power spectra of the Cosmic Microwave Background (CMB). We carry out the analysis both in real space by using the correlation function method, as well as in the spherical harmonic space. We find an intriguing similarity between the lensing kernels associated with LSS lensing and GW lensing. It is found that the lensing kernels only differ in relative negative signs and their form is very reminiscent of even and odd parity bipolar spherical harmonic coefficients. Through a numerical study of these lensing kernels, we establish that lensing due to GW is more efficient at distorting the CMB spectra as compared to LSS lensing, particularly for the polarization power spectra. Finally we argue that the CMB B-mode power spectra measurements can be used to place interesting constraints on GW energy densities.

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arXiv2013

A New Window into Stochastic Gravitational Wave Background

A stochastic gravitational wave background (SGWB) would gravitationally lens the cosmic microwave background (CMB) photons. We find that the lensing due to gravitational waves(GW) is more efficient as compared to lensing due to scalar density perturbations. Though the effect of lensing due to GW is found to effect all the four CMB power spectra, its effect is most prominently seen in the CMB polarization power spectra. This suggests that the measurements of the CMB angular power spectra could be used to constraining the energy density ($Ω_{GW}$) of the SGBW. In our analysis we find that the most stringent constraints on $Ω_{GW}$ are due to measurements of the angular power spectra of CMB temperature anisotropies. We show that in the future it will be possible to place more stringent bounds on $Ω_{GW}$ using improved upper limits or detections of the angular power spectra of the B-modes of CMB polarization at large multipoles.

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arXiv2013

Revealing Non-circular beam effect in WMAP-7 CMB maps with BipoSH measures of Statistical Isotropy

Mild, unavoidable deviations from circular-symmetry of instrumental beams in current Cosmic Microwave Background (CMB) experiments now pose a significant challenge to deriving high precision inferences from the high sensitivity and resolution of CMB measurements. We present analytic results, verified by numerical simulations, that CMB maps of cosmological signal that respect underlying statistical isotropy (SI) symmetry, measured with an instrument that has mildly non-circular (NC) beam would, nevertheless, exhibit SI violation. Further, we show that appropriate observable measures constructed within the Bipolar spherical harmonic (BipoSH) representation of SI violation capture subtle NC-beam effects coupled with the scan strategy of the instrument. Accompanying their latest 7-year data release, the WMAP team published very high significance measurements of non-zero BipoSH spectra, A^{20}_{l l} and A^{20}_{l-2 l}, in the "W" and "V" band of the experiment. We present a strong case that the BipoSH measurement are primarily explained by the quadrupolar (m=2) component of the NC-beams, b_{l2}, of the respective channels. The fact that subtle levels of non-circularity, e.g., WMAP beams |b_{l2}|/b_{l0} < 0.01, lead to measurable BipoSH spectra points to the immense promise and potential of the BipoSH representation. The key result of this work is that using BipoSH measurements it is possible to estimate an equivalent single hit,'parallel transported' effective NC-beam that matches both the angular power spectrum and the non-zero BipoSH measurements of the observed maps. Hence, BipoSH analysis provides a very simple and effective characterization of CMB maps made with NC-beam. (Abridged)

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arXiv2013

Removing the ISW-lensing bias from the local-form primordial non-Gaussianity estimation

The Integrated Sachs-Wolfe (ISW) effect produces a secondary temperature anisotropy of CMB. The main contribution comes from z<2, where dark energy leads to a decay of potentials. As the same photons are gravitationally lensed by these decaying potentials, there exists a high degree of correlation between the ISW effect and CMB lensing, leading to a non-zero three-point correlation (bispectrum) of the observed temperature anisotropy. This ISW-lensing bispectrum, whose shape resembles that of the so-called "local-form" primordial bispectrum parametrized by fNL, is known to be the largest contamination of fNL. In order to avoid a spurious detection of primordial non-Gaussianity, we need to remove the ISW-lensing bias. In this work, we investigate three debiasing methods: (I) subtraction of an expected, ensemble average of the ISW-lensing bispectrum; (II) subtraction of a measured ISW-lensing bispectrum; and (III) direct subtraction of an estimated ISW signal from an observed temperature map. One may use an estimation of the ISW map from external non-CMB data or that from the CMB data themselves. As the methods II and III are based on fewer assumptions about the nature of dark energy, they are preferred over the method I. While the methods I and II yield unbiased estimates of fNL with comparable error bars, the method III yields a biased result when the underlying primordial fNL is non-zero and the ISW map is estimated from a lensing potential reconstructed from the observed temperature map. One of the sources of the bias is a lensing reconstruction noise bias which is independent of fNL and can be calculated precisely, but other fNL-dependent terms are difficult to compute reliably. We thus conclude that the method II is the best, model-independent way to remove the ISW-lensing bias of fNL, enabling us to test the physics of inflation with smaller systematic errors.

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arXiv2011

WMAP anomaly : Weak lensing in disguise

Statistical isotropy (SI) has been one of the simplifying assumptions in cosmological model building. Experiments like WMAP and PLANCK are attempting to test this assumption by searching for specific signals in the Cosmic Microwave Background (CMB) two point correlation function. Modifications to this correlation function due to gravitational lensing by the large scale structure (LSS) surrounding us have been ignored in this context. Gravitational lensing will induce signals which mimic isotropy violation even in an isotropic universe. The signal detected in the Bipolar Spherical Harmonic (BipoSH) coefficients $A^{20}_{ll}$ by the WMAP team may be explained by accounting for the lensing modifications to these coefficients. Further the difference in the amplitude of the signal detected in the V-band and W-band maps can be explained by accounting for the differences in the designed angular sensitivity of the instrumental beams. The arguments presented in this article have crucial implications for SI violation studies. Constraining SI violation will only be possible by complementing CMB data sets with all sky measurements of the large scale dark matter distribution. Till that time, the signal detected in the BipoSH coefficients from WMAP-7 could also be yet another suggested evidence of strong deviations from the standard $Λ$CDM cosmology based on homogeneous and isotropic FRW models.

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arXiv2011

Statistics of Bipolar Representation of CMB maps

Gaussianity 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($A^{LM}_{l_1 l_2}$), 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 $M\neq0$, 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.

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