Violation Of Statistical Isotropy Research Articles

Constraints on Bianchi-I type universe with SH0ES anchored Pantheon+ SNIa data

We study the Bianchi-I cosmological model motivated by signals of statistical isotropy violation seen in cosmic microwave background (CMB) observations and others. To that end, we consider various kinds of anisotropic matter that source anisotropy in our model, specifically Cosmic strings, Magnetic fields, Domain walls and Lorentz violation generated magnetic fields. These anisotropic matter sources, taking one at a time, are studied for their co-evolution with standard model (isotropic) sources viz., dust-like (dark/normal) matter, and dark energy modelled as cosmological constant. We constrain the Hubble parameter, density fractions of anisotropic matter, cold dark matter (CDM), and dark energy (Λ) in a Bianchi-I universe with planar symmetry i.e., which has a global ellipsoidal geometry, and try to find signatures of a cosmic preferred axis if any.The latest compilation of Type Ia Supernova (SNIa) data from Pantheon+SH0ES collaboration is used in our analysis to obtain constraints on cosmological parameters and any preferred axis for our universe.In our analysis, we found mild evidence for a cosmic preferred axis. It is interesting to note that this preferred axis lies broadly in the vicinity of other prominent cosmic anisotropy axes reported in the literature from diverse data sets.Also we find some evidence for non-zero (negative) cosmic shear and eccentricity that characterize different expansion rates in different directions and deviation from an isotropic scale factor respectively.The energy density fractions of two of the sources considered are found to be non-zero at a2σ confidence level.To be more conclusive, we require more SNIa host galaxy data for tighter constraints on distance and absolute magnitude calibration which are expected to be available from the future JWST observations and others.

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 ≳ 3 σ in Phase 2, with marginal detection possible in Phase 1.

Limits on statistical anisotropy from BOSS DR12 galaxies using bipolar spherical harmonics

We measure statistically anisotropic signatures imprinted in three-dimensional galaxy clustering using bipolar spherical harmonics (BipoSHs) in both Fourier space and configuration space. We then constrain a well-known quadrupolar anisotropy parameter $g_{2M}$ in the primordial power spectrum, parametrized by $P(\vec{k}) = \bar{P}(k) [ 1 + \sum_{M} g_{2M} Y_{2M}(\hat{k}) ]$, with $M$ determining the direction of the anisotropy. Such an anisotropic signal is easily contaminated by artificial asymmetries due to specific survey geometry. We precisely estimate the contaminated signal and finally subtract it from the data. Using the galaxy samples obtained by the Baryon Oscillation Spectroscopic Survey Data Release 12, we find no evidence for violation of statistical isotropy, $g_{2M}$ for all $M$ to be of zero within the $2\sigma$ level. The $g_{2M}$-type anisotropy can originate from the primordial curvature power spectrum involving a directional-dependent modulation $g_* (\hat{k} \cdot \hat{p})^2$. The bound on $g_{2M}$ is translated into $g_*$ as $-0.09 < g_* < 0.08$ with a $95\%$ confidence level when $\hat{p}$ is marginalized over.

Bayesian Cosmological inference beyond statistical isotropy

With advent of rich data sets, computationally challenge of inference in cosmology has relied on stochastic sampling method. First, I review the widely used MCMC approach used to infer cosmological parameters and present a adaptive improved implementation SCoPE developed by our group. Next, I present a general method for Bayesian inference of the underlying covariance structure of random fields on a sphere. We employ the Bipolar Spherical Harmonic (BipoSH) representation of general covariance structure on the sphere. We illustrate the efficacy of the method with a principled approach to assess violation of statistical isotropy (SI) in the sky maps of Cosmic Microwave Background (CMB) fluctuations. The general, principled, approach to a Bayesian inference of the covariance structure in a random field on a sphere presented here has huge potential for application to other many aspects of cosmology and astronomy, as well as, more distant areas of research like geosciences and climate modelling.

CMB anomalies after Planck

Several unexpected features have been observed in the microwave sky at large angular scales, both by WMAP and by Planck. Among those features is a lack of both variance and correlation on the largest angular scales, alignment of the lowest multipole moments with one another and with the motion and geometry of the solar system, a hemispherical power asymmetry or dipolar power modulation, a preference for odd parity modes and an unexpectedly large cold spot in the Southern hemisphere. The individual p-values of the significance of these features are in the per mille to per cent level, when compared to the expectations of the best-fit inflationary ΛCDM model. Some pairs of those features are demonstrably uncorrelated, increasing their combined statistical significance and indicating a significant detection of CMB features at angular scales larger than a few degrees on top of the standard model. Despite numerous detailed investigations, we still lack a clear understanding of these large-scale features, which seem to imply a violation of statistical isotropy and scale invariance of inflationary perturbations. In this contribution we present a critical analysis of our current understanding and discuss several ideas of how to make further progress.

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".

Litmus Test for Cosmic Hemispherical Asymmetry in the Cosmic Microwave Background B-Mode Polarization.

Recent measurements of the temperature field of the cosmic microwave background (CMB) provide tantalizing evidence for violation of statistical isotropy (SI) that constitutes a fundamental tenet of contemporary cosmology.CMB space based missions, WMAP, and Planck have observed a 7% departure in the SI temperature field at large angular scales. However, due to higher cosmic variance at low multipoles, the significance of this measurement is not expected to improve from any future CMB temperature measurements. We demonstrate that weak lensing of the CMB due to scalar perturbations produces a corresponding SI violation in B modes of CMB polarization at smaller angular scales. The measurability of this phenomenon depends upon the scales (l range) over which power asymmetry is present. Power asymmetry, which is restricted only to l<64 in the temperature field, cannot lead to any significant observable effect from this new window. However, this effect can put an independent bound on the spatial range of scales of hemispherical asymmetry present in the scalar sector.

Violation of statistical isotropy and homogeneity in the 21-cm power spectrum

Most inflationary models predict primordial perturbations to be statistically isotropic and homogeneous. Cosmic microwave background (CMB) observations, however, indicate a possible departure from statistical isotropy in the form of a dipolar power modulation at large angular scales. Alternative models of inflation, beyond the simplest single-field slow-roll models, can generate a small power asymmetry, consistent with these observations. Observations of clustering of quasars show, however, agreement with statistical isotropy at much smaller angular scales. Here, we propose to use off-diagonal components of the angular power spectrum of the 21-cm fluctuations during the dark ages to test this power asymmetry. We forecast results for the planned SKA radio array, a future radio array, and the cosmic-variance-limited case as a theoretical proof of principle. Our results show that the 21-cm line power spectrum will enable access to information at very small scales and at different redshift slices, thus improving upon the current CMB constraints by $\sim 2$ orders of magnitude for a dipolar asymmetry and by $\sim 1-3$ orders of magnitude for a quadrupolar asymmetry case.

Estimating statistical isotropy 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.

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.

Bayesian inference on the sphere beyond statistical isotropy

We present a general method for Bayesian inference of the underlying covariance structure of random fields on a sphere. We employ the Bipolar Spherical Harmonic (BipoSH) representation of general covariance structure on the sphere. We illustrate the efficacy of the method as a principled approach to assess violation of statistical isotropy (SI) in the sky maps of Cosmic Microwave Background (CMB) fluctuations. SI violation in observed CMB maps arise due to known physical effects such as Doppler boost and weak lensing; yet unknown theoretical possibilities like cosmic topology and subtle violations of the cosmological principle, as well as, expected observational artefacts of scanning the sky with a non-circular beam, masking, foreground residuals, anisotropic noise, etc. We explicitly demonstrate the recovery of the input SI violation signals with their full statistics in simulated CMB maps. Our formalism easily adapts to exploring parametric physical models with non-SI covariance, as we illustrate for the inference of the parameters of a Doppler boosted sky map. Our approach promises to provide a robust quantitative evaluation of the evidence for SI violation related anomalies in the CMB sky by estimating the BipoSH spectra along with their complete posterior.

Testing isotropy of cosmos with WMAP and PLANCK data

In recent years, there have been a large number of studies which support violation of statistical isotropy. Meanwhile, there are some studies which also found inconsistency. We use the power tensor method defined earlier in the literature to study the new CMBR data. The orientation of these three orthogonal vectors, as well as the power associated with each vector, contains information about possible violation of statistical isotropy. This information is encoded in two entropy measures, the power-entropy and alignment-entropy. We apply this method to WMAP 9-year and PLANCK data. Here, we also revisit the statistics to test high-[Formula: see text] anomaly reported in our earlier paper and find that the high degree of isotropy seen in earlier WMAP 5-year data is absent in the revised WMAP 9-year data.

Statistical diagnostics to identify galactic foregrounds in B-mode maps.

Recent developments in the search for inflationary gravitational waves in the cosmic microwave background polarization motivate the search for new diagnostics to distinguish the Galactic foreground contribution to B modes from the cosmic signal. We show that B modes from these foregrounds should exhibit a local hexadecapolar departure in power from statistical isotropy (SI). We present a simple algorithm to search for a uniform SI violation of this sort, as may arise in a sufficiently small patch of sky. We then show how to search for these effects if the orientation of the SI violation varies across the survey region, as is more likely to occur in surveys with more sky coverage. If detected, these departures from Gaussianity would indicate some level of Galactic foreground contamination in the B-mode maps. Given uncertainties about foreground properties, though, caution should be exercised in attributing a null detection to an absence of foregrounds.

Statistical isotropy violation of CMB Polarization sky due to Lorentz boost

In the frame of a moving observer, the Cosmic Microwave Background (CMB) fluctuation exhibits violation of Statistical Isotropy (SI). The SI violation effect from our local motion on CMB temperature fluctuation has been measured in the recent Planck results. We calculate the effect of our local motion with velocity $(\beta \equiv |\boldsymbol v|/c= 1.23 \times 10^{-3})$ on CMB polarization field. The Lorentz transformation of the polarization field leads to aberration in the direction of incoming photons and also modulation of the Stokes parameters, which results in mixing of power between different CMB multipoles. We show that for small values of $\beta$, the effect on the angular power spectra that corresponds to the diagonal terms in the spherical harmonic space is at $O(\beta^2)$. But non-zero off-diagonal terms at the linear order in $\beta$ could provide a measurable signature of SI violation in the Bipolar Spherical Harmonic (BipoSH) representation. We also calculate the measurability of $\beta$ from polarization maps from experiments like Planck and PRISM. It is possible to measure $\beta$ from the ideal, cosmic variance limited BipoSH spectra of $EE$, $TE$, $BB$, but not in $EB$ and $TB$. With the instrumental noise of and angular resolution of Planck, it is not possible to measure $\beta$ with high statistical significance from BipoSH spectra of polarization. PRISM can measure $\beta$ with high significance in both $EE$ and $TE$ BipoSH spectra, but not in $BB$, $EB$ and $TB$ BipoSH spectra.

Direction dependence of the power spectrum and its effect on the cosmic microwave background radiation

We study several anisotropic inflationary models and their implications for the observedviolation of statistical isotropy in the CMBR data. In two of these models the anisotropydecays very quickly during the inflationary phase of expansion. We explicitly show thatthese models lead to violation of isotropy only for low l CMBR modes. Our primary aimis to fit the observed alignment of l = 2,3 multipoles to the theoretical models. We usetwo measures, based on the power tensor, which contains information about the alignmentof each multipole, to quantify the anisotropy in data. One of the measures uses thedispersion in eigenvalues of the power tensor. We also define another measure which teststhe overall correlation between two different multipoles. We perturbatively compute thesemeasures of anisotropy and fix the theoretical parameters by making a best fit to l = 2,3multipoles. We show that some of the models studied are able to consistently explainthe observed violation of statistical isotropy.

Probing non-Gaussianities in the cosmic microwave background on an incomplete sky using surrogates

We demonstrate the feasibility to generate surrogates by Fourier-based methods for an incomplete data set. This is performed for the case of a CMB analysis, where astrophysical foreground emission, mainly present in the Galactic plane, is a major challenge. The shuffling of the Fourier phases for generating surrogates is now enabled by transforming the spherical harmonics into a new set of basis functions that are orthonormal on the cut sky. The results show that non-Gaussianities and hemispherical asymmetries in the CMB as identified in several former investigations, can still be detected even when the complete Galactic plane (|b| < 30{\deg}) is removed. We conclude that the Galactic plane cannot be the dominant source for these anomalies. The results point towards a violation of statistical isotropy.

P-odd universe, dark energy, and QCD

Cosmological observations on the largest scales exhibit a solid record of unexpected anomalies and alignments, apparently pointing towards a large scale violation of statistical isotropy. These include a variety of CMB measurements, as well as alignments of quasar polarisation vectors. In this paper we explore the possibility that several of the aforementioned large scale correlations are in fact not independent, and can be understood in a coherent way within the framework of a parity odd local Universe, and ultimately related to the nature of Dark Energy and its interactions with light.

Statistical isotropy violation of the CMB brightness fluctuations

Certain anomalies at large angular scales in the cosmic microwave background measured by WMAP have been suggested as possible evidence of breakdown of statistical isotropy(SI). Most CMB photons free-stream to the present from the surface of last scattering. It is thus reasonable to expect statistical isotropy violation in the CMB photon distribution observed now to have originated from SI violation in the baryon-photon fluid at last scattering, in addition to anisotropy of the primordial power spectrum studied earlier in literature. We consider the generalized anisotropic brightness distribution fluctuations, $\Delta(\vec{k}, \hat{n}, \tau)$ (at conformal time $\tau$) in contrast to the SI case where it is simply a function of $|\vec{k}|$ and $\hat{k} \cdot \hat{n}$. The brightness fluctuations expanded in Bipolar Spherical Harmonic (BipoSH) series, can then be written as $\Delta_{\ell_1 \ell_2}^{L M}(\vec{k}, \tau)$ where $L > 0$ terms encode deviations from statistical isotropy. We study the evolution of $\Delta_{\ell_1 \ell_2}^{L M}(\vec{k}, \tau)$ from non-zero terms $\Delta_{\ell_3 \ell_4}^{L M}(\vec{k}, \tau_s)$ at last scattering. Similar to the SI case, power at small spherical harmonic (SH) multipoles of $\Delta_{\ell_3 \ell_4}^{L M}(\vec{k},\tau_s)$ at the last scattering, is transferred to $\Delta_{\ell_1 \ell_2}^{L M}(\vec{k}, \tau)$ at larger SH multipoles. The structural similarity is more apparent in the asymptotic expression for large values of the final SH multipoles. This formalism allows an elegant identification of any SI violation observed today to a possible origin in the SI violation present in the baryon-photon fluid (eg., due to the presence of significant magnetic field).

No large-angle correlations on the non-Galactic microwave sky

We investigate the angular two-point correlation function of temperature in the WMAP maps. Updating and extending earlier results, we confirm the lack of correlations outside the Galaxy on angular scales greater than about 60 degrees at a level that would occur in 0.025 per cent of realizations of the concordance model. This represents a dramatic increase in significance from the original observations by the COBE-DMR and a marked increase in significance from the first-year WMAP maps. Given the rest of the reported angular power spectrum C_\ell, the lack of large-angle correlations that one infers outside the plane of the Galaxy requires covariance among the C_\ell up to \ell=5. Alternately, it requires both the unusually small (5 per cent of realizations) full-sky large-angle correlations, and an unusual coincidence of alignment of the Galaxy with the pattern of cosmological fluctuations (less than 2 per cent of those 5 per cent). We argue that unless there is some undiscovered systematic error in their collection or reduction, the data point towards a violation of statistical isotropy. The near-vanishing of the large-angle correlations in the cut-sky maps, together with their disagreement with results inferred from full-sky maps, remain open problems, and are very difficult to understand within the concordance model.

Testable polarization predictions for models of CMB isotropy anomalies

Anomalies in the large-scale cosmic microwave background (CMB) temperature sky measured by the Wilkinson Microwave Anisotropy Probe have been suggested as possible evidence for a violation of statistical isotropy on large scales. In any physical model for broken isotropy, there are testable consequences for the CMB polarization field. We develop simulation tools for predicting the polarization field in models that break statistical isotropy locally through a modulation field. We study two different models: dipolar modulation, invoked to explain the asymmetry in power between northern and southern ecliptic hemispheres, and quadrupolar modulation, posited to explain the alignments between the quadrupole and octopole. For the dipolar case, we show that predictions for the correlation between the first 10 multipoles of the temperature and polarization fields can typically be tested at better than the 98% CL. For the quadrupolar case, we show that the polarization quadrupole and octopole should be moderately aligned. Such an alignment is a generic prediction of explanations which involve the temperature field at recombination and thus discriminate against explanations involving foregrounds or local secondary anisotropy. Predicted correlations between temperature and polarization multipoles out to $\ensuremath{\ell}=5$ provide tests at the $\ensuremath{\sim}99%$ CL or stronger for quadrupolar models that make the temperature alignment more than a few percent likely. As predictions of anomaly models, polarization statistics move beyond the a posteriori inferences that currently dominate the field.