Violation Of 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.

Novel setup for detecting short-range anisotropic corrections to gravity

In this paper we argue that, even though there are strong theoretical and empirical reasons to expect a violation of spatial isotropy at short distances, contemporary setups for probing gravitational interactions at short distances have not been configured to measure such spatial anisotropies. We propose a simple modification to the state-of-the-art torsion pendulum design and numerically demonstrate that it suppresses signals due to the large spatially-isotropic component of the gravitational force while maintaining a high sensitivity to short-range spatial anisotropies. We incorporate anisotropy using both Yukawa-type and power-law-type short-distance corrections to gravity. The proposed differential torsion pendulum is shown to be capable of making sensitive measurements of small gravitational anisotropies and the resulting anisotropic torques are largely independent of the details of the underlying short-distance modification to gravity. Thus, if there is an anisotropic modification to gravity, from any theory, in any form of the modified potential, the proposed setup provides a practical means of detecting it.

Statistical anisotropy in galaxy ellipticity correlations

As well as the galaxy number density and peculiar velocity, the galaxy intrinsic alignment can be used to test the cosmic isotropy. We study distinctive impacts of the isotropy breaking on the configuration-space two-point correlation functions (2PCFs) composed of the spin-2 galaxy ellipticity field. For this purpose, we build a formalism for general types of the isotropy-violating 2PCFs and a methodology to efficiently compute them by generalizing the polypolar spherical harmonic decomposition approach to the spin-weighted version. As a demonstration, we analyze the 2PCFs when the matter power spectrum has a well-known g *-type isotropy-breaking term (induced by, e.g., dark vector fields). We then confirm that some anisotropic distortions indeed appear in the 2PCFs and their shapes rely on a preferred direction causing the isotropy violation, d̂. Such a feature can be a distinctive indicator for testing the cosmic isotropy. Comparing the isotropy-violating 2PCFs computed with and without the plane parallel (PP) approximation, we find that, depending on d̂, the PP approximation is no longer valid when an opening angle between the directions towards target galaxies is 𝒪(1°) for the density-ellipticity and velocity-ellipticity cross correlations and around 10° for the ellipticity auto correlation. This suggests that an accurate test for the cosmic isotropy requires the formulation of the 2PCF without relying on the PP approximation.

Structure Functions and Structure Parameters of Velocity Fluctuations in Numerically Simulated Atmospheric Convective Boundary Layer Flows

AbstractWe extend our previous study, which dealt with structure functions of potential temperature fluctuations, and focus on the characteristics of second-order velocity structure functions and corresponding structure parameters in the atmospheric convective boundary layer. We consider the three previously reported methods to compute the structure parameters of turbulent velocity fields: the direct method, the true spectral method, and the approximate spectral method. The methods are evaluated using high-resolution gridded numerical data from large-eddy simulations of shear-free and shear-driven convective boundary layers. Results indicate that the direct and true spectral methods are more suitable than the approximate spectral method, which overestimates the structure parameters of velocity as a result of assuming the inertial-subrange shape of the velocity spectrum for all turbulence scales. Results also suggest that structure parameters of vertical velocity fluctuations are of limited utility because of violations of local isotropy, especially in shear-free convective boundary layers.

Testing for gravitational preferred directions with galaxy and lensing surveys

We analyze the sensitivity of galaxy and weak-lensing surveys to detect preferred directions in the gravitational interaction. We consider general theories of gravity involving additional vector degrees of freedom with non-vanishing spatial components in the background. We use a model-independent parametrization of the perturbations equations in terms of four effective parameters, namely, the standard effective Newton constant Geff and slip parameter γ for scalar modes and two new parameters μQ and μh for vector and tensor modes respectively, which are required when preferred directions are present. We obtain the expressions for the multipole galaxy power spectrum in redshift space and for the weak-lensing shear, convergence and rotation spectra in the presence of preferred directions. By performing a Fisher matrix forecast analysis, we estimate the sensitivity of a future Euclid-like survey to detect this kind of modification of gravity. We finally compare with the effects induced by violations of statistical isotropy in the primordial power spectrum and identify the observables which could discriminate between them.

Inflation of the universe by the non-minimal Y (R )F 2 models

The cosmological solutions of the non-minimal [Formula: see text] theory, which are compatible with FRW spacetime, are investigated. In order to avoid the isotropy violation of a vector field, it can be considered that the presence of a triplet of vector fields satisfy SO(3) symmetry or the average of randomly oriented electromagnetic fields over the sufficiently large volume. By considering the symmetry arguments, the inflation driven by the non-minimally coupled vector fields is studied. Then the cosmological solutions and corresponding models are obtained with the power-law, hyperbolic and hybrid scale functions.

Sitoolbox: A package for Bayesian estimation of the isotropy violation in the CMB sky

ABSTRACT The standard model of cosmology predicts a statistically isotropic (SI) cosmic microwave background (CMB) sky. However, the SI violation signals are always present in an observed sky-map. Different cosmological artefacts, measurement effects, and unavoidable effects during data analysis, etc. may lead to isotropy violation in an otherwise SI sky. Therefore, a proper data analysis technique should calculate all these SI violation signals, so that they can be matched with SI violation signals from the known sources, and then conclude if there is any intrinsic SI violation in the CMB sky. In one of our recent works, we presented a general Bayesian formalism for measuring the isotropy violation signals in the CMB sky in the presence of an idealized isotropic noise. In this paper, we have extended the mechanism and develop a software package, sitoolbox, for measuring SI violation in presence of anisotropic noise and masking.

Joint Bayesian analysis of large angular scale CMB temperature anomalies

Cosmic microwave background measurements show an agreement with the concordance cosmology model except for a few notable anomalies: Power Suppression, the lack of large scale power in the temperature data compared to what is expected in the concordance model, and Cosmic Hemispherical Asymmetry, a dipolar breakdown of statistical isotropy. An expansion of the CMB covariance in Bipolar Spherical Harmonics naturally parametrizes both these large-scale anomalies, allowing us to perform an exhaustive, fully Bayesian joint analysis of the power spectrum and violations of statistical isotropy up to the dipole level. Our analysis sheds light on the scale dependence of the Cosmic Hemispherical Asymmetry. Assuming a scale-dependent dipole modulation model with a two-parameter power law form, we explore the posterior pdf of amplitude A(l = 16) and the power law index α and find the maximum a posteriori values A*(l = 16) = 0.064 ± 0.022 and α* = −0.92 ± 0.22. The maximum a posteriori direction associated with the Cosmic Hemispherical Asymmetry is (l,b) = (247.8o, −19.6o) in Galactic coordinates, consistent with previous analyses. We evaluate the Bayes factor BSI−DM to compare the Cosmic Hemispherical Asymmetry model with the isotropic model. The data prefer but do not substantially favor the anisotropic model (BSI−DM=0.4). We consider several priors and find that this evidence ratio is robust to prior choice. The large-scale power suppression does not soften when jointly inferring both the isotropic power spectrum and the parameters of the asymmetric model, indicating no evidence that these anomalies are coupled.

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.

The light speed versus the observer: the Kennedy\u2013Thorndike test from GRAAL-ESRF

High precision tests of the light speed constancy for all observers as a empirical basis of Special Relativity have continuously been among the goals of advanced experimental studies. Based on the Compton edge method proposed by us (Gurzadyan and Margarian in Phys Scr 53:513, 1996), a constraint on the one-way light speed isotropy and Lorentz invariance violation has been obtained at the dedicated GRAAL experiment at European Synchrotron Radiation Facility (ESRF, Grenoble) (Gurzadyan et al. in Mod Phys Lett A 20:1, 2005, Nuovo Cimento 122:515, 2007, Proceedings of the XII M. Grossmann meeting on general relativity, vol B. World Scientific, p 1495. arXiv:1004.2867, 2012; Bocquet et al. in Phys Rev Lett 104:241601, 2010). Using the GRAAL data we now get a new constraint on one of the key tests of Special Relativity—the Kennedy–Thorndike experiment (Kennedy and Thorndike in Phys Rev 42:400, 1932) in probing light speed invariance with respect to the velocity of the observer (apparatus). Our analysis takes advantage of GRAAL’s setup where two separate energy scales are involved: first, via the position of the Compton edge determining the light speed in the reference frame of incident 6 GeV electrons within the tagging system, second, in the calorimeter via the 1.27 MeV photons of the ^{22}Na source. The two energy scales are engaged to each other through production of eta mesons by tagged laser Compton backscattered gamma -rays. The accuracy of the calibration and stability of energies reached in each section enable us to obtain the limit of 7 times 10^{-12} for the Kennedy–Thorndike test, which improves the currently existing limits by three orders of magnitude.

Characteristics of the turbulent energy dissipation rate in a cylinder wake

This work aims to improve our understanding of the turbulent energy dissipation rate in the wake of a circular cylinder. Ten of the twelve velocity derivative terms which make up the energy dissipation rate are simultaneously obtained with a probe composed of four X-wires. Measurements are made in the plane of mean shear at$x/d=10$, 20 and 40, where$x$is the streamwise distance from the cylinder axis and$d$is the cylinder diameter, at a Reynolds number of$2.5\times 10^{3}$based on$d$and free-stream velocity. Both statistical and topological features of the velocity derivatives as well as the energy dissipation rate, approximated by a surrogate based on the assumption of homogeneity in the transverse plane, are examined. The spectra of the velocity derivatives indicate that local axisymmetry is first satisfied at higher wavenumbers while the departure at lower wavenumbers is caused by the Kármán vortex street. The spectral method proposed by Djenidi & Antonia (Exp. Fluids, vol. 53, 2012, pp. 1005–1013) based on the universality of the dissipation range of the longitudinal velocity spectrum normalized by the Kolmogorov scales also applies in the present flow despite the strong perturbation from the Kármán vortex street and violation of local isotropy at small$x/d$. The appropriateness of the spectral chart method is consistent with Antoniaet al.’s (Phys. Fluids, vol. 26, 2014, 45105) observation that the two major assumptions in Kolmogorov’s first similarity hypothesis, i.e. very large Taylor microscale Reynolds number and local isotropy, can be significantly relaxed. The data also indicate that vorticity spectra are more sensitive, when testing the first similarity hypothesis, than velocity spectra. They also reveal that the velocity derivatives$\unicode[STIX]{x2202}u/\unicode[STIX]{x2202}y$and$\unicode[STIX]{x2202}v/\unicode[STIX]{x2202}x$play an important role in the interaction between large and small scales in the present flow. The phase-averaged data indicate that the energy dissipation is concentrated mostly within the coherent spanwise vortex rollers, in contrast with the model of Hussain (J. Fluid Mech., vol. 173, 1986, pp. 303–356) and Hussain & Hayakawa (J. Fluid Mech., vol. 180, 1987, p. 193), who conjectured that it resides mainly in regions of strong turbulent mixing.

Testing the Isotropy of the Log N–log S Slope for the NVSS Radio Catalog

Abstract The cumulative number count N of sources above a threshold is known to approximately follow a power-law behavior N ∝ S − x . We study the variation of spectral index x across the sky to look for possible signals of a violation of isotropy. We develop a rigorous algorithm of likelihood maximization to accurately fit for the spectral index. We divide the sky into upper and lower hemispheres for a particular choice of the z axis and determine the error normalized difference between the best fit values of the spectral indices between the two hemispheres. The maximum value of this difference obtained by varying over the z axis provides us with a measure of departure from isotropy. We find that the data support isotropy of the spectral index. We also perform a dipole fit to the spectral index as a function of the angular coordinates. The result is found to be consistent with isotropy.

A Bayesian Approach for Detection of Isotropy Violation of a Random Field Over a Sphere

We present a general method for estimating the isotropy violation of random fields on a sphere using a Bayesian formalism. We use Bipolar Spherical Harmonic (BipoSH) representation of general covariance structure on the sphere. 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.

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".

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.

Orthogonal bipolar spherical harmonics 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.

Detectability of Torus Topology

AbstractThe global shape, or topology, of the universe is not constrained by the equations of General Relativity, which only describe the local universe. As a consequence, the boundaries of space are not fixed and topologies different from the trivial infinite Euclidean space are possible. The cosmic microwave background (CMB) is the most efficient tool to study topology and test alternative models. Multi-connected topologies, such as the 3-torus, are of great interest because they are anisotropic and allow us to test a possible violation of isotropy in CMB data. We show that the correlation function of the coefficients of the expansion of the temperature and polarization anisotropies in spherical harmonics encodes a topological signature. This signature can be used to distinguish an infinite space from a multi-connected space on sizes larger than the diameter of the last scattering surface (DLSS). With the help of the Kullback-Leibler divergence, we set the size of the edge of the biggest distinguishable torus with CMB temperature fluctuations and E-modes of polarization to 1.15 DLSS. CMB temperature fluctuations allow us to detect universes bigger than the observable universe, whereas E-modes are efficient to detect universes smaller than the observable universe.

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.

Calibration errors unleashed: effects on cosmological parameters and requirements for large-scale structure surveys

Imperfect photometric calibration of galaxy surveys due to either astrophysical or instrumental effects leads to biases in measuring galaxy clustering and in the resulting cosmological parameter measurements. More interestingly (and disturbingly), the spatially varying calibration also generically leads to violations of statistical isotropy of the galaxy clustering signal. Here we develop, for the first time, a formalism to propagate the effects of photometric calibration variations with arbitrary spatial dependence across the sky to the observed power spectra and to the cosmological parameter constraints. We develop an end-to-end pipeline to study the effects of calibration, and illustrate our results using specific examples including Galactic dust extinction and survey-dependent magnitude limits as a function of zenith angle of the telescope. We establish requirements on the control of calibration so that it doesn't significantly bias constraints on dark energy and primordial non-Gaussianity. Two principal findings are: 1) largest-angle photometric calibration variations (dipole, quadrupole and a few more modes, though not the monopole) are the most damaging, and 2) calibration will need to be understood at the 0.1%-1% level (i.e. rms variations mapped out to accuracy between 0.001 and 0.01 mag), though the precise requirement strongly depends on the faint-end slope of the luminosity function and the redshift distribution of galaxies in the survey.