We study two key issues militating against the use of the anisotropic three-point correlation function (3PCF) for cosmological parameter inference: difficulties with its computational estimation and high-dimensionality. We show how high-dimensionality may be reduced significantly by multipole decompositions of all angular dependence. This allows deriving the full expression for the multipole moments of the anisotropic 3PCF and its covariance matrix in a basis where the dimensionality reduces from nine to two at each multipole in the plane-parallel limit. We use 2D FFTLog formalism to show how the multipole moments with double momentum integrals over the product of bispectrum and two highly oscillating spherical Bessel functions and its covariance with double momentum integrals over the product of three galaxy power spectra and a combination of four highly oscillating spherical Bessel functions may be computed optimally.
Baryon acoustic oscillations (BAOs) imprinted in the galaxy power spectrum can be used as a standard ruler to determine angular diameter distance and Hubble parameter at high redshift galaxies. Combining redshift distortion effect which apparently distorts the galaxy clustering pattern, we can also constrain the growth rate of large-scale structure formation. Usually, future forecast for constraining these parameters from galaxy redshift surveys has been made with a full 2D power spectrum characterized as function of wavenumber $k$ and directional cosine $μ$ between line-of-sight direction and…
We present a novel mathematical formalism that allows to easily compute the expected kinetic Sunyaev Zeldovich (kSZ) signal in intensity and polarization due to an anisotropic primordial Cosmic Microwave Background (CMB). We derive the expected intensity and polarization distortions in the direction of non-moving galaxy clusters and then we generalize our calculations for non-zero peculiar velocity. We show that, in the direction of moving clusters, low CMB multipoles impose intensity and polarization spectral distortions with different frequency dependences. The polarization signal primarily …
In this work, we study a direction dependent power spectrum in anisotropic Finsler space-time. We use this direction dependent power spectrum to address the low-l power observed in WMAP and PLANCK data. The angular power spectrum of the temperature fluctuations has a lower amplitude in comparison to the $Λ$CDM model in the multipole range l = 2-40. Our theoretical model gives a correction to the isotropic angular power spectrum $C^{TT}_l$ due to the breaking of the rotational invariance of the primordial power spectrum. We estimate best-fit model parameters along with the six $Λ$CDM cosmologic…
We consider an inhomogeneous model and independently an anisotropic model of primordial power spectrum in order to describe the observed hemispherical anisotropy in Cosmic Microwave Background Radiation. This anisotropy can be parametrized in terms of the dipole modulation model of the temperature field. Both the models lead to correlations between spherical harmonic coefficients corresponding to multipoles, l and l \pm 1. We obtain the model parameters by making a fit to TT correlations in CMBR data. Using these parameters we predict the signature of our models for correlations among differen…
The most commonly used estimators of the anisotropic galaxy power spectrum employ Fast Fourier transforms, and rely on a specific choice of the line-of-sight that breaks the symmetry between the galaxy pair. This leads to wide-angle effects, including the presence of odd power spectrum multipoles like the dipole ($\ell = 1$) and octopole ($\ell = 3$). In Fourier-space these wide-angle effects also couple to the survey window function. We present a self-consistent framework extending the commonly used window function treatment to include the wide-angle effects. We show that our framework can su…
We apply our symmetry based Power tensor technique to test conformity of PLANCK Polarization maps with statistical isotropy. On a wide range of angular scales (l=40-150), our preliminary analysis detects many statistically anisotropic multipoles in foreground cleaned full sky PLANCK polarization maps viz., COMMANDER and NILC. We also study the effect of residual foregrounds that may still be present in the galactic plane using both common UPB77 polarization mask, as well as the individual component separation method specific polarization masks. However some of the statistically anisotropic mod…
Scalar-induced gravitational waves (SIGWs) are attracting growing attention for probing extremely short-scale scalar perturbations via gravitational wave measurements. In this paper, we investigate the SIGWs from statistically anisotropic scalar perturbations, which are motivated in inflationary scenarios in the presence of, e.g., a vector field. While the ensemble average of the SIGW energy spectrum is isotropic for the standard statistically isotropic scalar perturbations, the statistical anisotropy in the source introduces the multipole moments of the differential SIGW energy spectrum. We c…
We develop a possibility of generating tensor non-Gaussianity in a kind of anisotropic inflation, where a $U(1)$ gauge field is kinetically coupled to a spectator scalar field. Owing to this coupling, the coherent mode of the electric field appears and softly breaks the isotropy of the Universe. We compute the bispectrum of linearly-polarized tensor perturbations sourced by the gauge field and find that it is strongly red-tilted and has distinctive statistical anisotropies including higher-order multipole moments. Interestingly, the tensor bispectra with the specific combinations of linear pol…
Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials.…
We forecast the benefits induced by adding the bispectrum anisotropic signal to the standard, two- and three-point, clustering statistics analysis. In particular, we forecast cosmological parameter constraints including the bispectrum higher multipoles terms together with the galaxy power spectrum (monopole plus quadrupole) and isotropic bispectrum (monopole) data vectors. To do so, an analytical covariance matrix model is presented. This template is carefully calibrated on well-known terms of a numerical covariance matrix estimated from a set of simulated galaxy catalogues. After testing the …
From quantum fluctuations to galaxy power spectrum multipoles
Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo（数据驱动发现中心，卡弗里宇宙学前沿研究所（WPI），UTIAS，东京大学）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（卡弗里宇宙学前沿研究所（WPI），UTIAS，东京大学）
We study the sensitivity of a pair of Einstein Telescopes (ET) (hypothetically located at the two sites currently under consideration for ET) to the anisotropies of the Stochastic Gravitational Wave Background (SGWB). We focus on the $\ell =0,2,4$ multipoles of an expansion of the SGWB in spherical harmonics, since the sensitivity to other multipoles is suppressed due to the fact that this pair of detector operates in a regime for which the product between the observed frequency and the distance between the two sites is much smaller than one. In this regime, the interferometer overlap function…
We present a consistent δN formalism for curvature perturbations in anisotropic cosmological backgrounds. We employ our δN formalism to calculate the power spectrum, the bispectrum and the trispectrum in models of anisotropic inflation with the background gauge fields in Bianchi I universe. Our results coincide exactly with the recent results obtained from in-in formalism. To satisfy the observational constraints the anisotropies generated on power spectrum are kept small but large orientation-dependent non-Gaussianities can be generated. We study the Suyama-Yamaguchi inequality for the amplit…
We assess the performance of the Taruya, Nishimichi and Saito (TNS) model for the halo redshift space power spectrum, focusing on utilising mildly non-linear scales to constrain the growth rate of structure f. Using simulations with volume and number density typical of forthcoming Stage IV galaxy surveys, we determine ranges of validity for the model at redshifts z = 0.5 and z = 1. We proceed to perform a Bayesian MCMC analysis utilising the monopole, quadrupole, and hexadecapole spectra, followed by an exploratory Fisher matrix analysis. As previously noted in other forecasts as well as in re…
Using the NRGR effective field theory formalism we calculate the remaining source multipole moments necessary to obtain the spin contributions to the gravitational wave amplitude to 2.5 Post-Newtonian (PN) order. We also reproduce the tail contribution to the waveform linear in spin at 2.5PN arising from the nonlinear interaction between the current quadrupole and the mass monopole.
Despite being designed as an interferometer, the MeerKAT radio array (an SKA pathfinder) can also be used in autocorrelation (`single-dish') mode, where each dish scans the sky independently. Operating in this mode allows extremely high survey speeds to be achieved, albeit at significantly lower angular resolution. We investigate the recovery of the baryon acoustic oscillation (BAO) scale from multipoles of the redshift-space correlation function as measured by a low angular resolution 21cm intensity mapping survey of this kind. Our approach is to construct an analytic model of the multipoles …
A fundamental assumption in cosmology is that of statistical isotropy - that the universe, on average, looks the same in every direction in the sky. Statistical isotropy has recently been tested stringently using Cosmic Microwave Background (CMB) data, leading to intriguing results on large angular scales. Here we apply some of the same techniques used in the CMB to the distribution of galaxies on the sky. Using the multipole vector approach, where each multipole in the harmonic decomposition of galaxy density field is described by unit vectors and an amplitude, we lay out the basic formalism …
The redshift-space bispectrum (three point statistics) of galaxies depends on the expansion rate, the growth rate, and geometry of the Universe, and hence can be used to measure key cosmological parameters. In a homogeneous Universe the bispectrum is a function of five variables and unlike its two point statistics counterpart -- the power spectrum, which is a function of only two variables -- is difficult to analyse unless the information is somehow reduced. The most commonly considered reduction schemes rely on computing angular integrals over possible orientations of the bispectrum triangle,…
We study the evolution of the metric perturbations in a Bianchi background in the long-wavelength limit. By applying the gradient expansion to the equations of motion we exhibit a generalized "Separate Universe" approach to the cosmological perturbation theory. Having found this consistent separate universe picture, we introduce the $δM $ formalism for calculating the evolution of the linear tensor perturbations in anisotropic inflation models in {\it almost} the same way that the so-called $δN$ formula is applied to the super-horizon dynamics of the curvature perturbations. Similar to her twi…
To fully extract cosmological information from nonlinear galaxy distribution in redshift space, it is essential to include higher-order statistics beyond the two-point correlation function. In this paper, we propose a new decomposition formalism for computing the anisotropic bispectrum in redshift space and for measuring it from galaxy samples. Our formalism uses tri-polar spherical harmonic decomposition with zero total angular momentum to compress the 3D modes distribution in the redshift-space bispectrum. This approach preserves three fundamental properties of the Universe: statistical homo…
We study several anisotropic inflationary models and their implications for the observed violation of statistical isotropy in the CMBR data. In two of these models the anisotropy decays very quickly during the inflationary phase of expansion. We explicitly show that these models lead to violation of isotropy only for low l CMBR modes. Our primary aim is to fit the observed alignment of l=2,3 multipoles to the theoretical models. We use two measures, based on the power tensor, which contains information about the alignment of each multipole, to quantify the anisotropy in data. One of the measur…
Classifying inflationary scenarios according to their scaling properties is a powerful way to connect theory with observations. A useful tool to make such a classification is the beta-function formalism. By describing inflation in terms of renormalization group equations, within this framework, it is possible to define universality classes, which can be considered as sets of theories that share a common scale invariant limit. In this paper we apply the formalism to define such classes of universality for models of inflation where the inflaton is coupled to gauge fields. We show that the formal…
In the separate universe approach, an inhomogeneous universe is rephrased as a set of glued numerous homogeneous local patches. This is the essence of the gradient expansion and the $δN$ formalism, which have been widely used in solving a long wavelength evolution of the universe. In this paper, we show that the separate universe approach can be generically used, as long as a theory under consideration is local and preserves the spatial diffeomorphism invariance. Focusing on these two conditions, we also clarify the condition for the existence of the so-called Weinberg's adiabatic mode. Remark…
We introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of extended objects in Lagrangian space. In LEFT the resulting finite size effects are described using a multipole expansion parameterized by a set of time dependent coefficients and organized in powers of the ratio of the wavenumber of interest $k$ over the non-linear scale $k_{\rm NL}$. The multipoles encode the effects of the short distance modes on the long-wavel…
