Stable Clustering Ansatz, Consistency Relations and Gravity Dual of Large-Scale Structure

Gravitational clustering in the nonlinear regime remains poorly understood. Gravity dual of gravitational clustering has recently been proposed as a means to study the nonlinear regime. The stable clustering ansatz remains a key ingredient to our understanding of gravitational clustering in the highly nonlinear regime. We study certain aspects of violation of the stable clustering ansatz in the gravity dual of Large Scale Structure (LSS). We extend the recent studies of gravitational clustering using AdS gravity dual to take into account possible departure from the stable clustering ansatz and to arbitrary dimensions. Next, we extend the recently introduced consistency relations to arbitrary dimensions. We use the consistency relations to test the commonly used models of gravitational clustering including the halo models and hierarchical ans\"atze. In particular we establish a tower of consistency relations for the hierarchical amplitudes: $Q, R_a, R_b, S_a,S_b,S_c$ etc. as a functions of the scaled peculiar velocity $h$. We also study the variants of popular halo models in this context. In contrast to recent claims, none of these models, in their simplest incarnation, seem to satisfy the consistency relations in the soft limit.Comment: 21 pages, 4 figure

Symmetries, Invariants and Generating Functions: Higher-order Statistics of Biased Tracers

Gravitationally collapsed objects are known to be biased tracers of an underlying density contrast. Using symmetry arguments, generalised biasing schemes have recently been developed to relate the halo density contrast $\delta_h$ with the underlying density contrast $\delta$, divergence of velocity $\theta$ and their higher-order derivatives. This is done by constructing invariants such as $s, t, \psi,\eta$. We show how the generating function formalism in Eulerian standard perturbation theory (SPT) can be used to show that many of the additional terms based on extended Galilean and Lifshitz symmetry actually do not make any contribution to the higher-order statistics of biased tracers. Other terms can also be drastically simplified allowing us to write the vertices associated with $\delta_h$ in terms of the vertices of $\delta$ and $\theta$, the higher-order derivatives and the bias coefficients. We also compute the cumulant correlators (CCs) for two different tracer populations. These perturbative results are valid for tree-level contributions but at an arbitrary order. We also take into account the stochastic nature bias in our analysis. Extending previous results of a local polynomial model of bias, we express the one-point cumulants ${\cal S}_N$ and their two-point counterparts, the CCs i.e. ${\cal C}_{pq}$, of biased tracers in terms of that of their underlying density contrast counterparts. As a by-product of our calculation we also discuss the results using approximations based on Lagrangian perturbation theory (LPT).Comment: 15 page

Reconstructing the Thermal Sunyaev-Zel'dovich Effect in 3D

The thermal Sunyaev-Zel'dovich (tSZ) effect measures the line-of-sight projection of the thermal pressure of free electrons and lacks any redshift information. By cross correlating the tSZ effect with an external cosmological tracer we can recover a good fraction of this lost information. Weak lensing (WL) is thought to provide an unbiased probe of the dark Universe, with many WL surveys having sky coverage that overlaps with tSZ surveys. Generalising the tomographic approach, we advocate the use of the spherical Fourier-Bessel (sFB) expansion to perform an analysis of the cross-correlation between the projected (2D) tSZ Compton $y$-parameter maps and 3D weak lensing convergence maps. We use redshift dependent linear biasing and the halo model as a tool to investigate the tSZ-WL cross-correlations in 3D. We use the Press-Schechter (PS) and the Sheth-Tormen (ST) mass-functions in our calculations, finding that the results are quite sensitive to detailed modelling. We provide detailed analysis of surveys with photometric and spectroscopic redshifts. The signal-to-noise (S/N) of the cross-spectra $\mathcal{C}_{\ell} (k)$ for individual 3D modes, defined by the radial and tangential wave numbers $(k;\ell)$, remains comparable to, but below, unity though optimal binning is expected to improve this. The results presented can be generalised to analyse other CMB secondaries, such as the kinetic Sunyaev-Zel'dovich (kSZ) effect.Comment: 27 pages, 12 Figures. Published in MNRA

Principal Components of CMB non-Gaussianity

The skew-spectrum statistic introduced by Munshi & Heavens (2010) has recently been used in studies of non-Gaussianity from diverse cosmological data sets including the detection of primary and secondary non-Gaussianity of Cosmic Microwave Background (CMB) radiation. Extending previous work, focussed on independent estimation, here we deal with the question of joint estimation of multiple skew-spectra from the same or correlated data sets. We consider the optimum skew-spectra for various models of primordial non-Gaussianity as well as secondary bispectra that originate from the cross-correlation of secondaries and lensing of CMB: coupling of lensing with the Integrated Sachs-Wolfe (ISW) effect, coupling of lensing with thermal Sunyaev-Zeldovich (tSZ), as well as from unresolved point-sources (PS). For joint estimation of various types of non-Gaussianity, we use the PCA to construct the linear combinations of amplitudes of various models of non-Gaussianity, e.g. $f^{\rm loc}_{\rm NL},f^{\rm eq}_{\rm NL},f^{\rm ortho}_{\rm NL}$ that can be estimated from CMB maps. Bias induced in the estimation of primordial non-Gaussianity due to secondary non-Gaussianity is evaluated. The PCA approach allows one to infer approximate (but generally accurate) constraints using CMB data sets on any reasonably smooth model by use of a lookup table and performing a simple computation. This principle is validated by computing constraints on the DBI bispectrum using a PCA analysis of the standard templates.Comment: 17 pages, 5 figures, 4 tables. Matches published versio

Consistency Relations in Effective Field Theory

The consistency relations in large scale structure relate the lower-order correlation functions with their higher-order counterparts. They are direct outcome of the underlying symmetries of a dynamical system and can be tested using data from future surveys such as Euclid. Using techniques from standard perturbation theory (SPT), previous studies of consistency relation have concentrated on continuity-momentum (Euler)-Poisson system of an ideal fluid. We investigate the consistency relations in effective field theory (EFT) which adjusts the SPT predictions to account for the departure from the ideal fluid description on small scales. We provide detailed results for the 3D density contrast $\delta$ as well as the {\em scaled} divergence of velocity $\bar\theta$. Assuming a $\Lambda$CDM background cosmology, we find the correction to SPT results becomes important at $k \gtrsim 0.05 \rm h/Mpc$ and that the suppression from EFT to SPT results that scales as square of the wave number $k$, can reach $40\%$ of the total at $k \approx 0.25\rm h/Mpc$ at $z=0$. We have also investigated whether effective field theory corrections to models of primordial non-Gaussianity can alter the squeezed limit behaviour, finding the results to be rather insensitive to these counterterms. In addition, we present the EFT corrections to the squeezed limit of the bispectrum in redshift space which may be of interest for tests of theories of modified gravity.Comment: 23 pages + bibliography, 6 figures. Minor changes to match version accepted for publication by JCA

The Statistics of Cosmological Lyman-alpha Absorption

We study the effect of the non-Gaussianity induced by gravitational evolution upon the statistical properties of absorption in quasar (QSO) spectra. Using the generic hierarchical ansatz and the lognormal approximation we derive the analytical expressions for the one-point PDF as well as for the joint two-point probability distribution (2PDF) of transmitted fluxes in two neighbouring QSOs. These flux PDFs are constructed in 3D as well as in projection (i.e. in 2D). The PDFs are constructed by relating the lower-order moments, i.e. cumulants and cumulant correlators, of the fluxes to the 3D neutral hydrogen distribution which is, in turn, expressed as a function of the underlying dark matter distribution. The lower-order moments are next modelled using a generating function formalism in the context of a {\em minimal tree-model} for the higher-order correlation hierarchy. These different approximations give nearly identical results for the range of redshifts probed, and we also find a very good agreement between our predictions and outputs of hydrodynamical simulations. The formalism developed here for the joint statistics of flux-decrements concerning two lines of sight can be extended to multiple lines of sight, which could be particularly important for the 3D reconstruction of the cosmic web from QSO spectra (e.g. in the BOSS survey). These statistics probe the underlying projected neutral hydrogen field and are thus linked to "hot-spots" of absorption. The results for the PDF and the bias presented here use the same functional forms of scaling functions that have previously been employed for the modelling of other cosmological observation such as the Sunyaev-Zel'dovich effect.Comment: 17 pages, 8 figure