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Register a new userImpact of cosmological signatures in two-point statistics beyond the linear regime
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Some beyond $Lambda$CDM cosmological models have dark-sector energy densities that suffer phase transitions. Fluctuations entering the horizon during such a transition can receive enhancements that ultimately show up as a distinctive bump in the power spectrum relative to a model with no phase transition. In this work, we study the non-linear evolution of such signatures in the matter power spectrum and correlation function using N-body simulations, perturbation theory and HMcode - a halo-model based method. We focus on modelling the response, computed as the ratio of statistics between a model containing a bump and one without it, rather than in the statistics themselves. Instead of working with a specific theoretical model, we inject a parametric family of Gaussian bumps into otherwise standard $Lambda$CDM spectra. We find that even when the primordial bump is located at linear scales, non-linearities tend to produce a second bump at smaller scales. This effect is understood within the halo model due to a more efficient halo formation. In redshift space these nonlinear signatures are partially erased because of the damping along the line-of-sight direction produced by non-coherent motions of particles at small scales. In configuration space, the bump modulates the correlation function reflecting as oscillations in the response, as it is clear in linear Eulerian theory; however, they become damped because large scale coherent flows have some tendency to occupy regions more depleted of particles. This mechanism is explained within Lagrangian Perturbation Theory and well captured by our simulations.
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Simple parameter-free analytic bias functions for the two-point correlation of densities in spheres at large separation are presented. These bias functions generalize the so-called Kaiser bias to the mildly non-linear regime for arbitrary density contrasts. The derivation is carried out in the context of large deviation statistics while relying on the spherical collapse model. A logarithmic transformation provides a saddle approximation which is valid for the whole range of densities and shown to be accurate against the 30 Gpc cube state-of-the-art Horizon Run 4 simulation. Special configurations of two concentric spheres that allow to identify peaks are employed to obtain the conditional bias and a proxy to BBKS extrema correlation functions. These analytic bias functions should be used jointly with extended perturbation theory to predict two-point clustering statistics as they capture the non-linear regime of structure formation at the percent level down to scales of about 10 Mpc/h at redshift 0. Conversely, the joint statistics also provide us with optimal dark matter two-point correlation estimates which can be applied either universally to all spheres or to a restricted set of biased (over- or underdense) pairs. Based on a simple fiducial survey, this estimator is shown to perform five times better than usual two-point function estimators. Extracting more information from correlations of different types of objects should prove essential in the context of upcoming surveys like Euclid, DESI, PFS or LSST.
Cosmological studies of large-scale structure have relied on two-point statistics, not fully exploiting the rich structure of the cosmic web. In this paper we show how to capture some of this cosmic web information by using the minimum spanning tree (MST), for the first time using it to estimate cosmological parameters in simulations. Discrete tracers of dark matter such as galaxies, $N$-body particles or haloes are used as nodes to construct a unique graph, the MST, that traces skeletal structure. We study the dependence of the MST on cosmological parameters using haloes from a suite of COLA simulations with a box size of $250 h^{-1}{rm Mpc}$, varying the amplitude of scalar fluctuations $left(A_{rm s}right)$, matter density $left(Omega_{rm m}right)$, and neutrino mass $left(sum m_{ u}right)$. The power spectrum $P$ and bispectrum $B$ are measured for wavenumbers between $0.125$ and $0.5$ $h{rm Mpc}^{-1}$, while a corresponding lower cut of $sim12.6$ $h^{-1}{rm Mpc}$ is applied to the MST. The constraints from the individual methods are fairly similar but when combined we see improved $1sigma$ constraints of $sim 17%$ ($sim 12%$) on $Omega_{rm m}$ and $sim 12%$ ($sim 10%$) on $A_{rm s}$ with respect to $P$ ($P+B$) thus showing the MST is providing additional information. The MST can be applied to current and future spectroscopic surveys (BOSS, DESI, Euclid, PSF, WFIRST, and 4MOST) in 3D and photometric surveys (DES and LSST) in tomographic shells to constrain parameters and/or test systematics.
The combination of two- and three-point clustering statistics of galaxies and the underlying matter distribution has the potential to break degeneracies between cosmological parameters and nuisance parameters and can lead to significantly tighter constraints on parameters describing the composition of the Universe and the dynamics of inflation. Here we investigate the relation between biases in the estimated parameters and inaccurate modelling of non-linear redshift-space distortions for the power spectrum and bispectrum of projected galaxy density fields and lensing convergence. Non-linear redshift-space distortions are one of the leading systematic uncertainties in galaxy clustering. Projections along the line of sight suppress radial modes and are thus allowing a trade-off between biases due to non-linear redshift-space distortions and statistical uncertainties. We investigate this bias-error trade-off for a CMASS-like survey with a varying number of redshift bins. Improved modelling of the non-linear redshift-space distortions allows the recovery of more radial information when controlling for biases. Not modelling non-linear redshift space distortions inflates error bars for almost all parameters by 20%. The information loss for the amplitude of local non-Gaussianities is smaller, since it is best constrained from large scales. In addition, we show empirically that one can recover more than 99% of the 3D power spectrum information if the depth of the tomographic bins is reduced to 10 $h^{-1}$Mpc.
We introduce a novel approach, the Cosmological Trajectories Method (CTM), to model nonlinear structure formation in the Universe by expanding gravitationally-induced particle trajectories around the Zeldovich approximation. A new Beyond Zeldovich approximation is presented, which expands the CTM to leading second-order in the gravitational interaction and allows for post-Born gravitational scattering. In the Beyond Zeldovich approximation we derive the exact expression for the matter clustering power spectrum. This is calculated to leading order and is available in the CTM MODULE. We compare the Beyond Zeldovich approximation power spectrum and correlation function to other methods including 1-loop Standard Perturbation Theory (SPT), 1-loop Lagrangian Perturbation Theory (LPT) and Convolution Lagrangian Perturbation Theory (CLPT). We find that the Beyond Zeldovich approximation power spectrum performs well, matching simulations to within $pm{10}%$, on mildly non-linear scales, and at redshifts above $z=1$ it outperforms the Zeldovich approximation. We also find that the Beyond Zeldovich approximation models the BAO peak in the correlation function at $z=0$ more accurately, to within $pm{5}%$ of simulations, than the Zeldovich approximation, SPT 1-loop and CLPT.
We use weak lensing data from the Hubble Space Telescope COSMOS survey to measure the second- and third-moments of the cosmic shear field, estimated from about 450,000 galaxies with average redshift <z> ~ 1.3. We measure two- and three-point shear statistics using a tree-code, dividing the signal in E, B and mixed components. We present a detection of the third-order moment of the aperture mass statistic and verify that the measurement is robust against systematic errors caused by point spread function (PSF) residuals and by the intrinsic alignments between galaxies. The amplitude of the measured three-point cosmic shear signal is in very good agreement with the predictions for a WMAP7 best-fit model, whereas the amplitudes of potential systematics are consistent with zero. We make use of three sets of large Lambda CDM simulations to test the accuracy of the cosmological predictions and to estimate the influence of the cosmology-dependent covariance. We perform a likelihood analysis using the measurement and find that the Omega_m-sigma_8 degeneracy direction is well fitted by the relation: sigma_8 (Omega_m/0.30)^(0.49)=0.78+0.11/-0.26. We present the first measurement of a more generalised three-point shear statistic and find a very good agreement with the WMAP7 best-fit cosmology. The cosmological interpretation of this measurement gives sigma_8 (Omega_m/0.30)^(0.46)=0.69 +0.08/-0.14. Furthermore, the combined likelihood analysis of this measurement with the measurement of the second order moment of the aperture mass improves the accuracy of the cosmological constraints, showing the high potential of this combination of measurements to infer cosmological constraints.
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