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Register a new userProjected two- and three-point statistics: Forecasts and mitigation of non-linear RSDs
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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.
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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.
Modelling uncertainties at small scales, i.e. high $k$ in the power spectrum $P(k)$, due to baryonic feedback, nonlinear structure growth and the fact that galaxies are biased tracers poses a significant obstacle to fully leverage the constraining power of the {it Euclid} wide-field survey. $k$-cut cosmic shear has recently been proposed as a method to optimally remove sensitivity to these scales while preserving usable information. In this paper we generalise the $k$-cut cosmic shear formalism to $3 times 2$ point statistics and estimate the loss of information for different $k$-cuts in a $3 times 2$ point analysis of the {it Euclid} data. Extending the Fisher matrix analysis of~citet{blanchard2019euclid}, we assess the degradation in constraining power for different $k$-cuts. We work in the idealised case and assume the galaxy bias is linear, the covariance is Gaussian, while neglecting uncertainties due to photo-z errors and baryonic feedback. We find that taking a $k$-cut at $2.6 h {rm Mpc} ^{-1}$ yields a dark energy Figure of Merit (FOM) of 1018. This is comparable to taking a weak lensing cut at $ell = 5000$ and a galaxy clustering and galaxy-galaxy lensing cut at $ell = 3000$ in a traditional $3 times 2$ point analysis. We also find that the fraction of the observed galaxies used in the photometric clustering part of the analysis is one of the main drivers of the FOM. Removing $50 % (90 %)$ of the clustering galaxies decreases the FOM by $19 % (62 %)$. Given that the FOM depends so heavily on the fraction of galaxies used in the clustering analysis, extensive efforts should be made to handle the real-world systematics present when extending the analysis beyond the luminous red galaxy (LRG) sample.
We present the 2-point function from Fast and Accurate Spherical Bessel Transformation (2-FAST) algorithm for a fast and accurate computation of integrals involving one or two spherical Bessel functions. These types of integrals occur when projecting the galaxy power spectrum $P(k)$ onto the configuration space, $xi_ell^ u(r)$, or spherical harmonic space, $C_ell(chi,chi)$. First, we employ the FFTlog transformation of the power spectrum to divide the calculation into $P(k)$-dependent coefficients and $P(k)$-independent integrations of basis functions multiplied by spherical Bessel functions. We find analytical expressions for the latter integrals in terms of special functions, for which recursion provides a fast and accurate evaluation. The algorithm, therefore, circumvents direct integration of highly oscillating spherical Bessel functions.
Accurate knowledge of the effect of feedback from galaxy formation on the matter distribution is a key requirement for future weak lensing experiments. Recent studies using hydrodynamic simulations have shown that different baryonic feedback scenarios lead to significantly different two-point shear statistics. In this paper we extend earlier work to three-point shear statistics. We show that, relative to the predictions of dark matter only models, the amplitude of the signal can be reduced by as much as 30-40% on scales of a few arcminutes. We find that baryonic feedback may affect two- and three-point shear statistics differently and demonstrate that this can be used to assess the fidelity of various feedback models. In particular, upcoming surveys such as Euclid might be able to discriminate between different feedback models by measuring both second- and third-order statistics. Because it will likely remain impossible to predict baryonic feedback with high accuracy from first principles, we argue in favour of phenomenological models that can capture the relevant effects of baryonic feedback processes in addition to changes in cosmology. We construct such a model by modifying the dark matter-only halo model to characterise the generic effects of energetic feedback using a small number of parameters. We use this model to perform a likelihood analysis in a simplified case in which two- and three-point shear statistics are measured between 0.5 and 20 arcmin and in which the amplitude of fluctuations, sigma8, the matter density parameter, Om, and the dark energy parameter, w0, are the only unknown free parameters. We demonstrate that for weak lensing surveys such as Euclid, marginalising over the feedbac parameters describing the effects of baryonic processes, such as outflows driven by feedback from star formation and AGN, may be able to mitigate the bias affecting Om, sigma8 and w0.
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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