Reconstructing the Gaussian initial conditions at the beginning of the Universe from the survey data in a forward modeling framework is a major challenge in cosmology. This requires solving a high dimensional inverse problem with an expensive, non-li
near forward model: a cosmological N-body simulation. While intractable until recently, we propose to solve this inference problem using an automatically differentiable N-body solver, combined with a recurrent networks to learn the inference scheme and obtain the maximum-a-posteriori (MAP) estimate of the initial conditions of the Universe. We demonstrate using realistic cosmological observables that learnt inference is 40 times faster than traditional algorithms such as ADAM and LBFGS, which require specialized annealing schemes, and obtains solution of higher quality.
Fundamental plane of elliptical galaxies can be used to predict the intrinsic size of galaxies and has a number of plausible application to study cosmology and galaxy physics. We present a detailed analysis of the fundamental plane of the SDSS-III BO
SS LOWZ and CMASS galaxies. For the standard fundamental plane, we find a strong redshift evolution for the mean residual and show that it is primarily driven by the redshift evolution of the surface brightness of the galaxies. After correcting for the redshift evolution, the FP residuals are strongly correlated with the galaxy properties and some observational systematics. We show that the variations in the FP between the central and satellite galaxies, that have been observed in the literature, can primarily be explained by the correlation of the FP with the galaxy luminosity. We also measure the cross correlations of the FP residuals with the galaxy density field. The amplitude of the cross correlations depends on the galaxy properties and environment with brighter and redder galaxies showing stronger correlation. In general, galaxies in denser environments (higher galaxy bias ) show stronger correlations. We also compare FP amplitude with the amplitudes of intrinsic alignments of galaxy shapes (IA), finding the two to be correlated. Finally, using the FP residuals we also study the impact of intrinsic alignments on the constraint of growth rate using redshift space distortions. We do not observe any significant trends in measurements of the growth rate $f$ as function of the amplitude of FP-density correlations, resulting in null detection of the effects of IA on the RSD measurements.
Clustering of large-scale structure provides significant cosmological information through the power spectrum of density perturbations. Additional information can be gained from higher-order statistics like the bispectrum, especially to break the dege
neracy between the linear halo bias $b_1$ and the amplitude of fluctuations $sigma_8$. We propose new simple, computationally inexpensive bispectrum statistics that are near optimal for the specific applications like bias determination. Corresponding to the Legendre decomposition of nonlinear halo bias and gravitational coupling at second order, these statistics are given by the cross-spectra of the density with three quadratic fields: the squared density, a tidal term, and a shift term. For halos and galaxies the first two have associated nonlinear bias terms $b_2$ and $b_{s^2}$, respectively, while the shift term has none in the absence of velocity bias (valid in the $k rightarrow 0$ limit). Thus the linear bias $b_1$ is best determined by the shift cross-spectrum, while the squared density and tidal cross-spectra mostly tighten constraints on $b_2$ and $b_{s^2}$ once $b_1$ is known. Since the form of the cross-spectra is derived from optimal maximum-likelihood estimation, they contain the full bispectrum information on bias parameters. Perturbative analytical predictions for their expectation values and covariances agree with simulations on large scales, $klesssim 0.09h/mathrm{Mpc}$ at $z=0.55$ with Gaussian $R=20h^{-1}mathrm{Mpc}$ smoothing, for matter-matter-matter, and matter-matter-halo combinations. For halo-halo-halo cross-spectra the model also needs to include corrections to the Poisson stochasticity.
