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.
The long wavelength modes lost to bright foregrounds in the interferometric 21-cm surveys can partially be recovered using a forward modeling approach that exploits the non-linear coupling between small and large scales induced by gravitational evolu
tion. In this work, we build upon this approach by considering how adding external galaxy distribution data can help to fill in these modes. We consider supplementing the 21-cm data at two different redshifts with a spectroscopic sample (good radial resolution but low number density) loosely modeled on DESI-ELG at $z=1$ and a photometric sample (high number density but poor radial resolution) similar to LSST sample at $z=1$ and $z=4$ respectively. We find that both the galaxy samples are able to reconstruct the largest modes better than only using 21-cm data, with the spectroscopic sample performing significantly better than the photometric sample despite much lower number density. We demonstrate the synergies between surveys by showing that the primordial initial density field is reconstructed better with the combination of surveys than using either of them individually. Methodologically, we also explore the importance of smoothing the density field when using bias models to forward model these tracers for reconstruction.
We present FlowPM, a Particle-Mesh (PM) cosmological N-body code implemented in Mesh-TensorFlow for GPU-accelerated, distributed, and differentiable simulations. We implement and validate the accuracy of a novel multi-grid scheme based on multiresolu
tion pyramids to compute large scale forces efficiently on distributed platforms. We explore the scaling of the simulation on large-scale supercomputers and compare it with corresponding python based PM code, finding on an average 10x speed-up in terms of wallclock time. We also demonstrate how this novel tool can be used for efficiently solving large scale cosmological inference problems, in particular reconstruction of cosmological fields in a forward model Bayesian framework with hybrid PM and neural network forward model. We provide skeleton code for these examples and the entire code is publicly available at https://github.com/modichirag/flowpm.
A common statistical problem in econometrics is to estimate the impact of a treatment on a treated unit given a control sample with untreated outcomes. Here we develop a generative learning approach to this problem, learning the probability distribut
ion of the data, which can be used for downstream tasks such as post-treatment counterfactual prediction and hypothesis testing. We use control samples to transform the data to a Gaussian and homoschedastic form and then perform Gaussian process analysis in Fourier space, evaluating the optimal Gaussian kernel via non-parametric power spectrum estimation. We combine this Gaussian prior with the data likelihood given by the pre-treatment data of the single unit, to obtain the synthetic prediction of the unit post-treatment, which minimizes the error variance of synthetic prediction. Given the generative model the minimum variance counterfactual is unique, and comes with an associated error covariance matrix. We extend this basic formalism to include correlations of primary variable with other covariates of interest. Given the probabilistic description of generative model we can compare synthetic data prediction with real data to address the question of whether the treatment had a statistically significant impact. For this purpose we develop a hypothesis testing approach and evaluate the Bayes factor. We apply the method to the well studied example of California (CA) tobacco sales tax of 1988. We also perform a placebo analysis using control states to validate our methodology. Our hypothesis testing method suggests 5.8:1 odds in favor of CA tobacco sales tax having an impact on the tobacco sales, a value that is at least three times higher than any of the 38 control states.
We investigate the range of applicability of a model for the real-space power spectrum based on N-body dynamics and a (quadratic) Lagrangian bias expansion. This combination uses the highly accurate particle displacements that can be efficiently achi
eved by modern N-body methods with a symmetries-based bias expansion which describes the clustering of any tracer on large scales. We show that at low redshifts, and for moderately biased tracers, the substitution of N-body-determined dynamics improves over an equivalent model using perturbation theory by more than a factor of two in scale, while at high redshifts and for highly biased tracers the gains are more modest. This hybrid approach lends itself well to emulation. By removing the need to identify halos and subhalos, and by not requiring any galaxy-formation-related parameters to be included, the emulation task is significantly simplified at the cost of modeling a more limited range in scale.
We study the impact of lensing corrections on modeling cross correlations between CMB lensing and galaxies, cosmic shear and galaxies, and galaxies in different redshift bins. Estimating the importance of these corrections becomes necessary in the li
ght of anticipated high-accuracy measurements of these observables. While higher order lensing corrections (sometimes also referred to as post Born corrections) have been shown to be negligibly small for lensing auto correlations, they have not been studied for cross correlations. We evaluate the contributing four-point functions without making use of the Limber approximation and compute line-of-sight integrals with the numerically stable and fast FFTlog formalism. We find that the relative size of lensing corrections depends on the respective redshift distributions of the lensing sources and galaxies, but that they are generally small for high signal-to-noise correlations. We point out that a full assessment and judgement of the importance of these corrections requires the inclusion of lensing Jacobian terms on the galaxy side. We identify these additional correction terms, but do not evaluate them due to their large number. We argue that they could be potentially important and suggest that their size should be measured in the future with ray-traced simulations. We make our code publicly available.
Upcoming 21-cm intensity surveys will use the hyperfine transition in emission to map out neutral hydrogen in large volumes of the universe. Unfortunately, large spatial scales are completely contaminated with spectrally smooth astrophysical foregrou
nds which are orders of magnitude brighter than the signal. This contamination also leaks into smaller radial and angular modes to form a foreground wedge, further limiting the usefulness of 21-cm observations for different science cases, especially cross-correlations with tracers that have wide kernels in the radial direction. In this paper, we investigate reconstructing these modes within a forward modeling framework. Starting with an initial density field, a suitable bias parameterization and non-linear dynamics to model the observed 21-cm field, our reconstruction proceeds by combining the likelihood of a forward simulation to match the observations (under given modeling error and a data noise model) with the Gaussian prior on initial conditions and maximizing the obtained posterior. For redshifts $z=2$ and $4$, we are able to reconstruct 21cm field with cross correlation, $r_c > 0.8$ on all scales for both our optimistic and pessimistic assumptions about foreground contamination and for different levels of thermal noise. The performance deteriorates slightly at $z=6$. The large-scale line-of-sight modes are reconstructed almost perfectly. We demonstrate how our method also reconstructs baryon acoustic oscillations, outperforming standard methods on all scales. We also describe how our reconstructed field can provide superb clustering redshift estimation at high redshifts, where it is otherwise extremely difficult to obtain dense spectroscopic samples, as well as open up cross-correlation opportunities with projected fields (e.g. lensing) which are restricted to modes transverse to the line of sight.
This paper introduces the Hidden Valley simulations, a set of trillion-particle N-body simulations in gigaparsec volumes aimed at intensity mapping science. We present details of the simulations and their convergence, then specialize to the study of
21-cm fluctuations between redshifts 2 and 6. Neutral hydrogen is assigned to halos using three prescriptions, and we investigate the clustering in real and redshift-space at the 2-point level. In common with earlier work we find the bias of HI increases from near 2 at z = 2 to 4 at z = 6, becoming more scale dependent at high z. The level of scale-dependence and decorrelation with the matter field are as predicted by perturbation theory. Due to the low mass of the hosting halos, the impact of fingers of god is small on the range relevant for proposed 21-cm instruments. We show that baryon acoustic oscillations and redshift-space distortions could be well measured by such instruments. Taking advantage of the large simulation volume, we assess the impact of fluctuations in the ultraviolet background, which change HI clustering primarily at large scales.
We present a method to reconstruct the initial conditions of the universe using observed galaxy positions and luminosities under the assumption that the luminosities can be calibrated with weak lensing to give the mean halo mass. Our method relies on
following the gradients of forward model and since the standard way to identify halos is non-differentiable and results in a discrete sample of objects, we propose a framework to model the halo position and mass field starting from the non-linear matter field using Neural Networks. We evaluate the performance of our model with multiple metrics. Our model is more than $95%$ correlated with the halo-mass fields up to $ksim 0.7 {rm h/Mpc}$ and significantly reduces the stochasticity over the Poisson shot noise. We develop a data likelihood model that takes our modeling error and intrinsic scatter in the halo mass-light relation into account and show that a displaced log-normal model is a good approximation to it. We optimize over the corresponding loss function to reconstruct the initial density field and develop an annealing procedure to speed up and improve the convergence. We apply the method to halo number densities of $bar{n} = 2.5times 10^{-4} -10^{-3}({rm h/Mpc})^3$, typical of current and future redshift surveys, and recover a Gaussian initial density field, mapping all the higher order information in the data into the power spectrum. We show that our reconstruction improves over the standard reconstruction. For baryonic acoustic oscillations (BAO) the gains are relatively modest because BAO is dominated by large scales where standard reconstruction suffices. We improve upon it by $sim 15-20%$ in terms of error on BAO peak as estimated by Fisher analysis at $z=0$. We expect larger gains will be achieved when applying this method to the broadband linear power spectrum reconstruction on smaller scales.
