The late 2010s saw many attempts to go beyond the standard perturbative methods for inferring cosmological parameters from spectroscopic galaxy surveys by developing `reconstruction' methods. Essentially the idea is to take one realization of the cosmic initial conditions, evolve it to the (highly-nonlinear) present with a simulation and then compare with observations.  The differences between the simulated and observed can then  be used to make a better guess for the initial conditions....the process keeps repeating until the initial conditions that best reproduce the observations are found.  Many studies have tried to do this on simulated observations.  The results of these studies are interesting, showing that they could improve by factors of a few in wavenumber over traditional techniques (which is a substantial increase in information!).  Interestingly, essentially all studies found similar success in what modes could be reconstructed despite varied methods for doing the reconstruction.  There was little understanding of what was setting which modes could be reconstructed, or even why reconstruction works at all (these algorithms could have gotten stuck in a `local minimum' much further from the truth than they do).  By considering a toy problem that is similar to our Universe, I think I was able to provide these answers.  The limit actually is set by the number of galaxies in the survey and not by shot noise, as had been thought.  However, others have not yet appreciated the resulting paper, as evidenced by the scant number of citations to this work... 

In 2019, my research program had a UV-background-fluctuation flair.  Avery Meiksin and I extended the  interesting models by Andrew Pontzen for how the UV background could affect 3D Lyman-alpha forest analyses.  Building upon this work, then-finishing graduate student Phoebe Upton Sanderbeck wrote a fun paper on how UV background fluctuations could affect galaxy surveys, which involved both linear theory calculations for the UV background (shown on the left) but also back-of-the-envelope estimates for the coupling of this background to galaxy properties.  For some galaxy surveys, namely those that target 21cm or Lyman-alpha emission, this coupling is more straightforward to estimate as the effect is more direct.  For other surveys, the effect enters via the poorly understood coupling of the UV background to galaxy properties. (There must be some coupling as the UV background suppresses cooling of gas onto galaxies!)  Even though the coupling should be small, we showed that owing to the very large size of these fluctuations on horizon scales (as a major source of UV photons, quasars, are very rare!), our estimates suggested that they could be large enough to result in these fluctuations biasing searches for inflationary non-Gaussianity.  

2022: We are continuing to investigate this idea with Marilena Loverde and her graduate student Charuhas Shiveshwarkar in the context of the soon-to-launch SPHEREx satellite, which should significantly improve constraints  on inflationary non-Gaussianity, 

Linear-order cosmological perturbation theory has been tremendously useful for understanding the anisotropies in the Cosmic Microwave Background.  As time proceeds and more structure forms, linear order becomes less and less accurate, but there is still a range of scales over which the cosmic matter fluctuations are still perturbative (and so one does not have to run expensive simulations).  However, higher order perturbation theories have not been nearly as successful, with standard theories resulting in infinities for many cosmologies.  

There has been a lot of activity between 2010-2020 to try to correct the deficiencies of standard perturbation theories.  Martin White and I wrote a paper that attempted to understand many of these recent developments and test how well they fare, specializing to the case of 1D dynamics.  1D is the case of gravitationally interacting sheets.  Despite this high degree of symmetry, the same dynamical equations (such as the continuity and Euler equation in the standard Eulerian formulation) apply as in 3D and, by extension, 1D cosmological perturbation theories make all of the same assumptions. However, in 1D both the numerical simulations and analytic calculations are considerably simplified. The three-dimensional d3k integrals that occur in all 3D calculations collapse to one-dimensional dk integrals, allowing the computation of higher-order solutions more easily. Simulations are able to have much higher dynamic range in wavenumber in 1D than in 3D for the same memory and operation count. [Ten million 1D sheets results in the same accuracy as 10 billion 3D particles at mildly nonlinear wavenumbers in a cosmology like our own.]  The reduced cost of simulations allows us to test most of the assumptions of different perturbative approaches on a wide range of cosmological models. A final advantage is that 1D allows us to calculate the results of both Eulerian and Lagrangian perturbation theory at infinite order (both yielding the linear order Lagrangian Zeldovich approximation). We show that standard Eulerian and Lagrangian perturbation theories evaluated at infinite order do not yield a correct prediction for the matter power spectrum at any mildly nonlinear scale in any cosmology that we considered because these theories err at describing the dynamics around collapsed structures.  Newer effective perturbation theories that attempt to solve perturbatively equations for the dynamics of smoothed fields (and which really put perturbation theory on a rigorous footing) do considerably better.   

  In 3D, effective theories have only really been tested on a single cosmology (the concordance one), and at the time there were arguments over whether they are really superior (especially since the effective theories introduce new ``free’’ parameters).  Our 1D calculations, like those shown in the figure on left, for multiple cosmologies I think helped to sway the detractors.  

Cosmologists often attempt to measure small signals, from the 10^{-5} angular fluctuations in the brightness temperature of the cosmic microwave background (CMB), to the 10% enhancement in the correlation function of galaxies at 100 Mpc separations (resulting from baryons being dragged around by the CMB in the early Universe), to the weak 21cm emission signal from when the Universe was just several hundred million years young and still had most of its hydrogen in atomic form.  Since cosmological signals are nearly Gaussian random fields when smoothed over sufficiently large scales, one can write down the optimal method to measure them in this Gaussian limit.  Sometimes the optimal method is not practical to apply to real data or does not reduce to intuitive expressions, but sometimes this exercise is quite fruitful.

We investigated how to best infer the redshift distribution of galaxies with unknown redshifts by cross correlating them with galaxy populations for which the redshifts are ``known’’ via spectroscopy.  Since galaxies trace the same large-scale density field, the proximity of the unknown galaxies to the known galaxies allows  the inference of how well they trace each other in redshift.  It turns out that the optimal way to do this is simple and in very relevant limits boils down to intuitive analytic expressions.   The image below shows a 155 sq deg survey done by the Canada France Hawaii telescope.  Most of the objects are galaxies (there are 38 million objects that have been identified in the high resolution version of this image!).  This is just one of many deep galaxy surveys we have of the sky.  Our method can be applied to different types of extragalactic sources in such fields to learn their redshift distribution.  

In particular, we showed that it typically takes about 1000 sources with known redshifts per unit redshift to measure the redshift distribution of sources in the overlapping redshift interval (and does not depend on the angular density of known sources).  An important application of this technique is to calibrate redshift estimates of galaxies made from broad photometric bands.  Upcoming weak lensing surveys (aimed at precision cosmology) require extremely precise calibration of these redshifts in order for source redshift errors to not limit cosmological parameter determinations. 

I have  worked on how much we can learn from 3D correlations in the Lyman-alpha forest. This measurement is one of the science drivers of the BOSS instrument on the Sloan telescope (part of SDSSIII) as well as future spectroscopic cosmological efforts such as DESI.  The green region in the top panel shows a slice through a 3D map of the universe made with the BOSS instrument; the green shows the volume covered by 105 Lyman-alpha forest sightlines, which spans a volume larger than that covered by galaxies!

However, just as BOSS was beginning to take its first data, it was unclear (except perhaps to Pat McDonald) what sets the sensitivity to cosmological correlations in such a measurement (which must come from combination of S/N, quasar density, and spectral resolution) nor how a survey’s strategy should be optimized to maximize returns.  Martin White and I wrote a paper that attempted to answer these questions. Martin and I showed that the sensitivity of such surveys (given their volume) can be calculated to high accuracy from a single number, a S/N-weighted number density of quasars.  Our results allowed us and others to quickly investigate survey optimizations.  We showed that the BOSS quasar survey, which piggy-backs on the BOSS galaxies survey (the primary science of BOSS) and hence has little freedom in optimizing its strategy, is still close to the optimal quasar survey for this science that could be performed with the Sloan telescope.  We also were able to calculate the effective volumes of 3D Lyman-alpha surveys.  Our simple formulas have been used to plan the survey strategies of the next generation of 3D Lyman-alpha forest surveys.