Gravity, Inflation, and Galaxies: Fundamental Physics with Large-Scale Structure

Cosmology offers fascinating possibilities to test our understanding of gravity on large scales, and to probe the origin of structure in the Universe. Cosmology has evolved from a speculative branch of theoretical physics into precision science at the intersection of gravity, particle- and astrophysics. Despite all we have learned however, we still do not understand why the expansion of the Universe accelerates, and how the structure in the Universe originated. All structure in the universe, including galaxies, stars, planets, and ultimately, us, arose from the initial seed fluctuations under the action of gravity, so that these questions directly concern our origins. This project aims at using large-scale structure, the distribution of galaxy positions and their shapes, in a statistical way to shed light on these open questions. The goal of the project is to first, probe our theory of gravity, General Relativity, on cosmological scales. Second, it aims to shed light on the origin of the initial seed fluctuations out of which all structure in the Universe formed, by constraining the physics and energy scale of inflation. While seemingly unrelated, the main challenge in both research directions consists in understanding the nonlinear physics of structure formation, which is dominated by gravity on scales larger than a few Mpc. By making progress in this understanding, we can unlock a rich trove of information on fundamental physics from large-scale structure. The research goals are pursued on the three fronts of analytical theory, numerical simulations, and confrontation with data. With space missions, such as Planck and Euclid, as well as ground-based surveys delivering data sets of unprecedented size and quality at this very moment, the methods developed during the course of this project should deliver exciting new insights on gravity and inflation.

In order to test gravity, we need to make sure that our methods work for theories different from General Relativity as well. Speedup methods for modified gravity N-body simulations were developed and applied to generate simulated galaxy redshift survey catalogs in modified gravity scenarios. These catalogs allowed for a self-consistent test of data analysis pipelines for testing gravity using galaxy velocitie. This is an important milestone toward the goal of robust tests of gravity using large-scale structure. Ongoing work focuses on simulations of clustering dark energy models. These are well motivated theoretically, and moreover can be mistaken for a modification of gravity if not understood properly. In order to simulate structure formation in this scenario, dark energy has to be treated as a fluid with small speed of sound and nontrivial equation of state.

Significant progress was further made on rigorously understanding the impact of single-field inflationary models, the simplest inflationary scenario, on the statistics of large-scale structure. Theoretical advances in the modeling of tidal alignments have also been made.

With the advances in simulation and theoretical approaches described above, the modeling of observables in large-scale structure is nearing completion. However, two challenges need to be surmounted in order to obtain constraints on gravity and inflation: a) the covariance (error bar) of observables such as the weak lensing power spectrum needs to be understood; b) in case of galaxy clustering, it has become very clear that including higher-order statistics is essential. Measuring these becomes increasingly complicated and costly however. The PI's team has made progress in developing novel methodology to deal with both challenges: the PI's team developed the response approach to covariances of large-scale structure observables, which has greatly advanced the state of understanding and simplified their calculation. In a separate direction, significant efforts of the PI's team, are devoted to developing optimal inference approaches to large-scale structure which avoid complicated and costly measurements of higher-order statistics. These approaches go far beyond the current state-of-the-art in the field, which is restricted to two-point functions, and will have a significant impact on both research goals. A first proof of concept and quantitative results were published in 2019.

The optimal inference approach recently developed in this project constitutes a completely new methodology for the analysis of galaxy clustering. By combining a rigorous theoretical model (effective field theory) for galaxy clustering with a full Bayesian inference framework, robust inferences can be made from mildly nonlinear scales that include the information from higher-order statistics without having to explicitly measure the latter. Moreover, the full proper covariance of all these statistics is automatically included by virtue of the Bayesian framework. No other approach presented in the literature has this feature. The price to be paid is significant numerical cost. However, the PI's collaborators J. Jasche and G. Lavaux have demonstrated that this cost is manageable even for large current data sets.

The next goal is to take this methodology closer to the application to data, by including physical and observational effects that need to be included step by step. Finally, an application to large survey data sets should then yield competitive and extremely robust constraints on gravity and inflation.

Periodic Reporting for period 4 - GrInflaGal (Gravity, Inflation, and Galaxies: Fundamental Physics with Large-Scale Structure)

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