Cosmologists are throwing away nearly half the data from their most powerful telescopes because they lack the mathematical tools to interpret it. The Dark Energy Survey (DES) used only 55% of its photometric data points when testing gravity, discarding everything from non-linear scales where matter clumps chaotically. This research aims to recover that lost information. The problem is that current models of gravity—Einstein’s general relativity—work beautifully on linear scales where the universe is smooth, but break down on non-linear scales where galaxies cluster and dark matter collapses. Stage-IV surveys like Euclid and the Vera Rubin Observatory will produce vastly more data, but without new methods, they will face the same limitation: forced to ignore the richest, most informative parts of the sky. This project will build two sets of tools. For spectroscopic surveys, the team will use perturbation theory to check whether standard template-fitting methods introduce bias when applied to non-standard gravity models. For photometric surveys, they will simulate the ratio of power spectra between modified gravity and standard cosmology—a quantity that is insensitive to cosmic variance—and marginalise over baryonic effects and intrinsic alignments. The work is fundamental science. It will not change anyone’s daily life directly. But if successful, it will allow cosmologists to test general relativity on cosmological scales using the full power of next-generation surveys, potentially revealing whether Einstein’s theory holds at the largest scales in the universe.
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Cosmology has entered an era of “Stage-IV” dark energy surveys. With the stage IV surveys, we can go beyond constraining the dark energy equation of state. We have demonstrated that it is indeed possible to test general relativity itself by combining various cosmology measurements achieved by these surveys. The major limitation currently in testing gravity using cosmological observations is that we need to throw away all the information on non-linear scales. For example, in the DES photometric analysis, only 55% of the data points were used to test gravity compared with the fiducial analysis in ?CDM as only the data points on linear scales could be used. In addition, the gravitational effects on matter are often obtained by using constraints on the growth rate from spectroscopic redshift distortions. These constraints are obtained assuming non-linear modelling in ?CDM and care needs to be taken when using them in beyond-?CDM models. This proposal will provide methodologies and tools to exploit the information available on non-linear scales to test general relativity on cosmological scales. For spectroscopic probes, we will utilise perturbation theory to perform a full shape analysis and template fitting. An important question is whether the constraints on the growth rate obtained by template fitting is biased due to the use of the ?CDM non-linear model or not. We will answer these questions using representative models within the effective field theory of dark energy. We utilise full N-body and approximate simulations developed by Koyama’s group to generate mock data. This analysis will inform the validity and limitation of the model independent approach, and we will explore a way to generalise this. For photometric probes, we can probe the matter power spectrum up to much larger wavenumbers. We will emulate the ratio between the power spectrum in modified gravity and ?CDM, which is insensitive to cosmic variance and resolution of simulations. Our approach is to parametrise baryonic effects and intrinsic alignments and marginalise over them. We will perform MCMC analysis using synthetic or simulated data in models which will be precisely constrained by Euclid and LSST. Based on the analysis in specific models, we investigate a way to include non-linear scales in a model independent way by marginalising over parameters describing non-linear effects. Based on these studies, we will extend the model independent tests of gravity to non-linear scales and provide much-needed tools to constrain highly pertinent models with the imminent next-generation data.
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