## Periodic Reporting for period 1 - CosTesGrav (Cosmological Tests of Gravity)

**Reporting period:**2015-09-01

**to**2017-02-28

## Summary of the context and overall objectives of the project

Einstein’s theory of General Relativity (GR) is tested accurately within the local universe i.e., the solar system, but this leaves open the possibility that it is not a good description at the largest scales in the Universe. The standard model of cosmology assumes GR as a theory to describe gravity on all scales. In 1998, astronomers made a surprising discovery that the expansion of the Universe is accelerating, not slowing down. This late-time acceleration of the Universe has become the most challenging problem in theoretical physics. Within the framework of GR, the acceleration would originate from an unknown “dark energy.” Alternatively, it could be that there is no dark energy and GR itself is in error on cosmological scales. The standard model of cosmology is based on a huge extrapolation of our limited knowledge of gravity. This discovery of the late time acceleration of the Universe may require us to revise the theory of gravity and the standard model of cosmology based on GR.

The main objective of my project is to develop cosmological tests of gravity and seek solutions to the origin of the observed accelerated expansion of the Universe by challenging conventional GR. Upcoming surveys will make cosmological tests of gravity a reality in the next five years. There are remaining issues in developing theoretical frameworks for probing gravitational physics on cosmological scales. We construct modified gravity theories as an alternative to dark energy and analyse “screening mechanisms” to restore GR on scales where it is well tested. We then develop better theoretical frameworks to perform cosmological tests of gravity that include non-linear scales by exploiting our theoretical knowledge of the models and our state-of-the-art simulations.

In order to achieve these goals, interdisciplinary approaches are essential. We need new ideas from particle physics to identify mechanisms responsible for the accelerated phases of expansion, novel computational methods to simulate the Universe governed by a modified law of gravity, and observational expertise to exploit the data from future massive astronomical surveys. This project will provide a new purpose for astronomical surveys to test gravity in the Universe in addition to testing the astrophysics of galaxies and stars, and maximise the scientific return from future massive surveys.

The main objective of my project is to develop cosmological tests of gravity and seek solutions to the origin of the observed accelerated expansion of the Universe by challenging conventional GR. Upcoming surveys will make cosmological tests of gravity a reality in the next five years. There are remaining issues in developing theoretical frameworks for probing gravitational physics on cosmological scales. We construct modified gravity theories as an alternative to dark energy and analyse “screening mechanisms” to restore GR on scales where it is well tested. We then develop better theoretical frameworks to perform cosmological tests of gravity that include non-linear scales by exploiting our theoretical knowledge of the models and our state-of-the-art simulations.

In order to achieve these goals, interdisciplinary approaches are essential. We need new ideas from particle physics to identify mechanisms responsible for the accelerated phases of expansion, novel computational methods to simulate the Universe governed by a modified law of gravity, and observational expertise to exploit the data from future massive astronomical surveys. This project will provide a new purpose for astronomical surveys to test gravity in the Universe in addition to testing the astrophysics of galaxies and stars, and maximise the scientific return from future massive surveys.

## Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

This project is composed of three main themes to achieve the objectives. I will describe main results achieved in the first financial period on each theme.

In theme 1 “Theoretical models”, we studied theoretical consistencies of various theoretical models such as vector Galileon, non-local gravity and quasi-dilaton massive gravity models. We have made significant contributions to the development of new classes of scalar tensor theory of gravity. These models include beyond Horndeski theories and we identified new non-linear interactions which break the screening mechanism inside extended objects. This finding was utilised in theme 3 to test these theories using astrophysical objects such as clusters of galaxies and neutron stars.

In theme 2 “Non-linear clustering”, we have developed a perturbation theory approach to predict quasi non-linear power spectra. We created a versatile code that can compute non-linear power spectra at one-loop order in standard perturbation theory in a wide variety of dark energy and modified gravity models including the effect of screening mechanisms. The code can also predict the power spectrum in the redshift space. The outputs of this code have been compared to N-body simulations. We also used hydro-dynamical simulations to test the methodology to constrain modified gravity models using clusters of galaxies by comparing lensing and X-ray masses. We created mock clusters and confirmed the power of our methodology, which can now be applied to larger cluster samples available with the next generation surveys.

As a co-lead of the work package on non-standard cosmological simulations, the PI has made an important contribution to the Euclid mission activities creating the simulation requirement document for Euclid.

In theme 3 “Cosmological tests of gravity”, we studied constraints on general classes of scalar tensor theory identified in theme 1. We showed that, in these models, screening mechanisms do not work in extended objects and we looked for novel probes of these theories by deriving modified properties of stars, galaxies and clusters of galaxies. We also initiated the study of neutron stars to provide strong field tests of these theories. For the tests of gravity on linear scales, we provided forecasts for extended BOSS survey and demonstrated the advantage of combining weak lensing and redshift distortion measurements.

In theme 1 “Theoretical models”, we studied theoretical consistencies of various theoretical models such as vector Galileon, non-local gravity and quasi-dilaton massive gravity models. We have made significant contributions to the development of new classes of scalar tensor theory of gravity. These models include beyond Horndeski theories and we identified new non-linear interactions which break the screening mechanism inside extended objects. This finding was utilised in theme 3 to test these theories using astrophysical objects such as clusters of galaxies and neutron stars.

In theme 2 “Non-linear clustering”, we have developed a perturbation theory approach to predict quasi non-linear power spectra. We created a versatile code that can compute non-linear power spectra at one-loop order in standard perturbation theory in a wide variety of dark energy and modified gravity models including the effect of screening mechanisms. The code can also predict the power spectrum in the redshift space. The outputs of this code have been compared to N-body simulations. We also used hydro-dynamical simulations to test the methodology to constrain modified gravity models using clusters of galaxies by comparing lensing and X-ray masses. We created mock clusters and confirmed the power of our methodology, which can now be applied to larger cluster samples available with the next generation surveys.

As a co-lead of the work package on non-standard cosmological simulations, the PI has made an important contribution to the Euclid mission activities creating the simulation requirement document for Euclid.

In theme 3 “Cosmological tests of gravity”, we studied constraints on general classes of scalar tensor theory identified in theme 1. We showed that, in these models, screening mechanisms do not work in extended objects and we looked for novel probes of these theories by deriving modified properties of stars, galaxies and clusters of galaxies. We also initiated the study of neutron stars to provide strong field tests of these theories. For the tests of gravity on linear scales, we provided forecasts for extended BOSS survey and demonstrated the advantage of combining weak lensing and redshift distortion measurements.

## Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

It has been a long standing question what the most general scalar tensor theory is. A theory proposed by Horndeski in 1974 was rediscovered and it was shown that this is the most general scalar tensor theory with second order equations of motion. Recently, it was pointed out that even with the presence of higher order time derivatives, if the theory satisfies degeneracy conditions, they do not lead to instabilities. This opens up a possibility to construct more general theories, beyond Horndeski theories. We have made significant contributions to the development of these theories and provided methods to test these theories. These developments not only make an impact on the theoretical studies of gravitational theories but also provide a basis for testing gravity on cosmological scales in a general framework.

We have developed theoretical tools to provide predictions for cosmological observations on non-linear scales. A lot of information is available on non-linear scales and it is vital to provide theoretical predictions on these scales to maximise the return from future surveys. The tools developed by this ERC grant will play crucial roles in testing non-standard cosmological models using future astronomical surveys.

We have developed theoretical tools to provide predictions for cosmological observations on non-linear scales. A lot of information is available on non-linear scales and it is vital to provide theoretical predictions on these scales to maximise the return from future surveys. The tools developed by this ERC grant will play crucial roles in testing non-standard cosmological models using future astronomical surveys.