## Periodic Reporting for period 4 - CosTesGrav (Cosmological Tests of Gravity)

Reporting period: 2020-03-01 to 2021-07-31

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.

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.

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.

This project is composed of three main themes to achieve the objectives.

In theme 1 “Theoretical models”, we studied theoretical consistencies of various theoretical models such as vector Galileon, non-local gravity and quasi-dilaton and generalised massive gravity models. Among them, generalised massive gravity models emerge as promising candidate to explain the accelerated expansion of the universe without the cosmological constant. We have made significant contributions to the development of new classes of scalar tensor theory of gravity. These theories have found a special place after almost simultaneous detections of gravitational waves and short gamma-ray bursts from a neutron star merger on 17 August 2017, which put a stringent constraint on the difference between the speed of gravitational waves and that of light. A subclass of these new theories satisfies the condition that these two speeds are equal thus it provides viable modified gravity models that can be tested by cosmological and astrophysical observations. We also studied early modified gravity models as a possible solution to the Hubble constant tension, the discrepancy of the measurement of the Hubble constant from local and cosmological measurements.

In theme 2 “Non-linear clustering”, we developed a perturbation theory approach to predict quasi non-linear power spectra in the redshift space. We also developed a fast approximate N-body method based on a combination of second order Lagrangian perturbation theory and particle mesh simulations. The combination of the semi-analytic approach based on the perturbation theory, fast approximate simulations and full N-body simulations opens a way to test modified gravity models in a consistent way including non-linear scales on which the bulk of information is available. We generated galaxy mock catalogues using the fast methods and showed that they can match the mocks based on full N-body simulations. 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.

In theme 3 “Cosmological tests of gravity”, we studied constraints on general classes of scalar tensor theory identified in theme 1. The screening mechanism does not work inside matter in some of these models and we looked for novel probes of these theories by deriving modified properties of stars, galaxies and clusters of galaxies. We also studied neutron stars to provide strong field tests of these theories.

We studied the performance of theoretical templates to constrain a modified gravity parameter using redshift space power spectra. We showed that the theoretical templates developed in theme 2 can reproduce the input modified gravity model parameter in an unbiased way.

For the tests of gravity on linear scales, we performed reconstruction of three time-dependent functions describing the expansion history of the Universe and gravitational effects on light and matter in the large-scale structure. Using the combination of latest cosmological observations, we have shown that current data can already constrain 15 combined modes of these three functions with respect to the theoretical prior. We showed that reconstruction of these three functions enables us to identify the phenomenological features that alternative theories would need to have in order to ease some of the tensions between datasets within the standard model, and deduce important constraints on broad classes of modified gravity models.

In theme 1 “Theoretical models”, we studied theoretical consistencies of various theoretical models such as vector Galileon, non-local gravity and quasi-dilaton and generalised massive gravity models. Among them, generalised massive gravity models emerge as promising candidate to explain the accelerated expansion of the universe without the cosmological constant. We have made significant contributions to the development of new classes of scalar tensor theory of gravity. These theories have found a special place after almost simultaneous detections of gravitational waves and short gamma-ray bursts from a neutron star merger on 17 August 2017, which put a stringent constraint on the difference between the speed of gravitational waves and that of light. A subclass of these new theories satisfies the condition that these two speeds are equal thus it provides viable modified gravity models that can be tested by cosmological and astrophysical observations. We also studied early modified gravity models as a possible solution to the Hubble constant tension, the discrepancy of the measurement of the Hubble constant from local and cosmological measurements.

In theme 2 “Non-linear clustering”, we developed a perturbation theory approach to predict quasi non-linear power spectra in the redshift space. We also developed a fast approximate N-body method based on a combination of second order Lagrangian perturbation theory and particle mesh simulations. The combination of the semi-analytic approach based on the perturbation theory, fast approximate simulations and full N-body simulations opens a way to test modified gravity models in a consistent way including non-linear scales on which the bulk of information is available. We generated galaxy mock catalogues using the fast methods and showed that they can match the mocks based on full N-body simulations. 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.

In theme 3 “Cosmological tests of gravity”, we studied constraints on general classes of scalar tensor theory identified in theme 1. The screening mechanism does not work inside matter in some of these models and we looked for novel probes of these theories by deriving modified properties of stars, galaxies and clusters of galaxies. We also studied neutron stars to provide strong field tests of these theories.

We studied the performance of theoretical templates to constrain a modified gravity parameter using redshift space power spectra. We showed that the theoretical templates developed in theme 2 can reproduce the input modified gravity model parameter in an unbiased way.

For the tests of gravity on linear scales, we performed reconstruction of three time-dependent functions describing the expansion history of the Universe and gravitational effects on light and matter in the large-scale structure. Using the combination of latest cosmological observations, we have shown that current data can already constrain 15 combined modes of these three functions with respect to the theoretical prior. We showed that reconstruction of these three functions enables us to identify the phenomenological features that alternative theories would need to have in order to ease some of the tensions between datasets within the standard model, and deduce important constraints on broad classes of modified gravity models.

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. We have made significant contributions to the development of more general scalar tensor theories beyond Horndeski. These developments not only made an impact on the theoretical studies of gravitational theories but also provided a basis for testing gravity on cosmological scales in a general framework. In fact, the constraint on the gravitational wave speed from the neutron star merger event on 17 August 2018 restricted significantly the Horndeski theory while a subclass of the extended theories satisfies this constraint.

We have developed various theoretical tools to provide predictions for cosmological observations on non-linear scales in modified gravity models. 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 project will play crucial roles in testing non-standard cosmological models using future astronomical surveys.

We performed for the first time a joint reconstruction of phenomenological functions in time describing the expansion history of the Universe and gravitational effects on light and matter in the large-scale structure using a combination of latest cosmological observations. We identified the phenomenological features that alternative theories would need to have in order to ease some of the tensions between datasets within the standard model of cosmology and deduced important constraints on broad classes of modified gravity models.

We have developed various theoretical tools to provide predictions for cosmological observations on non-linear scales in modified gravity models. 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 project will play crucial roles in testing non-standard cosmological models using future astronomical surveys.

We performed for the first time a joint reconstruction of phenomenological functions in time describing the expansion history of the Universe and gravitational effects on light and matter in the large-scale structure using a combination of latest cosmological observations. We identified the phenomenological features that alternative theories would need to have in order to ease some of the tensions between datasets within the standard model of cosmology and deduced important constraints on broad classes of modified gravity models.