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Modified Gravity as an Alternative to Dark Energy

Final Report Summary - MGATDE (Modified Gravity as an Alternative to Dark Energy)

The biggest problem in cosmology is explaining the recently observed accelerated expansion of the universe. Within the framework of General Relativity (GR), the acceleration originates from “dark energy”. The simplest option is the cosmological constant, first introduced by Einstein, but its required value is incredibly small and it cannot be explained by current particle physics. Alternatively, there could be no dark energy, but a large-distance modification to GR may account for the late-time acceleration of the universe

In this project, we studied various theoretical ideas to modify GR on large scales. We found that there often appears a new scalar degree of freedom in gravity that shows pathological behaviours. However, there has been significant progress in constructing healthy interactions for the scalar modes. One idea is to use the so-called “Galileon” interactions. We showed that in models with these Galileon interactions, it is possible to find accelerating solutions without the cosmological constant. The additional scalar mode mediates the fifth force, which is strongly constrained by the solar system experiments. The Galileon terms also help evade these constraints via the so-called Vainshtein mechanism; due to the non-linear interactions, the fifth force is suppressed on small scales.

The idea of Galileon interactions was used to develop consistent non-linear massive gravity models. Can the graviton have a mass? Attempts to answer this question date back to the work by Fierz and Pauli (FP) in 1939. In 2010, de Rham, Gabadadze & Tolley proposed a family of ghost-free extensions to the FP theory based on the idea of Galileon. We found solutions that exhibit the Vainshtein mechanism by which GR is restored on small scales. We also discovered the solutions where the acceleration of the Universe is realised by a small graviton’s mass. Unfortunately these solutions are found to suffer from instabilities and extensions to the original theory are being extensively studied. Although our quest for consistent modified gravity models as an alternative to dark energy still continues, this project contributed significantly to the development of new theoretical models.

From an observational perspective, the main objective was to develop efficient ways to combine observational data sets to distinguish modified gravity models from dark energy models based on GR. We have developed a systematic way to parametrise deviations from GR in the evolution of linear cosmological perturbations. Using current cosmological data, we put constraints on these parameters and demonstrated the power of our methodology when combining observations of structure formation and expansion history to test GR. We also showed that a Euclid-like space-based survey including both lensing and peculiar velocity measurements is essential to better constrain modifications to GR.

Although it is possible test GR in a model independent way on large scales, there is ample information available on small scales where clustering of dark matter becomes non-linear. However, it is difficult to predict the observables on non-linear scales in modified gravity models as it is necessary to take into account the screening mechanism to hide the fifth force properly. We developed a perturbation theory approach to solve the non-linear equation for the scalar mode. We also pioneered in the development of a self-adaptive particle-mesh N-body code to perform simulations in modified gravity models. We have studied in detail how the screening mechanism affects non-linear clustering of dark matter such as the power spectrum, mass function and density profile of dark matter halos. This is a major achievement which will enable us to exploit vast amount of information on non-linear scales to test modified gravity models. Based on these simulations, we also found unique signatures of screening mechanisms such as environmental dependence. This feature was used to put a strongest constraint on a modified gravity model using astrophysical objects.

In the next decade, massive astronomical surveys will enable us to test the theoretical ideas developed in this project. Observational tests proposed in this project can be implemented using actual data from the surveys. Cosmological tests of gravity have become one of main objectives of future astronomical surveys and this project contributed to the theoretical foundation of the tests.