## Does dark energy exist?

A major topic in cosmology is the accelerating expansion of the universe. In general relativity (GR), the acceleration is usually explained in terms of dark energy, but there are other possibilities.

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The simplest explanation of the accelerating expansion is the cosmological constant, first introduced by Einstein, but its required value cannot be explained by current physics. Alternatively, there could be no dark energy. A large-distance modification to the force of gravity may account for the late-time acceleration of the universe.

Funded by the EU, the MGATDE (Modified gravity as an alternative to dark energy) project studied theoretical ideas to modify GR on large scales. One idea was to use the so-called Galileon interactions. The researchers showed that in models with these Galileon interactions, it is possible to find accelerating solutions without the cosmological constant.

The idea of Galileon interactions was used to develop consistent non-linear massive gravity models. Another question was if the graviton has a mass. The team found solutions that exhibit the Vainshtein mechanism, under which GR is restored on small scales. They also discovered unstable solutions where the acceleration of the universe is explained by a small graviton mass.

From an observational perspective, the main objective was to develop efficient ways to use observational data sets to distinguish modified gravity models from dark energy models based on GR.

MGATDE showed that a space-based survey including both lensing and peculiar velocity measurements can significantly constrain modifications to GR.

Although it is possible test GR in a model-independent way on large scales, there is also information available on small scales, where the clustering of dark matter becomes non-linear. The project developed a perturbation theory approach to solve the non-linear equation for the scalar mode. This involved development of a self-adaptive particle-mesh N-body code to perform simulations in modified gravity models. This will enable the use of a vast amount of information on non-linear scales to test modified gravity models.

In the next decade, massive astronomical surveys will enable testing of the theoretical ideas developed in this project.

Funded by the EU, the MGATDE (Modified gravity as an alternative to dark energy) project studied theoretical ideas to modify GR on large scales. One idea was to use the so-called Galileon interactions. The researchers showed that in models with these Galileon interactions, it is possible to find accelerating solutions without the cosmological constant.

The idea of Galileon interactions was used to develop consistent non-linear massive gravity models. Another question was if the graviton has a mass. The team found solutions that exhibit the Vainshtein mechanism, under which GR is restored on small scales. They also discovered unstable solutions where the acceleration of the universe is explained by a small graviton mass.

From an observational perspective, the main objective was to develop efficient ways to use observational data sets to distinguish modified gravity models from dark energy models based on GR.

MGATDE showed that a space-based survey including both lensing and peculiar velocity measurements can significantly constrain modifications to GR.

Although it is possible test GR in a model-independent way on large scales, there is also information available on small scales, where the clustering of dark matter becomes non-linear. The project developed a perturbation theory approach to solve the non-linear equation for the scalar mode. This involved development of a self-adaptive particle-mesh N-body code to perform simulations in modified gravity models. This will enable the use of a vast amount of information on non-linear scales to test modified gravity models.

In the next decade, massive astronomical surveys will enable testing of the theoretical ideas developed in this project.