Constraining Non-local Gravity by S2 star orbits
  Non-local theories of gravity have recently gained a lot of interest because
they can suitably represent the behavior of gravitational interaction in the
ultraviolet regime. Furthermore, at infrared scales, they give rise to notable
cosmological effects which could be important to describe the dark energy
behavior. In particular, exponential forms of the distortion function seem
particularly useful for this purpose. Using Noether Symmetries, it can be shown
that the only non-trivial form of the distortion function is the exponential
one, which is working not only for cosmological mini-superspaces, but also in a
spherically symmetric spacetime. Taking this result into account, we study the
weak field approximation of this type of non-local gravity, and comparing with
the orbits of S2 stars around the Galactic center (NTT/VLT data), we set
constraints on the parameters of the theory. Non-local effects do not play a
significant role on the orbits of S2 stars around Sgr A*, but give richer
phenomenology at cosmological scales than the $\Lambda$CDM model. Also, we show
that non-local gravity model gives better agreement between theory and
astronomical observations than Keplerian orbits.
