Abstract
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.
Highlights
It is well established that General Relativity (GR), together with the associated concordance model in cosmology, ΛCDM, are the most successful explanations for gravitational and cosmological effects in the Universe
The inability to find a convincing explanation for the accelerated expansion of the Universe, the huge discrepancy between the theoretical and observed values of the cosmological constant at early and late times, the fact that no particle candidate for dark matter has been observed at fundamental scales, together with the failure to confirm the existence of supersymmetry at TeV scales, led the scientists to pursue alternative explanations for the gravitational interaction
Non-local gravity theories are very well motivated from cosmology, since they give a good explanation in the latetime acceleration of the Universe, without invoking exotic forms of matter-energy
Summary
It is well established that General Relativity (GR), together with the associated concordance model in cosmology, ΛCDM, are the most successful explanations for gravitational and cosmological effects in the Universe. They have both passed the observational tests with flying colors. The inability to find a convincing explanation for the accelerated expansion of the Universe, the huge discrepancy between the theoretical and observed values of the cosmological constant at early and late times, the fact that no particle candidate for dark matter has been observed at fundamental scales, together with the failure to confirm the existence of supersymmetry at TeV scales, led the scientists to pursue alternative explanations for the gravitational interaction. The interested reader is refereed to the exhausting literature [1–5]
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