Narrow Results

We find the linearized gravitational field of a static spherically symmetric mass distribution in massive conformal gravity and test it with some solar system experiments. The result is that the theory agrees with the general relativistic observations in the solar system for a determined lower bound on the graviton mass.

Using the quantum corrected Friedmann equation, obtained from the quantum Raychaudhuri equation, and assuming a small mass of the graviton (but consistent with observations and theory), we propose a resolution of the smallness problem (why is observed vacuum energy so small?) and the coincidence problem (why does it constitute most of the universe, about 70%, in the current epoch?).

We show from theoretical considerations, that if the graviton is massive, its mass is constrained to be about $10^{-32}{\mathrm{\text{eV/c}}}^2$. This estimate is consistent with those obtained from experiments, including the recent gravitational wave detection in advanced LIGO.

One of the most interesting astronomical objects is the Galactic Center. It is a subject of intensive astronomical observations in different spectral bands in recent years. We concentrate our discussion on a theoretical analysis of observational data of bright stars in the IR-band obtained with large telescopes. We also discuss the importance of VLBI observations of bright structures which could characterize the shadow at the Galactic Center. If we adopt general relativity (GR), there are a number of theoretical models for the Galactic Center, such as a cluster of neutron stars, boson stars, neutrino balls, etc. Some of these models were rejected or the range of their parameters is significantly constrained with consequent observations and theoretical analysis. In recent years, a number of alternative theories of gravity have been proposed because there are dark matter (DM) and dark energy (DE) problems. An alternative theory of gravity may be considered as one possible solution for such problems. Some of these theories have black hole solutions, while other theories have no such solutions. There are attempts to describe the Galactic Center with alternative theories of gravity and in this case one can constrain parameters of such theories with observational data for the Galactic Center. In particular, theories of massive gravity are intensively developing and theorists have overcome pathologies presented in the initial versions of these theories. In theories of massive gravity, a graviton is massive in contrast with GR where a graviton is massless. Now these theories are considered as an alternative to GR. For example, the LIGO–Virgo collaboration obtained the graviton mass constraint of about $1.2\times 10^{-22}$ eV in their first publication about the discovery of the first gravitational wave detection event that resulted of the merger of two massive black holes. Surprisingly, one could obtain a consistent and comparable constraint of graviton mass at a level around $m_g<2.9\times 10^{-21}$eV from the analysis of observational data on the trajectory of the star S2 near the Galactic Center. Therefore, observations of bright stars with existing and forthcoming telescopes such as the European extremely large telescope (E-ELT) and the thirty meter telescope (TMT) are extremely useful for investigating the structure of the Galactic Center in the framework of GR, but these observations also give a tool to confirm, rule out or constrain alternative theories of gravity. As we noted earlier, VLBI observations with current and forthcoming global networks (like the Event Horizon Telescope) are used to check the hypothesis about the presence of a supermassive black hole at the Galactic Center.

An experimental detection of graviton is extremely hard problem, however, there are different ways to evaluate a graviton mass if it is non-vanishing. Theories of massive gravity or theories with non-vanishing graviton mass initially have a number of pathologies such as discontinuities, ghosts etc. In last years theorists found ways to overcome weaknesses of such theories meanwhile observational features are also discussed. In the first publication reporting about the discovery of gravitational waves from the binary black hole system the LIGO-Virgo collaboration obtained the graviton mass constraint around $1.2\times 10^{-22}$ eV (later the estimate was improved with new data). A comparable and consistent graviton mass constraint around $2.9\times 10^{-21}$ eV has been obtained from analysis of the bright star S2 trajectory near the Galactic Center.

The case for a four-dimensional graviton mass (non zero) influencing reacceleration of the universe in both four and five dimensions is stated, with particular emphasis on the question whether 4D and 5D geometries as given here yield new physical insight as to cosmological evolution. Both cases give equivalent reacceleration one billion years ago, which leads to the question whether other criteria can determine the relative benefits of adding additional dimensions to cosmology models.