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In this paper we use a modification of the Newtonian gravitational potential with a non-linear Yukawa-like correction, as it was proposed by C. Will earlier to obtain new bounds on graviton mass from the observed orbits of S-stars around the Galactic Center (GC). This phenomenological potential differs from the gravitational potential obtained in the weak field limit of Yukawa gravity, which we used in our previous studies. We also assumed that the orbital precession of S-stars is close to the prediction of General Relativity (GR) for Schwarzschild precession, but with a possible small discrepancy from it. This assumption is motivated by the fact that the GRAVITY Collaboration in 2020 and in 2022 detected Schwarzschild precession in the S2 star orbit around the Supermassive Black Hole (SMBH) at the GC. Using this approach, we were able to constrain parameter $\lambda$ of the potential and, assuming that it represents the graviton Compton wavelength, we also found the corresponding upper bound of graviton mass. The obtained results were then compared with our previous estimates, as well as with the estimates of other authors., Comment: 16 pages, 4 tables, 3 figures. Accepted for publication in Symmetry

Here we study possible improvements of the existing constraints on the upper bound of graviton mass by the analysis of the stellar orbits around the SMBH at the GC in the framework of Yukawa gravity. A motivation for this study is a recent detection of Schwarzschild precession in the orbit of S2 star around the SMBH at the GC by the GRAVITY Collaboration. The authors indicated that the orbital precession of the S2 star is close to the General Relativity (GR) prediction, but with possible small deviation from it, and parametrized this effect by introducing an ad hoc factor in the parametrized PPN equations of motion. Here we use the value of this factor presented by GRAVITY in order to perform two-body simulations of the stellar orbits in massive gravity using equations of motion in the modified PPN formalism, as well as to constrain the range of massive interaction $\Lambda$. From the obtained values of $\Lambda$, and assuming that it corresponds to the Compton wavelength of graviton, we then calculated new estimates for the upper bound of graviton mass which are found to be independent, but consistent with the LIGO's estimate of graviton mass from the first GW signal GW150914 (later this graviton mass estimation was significantly improved with consequent observations of GW events). We also performed calculations including numerical simulations in order to constrain the bounds on graviton mass in the case of a small deviation of the stellar orbits from the corresponding GR predictions and showed that our method could further improve previous estimates for upper bounds on the graviton mass. It is also demonstrated that such analysis of the observed orbits of S-stars around the GC in the frame of the Yukawa gravity represents a tool for constraining the upper bound for the graviton mass, as well as for probing the predictions of GR or other gravity theories., Comment: 16 pages, 3 tables, 8 figures. Accepted for publication in Phys. Rev. D

We show that fundamental plane of elliptical galaxies can be used to obtain observational constraints on metric theories of gravity. Being it connected to global properties of ellipticals, it can fix parameters of modified gravity. Specifically, we use fundamental plane to constrain modified theories of gravity with Yukawa-like corrections which commonly emerge in the post-Newtonian limit. After giving examples on how these corrections are derived, we first analyze the velocity distribution of elliptical galaxies comparing theoretical results of modified gravity with Yukawa-like corrections with astronomical data. According to these results, it is possible to constrain the parameters of the corrections discriminating among classes of models compatible with astronomical observations. We conclude that fundamental plane can be used as a standard tool to probe different theories of gravity in the weak field limit., Comment: 13 pages, 7 figures, to be published in Phys. Dark. Univ. (2020)

The aim of our investigation is to derive a particular theory among the class of scalar-tensor(ST) theories of gravity, and then to test it by studying kinematics and dynamics of S-stars around supermassive black hole (BH) at Galactic Center (GC). We also discuss the Newtonian limit of this class of ST theories of gravity, as well as its parameters. We compare the observed orbit of S2 star with our simulated orbit which we obtained theoretically with the derived ST potential and constrained the parameters. Using the obtained best fit parameters we calculated orbital precession of S2 star in ST gravity,and found that it has the same direction as in General Relativity (GR), but causes much larger pericenter shift., Comment: 13 pages, 1 table, 6 figures. Accepted for publication in Facta Universitatis: Series Phys. Chem. Tech. (Invited lecture at Balkan Workshop 2018)

The global properties of elliptical galaxies are connected through the so-called fundamental plane of ellipticals, which is an empirical relation between their parameters: effective radius, central velocity dispersion and mean surface brightness within the effective radius. We investigated the relation between the parameters of the fundamental plane equation and the parameters of modified gravity potential $f(R)$. With that aim, we compared theoretical predictions for circular velocity in $f(R)$ gravity with the corresponding values from a large sample of observed elliptical galaxies. Besides, we consistently reproduced the values of coefficients of the fundamental plane equation as deduced from observations, showing that the photometric quantities like mean surface brightness are related to gravitational parameters. We show that this type of modified gravity, especially its power-law version - $R^n$, is able to reproduce the stellar dynamics in elliptical galaxies. Also, it is shown that $R^n$ gravity fits the observations very well, without need for a dark matter., Comment: 9 pages, 2 figures. Accepted for publication in Atoms

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., Comment: 6 pages, presented as an invited talk at the XXXI International Workshop on High Energy Physics (IHEP, Protvino, Russia)

Recently LIGO collaboration discovered gravitational waves \cite{Abbott_16} predicted 100 years ago by A. Einstein. Moreover, in the key paper reporting about the discovery, the joint LIGO \& VIRGO team presented an upper limit on graviton mass such as $m_g < 1.2 \times 10^{-22} eV$ (Abbott et al. (LIGO collaboration) PRL 116 (2016) 061102). Since the graviton mass limit is so small the authors concluded that their observational data do not show violations of classical general relativity. We consider another opportunity to evaluate a graviton mass from phenomenological consequences of massive gravity and show that an analysis of bright star trajectories could bound graviton mass with a comparable accuracy with accuracies reached with gravitational wave interferometers and expected with forthcoming pulsar timing observations for gravitational wave detection. It gives an opportunity to treat observations of bright stars near the Galactic Center as a wonderful tool not only for an evaluation specific parameters of the black hole but also to obtain constraints on the fundamental gravity law such as a modifications of Newton gravity law in a weak field approximation. In particular, we obtain bounds on a graviton mass based on a potential reconstruction at the Galactic Center., Comment: 8 pages, 1 figure

Here we investigate possible applications of observed stellar orbits around Galactic Center for constraining the R$^n$ gravity at Galactic scales. For that purpose, we simulated orbits of S2-like stars around the massive black hole at Galactic Center, and study the constraints on the R$^n$ gravity which could be obtained by the present and next generations of large telescopes. Our results show that R$^n$ gravity affects the simulated orbits in the qualitatively similar way as a bulk distribution of matter (including a stellar cluster and dark matter distributions) in Newton's gravity. In the cases where the density of extended mass is higher, the maximum allowed value of parameter $\beta$ in R$^n$ gravity is noticeably smaller, due to the fact that the both extended mass and $R^n$ gravity cause the retrograde orbital precession., Comment: 10 pages, 4 figures, accepted for publication in Advances in Space Research

In this paper we perform a detailed study of the masses and mixing of the single charmed scalar tetraquarks: $c q \bar{q} \bar{q}$. We also give a systematic analysis of these tetraquark states by weight diagrams, quantum numbers and flavor wave functions. Tetraquark masses are calculated using four different fits. The following SU(3)$_\mathrm{F}$ representations are discussed: $\bar{15}_\mathrm{S}$, $\bar{3}_\mathrm{S}$, $6_\mathrm{A}$ and $\bar{3}_\mathrm{A}$. We use the flavor-spin Glozman-Riska interaction Hamiltonian with SU(3) flavor symmetry breaking. There are 27 different tetraquarks composed of a charm quark $c$ and of the three light flavors $u, d, s$: 11 cryptoexotic (3 D$_\mathrm{s}^{+}$, 4 D$^{+}$, 4 D$^{0}$) and 16 explicit exotic states. We discuss D$_\mathrm{s}$ and its isospin partners in the same multiplet, as well as all the other four-quark states. Some explicit exotic states appear in the spectrum with the same masses as D$_\mathrm{s}^{+}$(2632) in $\bar{15}_\mathrm{S}$ and with the same masses as D$_\mathrm{s}^{+}$(2317) in $6_\mathrm{A}$ representation, which confirm the tetraquark nature of these states., Comment: 10 pages, 6 tables, 6 figures. Accepted for publication in Phys. Rev. D