Constraints on some alternative theories of gravity after GW170817

Among the observed gravitational wave (GW) signals at LIGO-Virgo, GW170817 is the only binary neutron star merger event with an electromnetic (EM) counterpart, the gamma-ray burst GRB-170817A. It opened up the window for multi-messenger astronomy leading to exciting new physics. It constrains many alternative/modified theories of gravity, such as the Horndeski theories of gravity. In this talk, I shall discuss our contribution in this direction about constraining some other alternative theories of classical gravity: (i) Born-Infeld (BI) gravity, (ii) higher curvature gravity, and (iii) f(R) gravity with screening mechanism. BI gravity is inspired from the BI nonlinear electrodynamics and possess a nonlinear matter-gravity coupling paradigm. This theory reduces to general relativity in vacuum but differs in the presence of matter. We show that the speed of gravitational waves propagating through the matter distribution is also different in BI gravity and we use this effect to constrain BI gravity. On the other hand, in higher curvature gravity, the study of the characteristics equation of the perturbation shows that the gravitational radiation follows the null geodesic of an `effective metric’ instead of the actual physical metric, leading to the time delay in GW and EM signals. Although, f(R) theories are insensitive to the time delay constraint, we exploited the fact that they possess an additional massive scalar degree of freedom apart from the massless spin-2 modes. The corresponding scalar field contributes an additional attractive, short-ranged “fifth” force affecting the gravitational wave radiation process. Using this feature, we also obtain an upper bound on f(R) theories from GW170817.