Probing massive gravitons in f(R) with lensed gravitational waves

We investigate the novel features of gravitational wave solutions in f(R) gravity under proper gauge considerations in the shifted Ricci scalar background curvature (R1+ϵ). The solution is further explored to study the modified dispersion relations for massive modes at local scales and to derive constraints on ϵ. Our analysis yields new insights as we scrutinize these dispersion effects on the polarization (modified Newman-Penrose content) and lensing properties of gravitational waves. It is discovered that the existing longitudinal scalar mode, and transverse breathing scalar mode are both independent of the mass parameter for ϵ<<1. Further, by analysing the lensing amplification factor for the point mass lens model, we show that lensing of gravitational wave is highly sensitive to these dispersion effects in the milli-Hertz frequency (wave optics regime). It is expected that ultra-light modes, having mass about O(10−15) eV for ϵ<<1(≈10−7) lensed by (103≤MLens≤106)M⊙ compact objects are likely to be detected by the advanced gravitational wave space-borne detectors, particularly within LISA's (The Laser Interferometer Space Antenna) sensitivity band.