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+& varepsilon;). The solution is further explored to study the modified dispersion relations for massive modes at local scales and to derive constraints on & varepsilon;. 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 & varepsilon;<<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 & varepsilon;<<1(approximate to 10-7) lensed by (10(3 )<= M-Lens <= 10(6))M-circle dot 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.