For the nonlocal action R + aR□^{-1}R, the quadrupole GW luminosity becomes (G/5c^5)[(1 + a/(3(6a-1)))⟨Q⃛_ij Q⃛_ij⟩ + ((1+7a)/(3(6a-1)))⟨Q⃛²⟩], with the claimed scalar-mode detectability resting on an invalid near-divergence estimate.
Scalar Mode Quadrupole Radiation from Astronomical Sources in $F(R)$ Modified Gravity
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abstract
We investigate the scalar mode quadrupole radiation of gravitational waves in $F(R)$ modified gravity. In $F(R)$ gravity a massive scalar mode appears in the gravitational waves. We find explicit expressions for the quadrupole radiation and the energy current of the scalar mode in general $F(R)$ gravity models. We consider a binary star and a bouncing star as astronomical sources of the gravitational waves and calculate the quadrupole radiation of the scalar and tensor modes. The scalar mode radiates under spherically symmetric conditions, but the tensor modes do not. The scalar mode mass is estimated for some typical energy scales. We show a possibility to detect the scalar mode in the future gravitational waves observation.
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Non-locality in Quadrupolar Gravitational Radiation
For the nonlocal action R + aR□^{-1}R, the quadrupole GW luminosity becomes (G/5c^5)[(1 + a/(3(6a-1)))⟨Q⃛_ij Q⃛_ij⟩ + ((1+7a)/(3(6a-1)))⟨Q⃛²⟩], with the claimed scalar-mode detectability resting on an invalid near-divergence estimate.