Abstract
We have computed the number of polarization modes of gravitational waves propagating in the Minkowski background in f(R) gravity. These are three of two from transverse-traceless tensor modes and one from a massive trace mode, which confirms the results found in the literature. There is no massless breathing mode and the massive trace mode corresponds to the Ricci scalar. A newly defined metric tensor in f(R) gravity satisfies the transverse-traceless (TT) condition as well as the TT wave equation.
Highlights
We have computed the number of polarization modes of gravitational waves propagating in the Minkowski background in f(R) gravity
These are three of two from transverse-traceless tensor modes and one from a massive trace mode, which confirms the results found in the literature
The observation of the polarization modes of gravitational waves will be a crucial tool to obtain valuable information about the black holes and the physics of the early universe. It is well-known that the Einstein gravity with two polarization degrees of freedom (DOF) is distinguished from the metric f(R) gravity with three DOF [19]
Summary
We note that (13) and (16) are the same when replacing δR by φ, but the fourth-order coupled equation (11) is quite different from the linearized Einstein equation (15). This indicates that (11) can be reduced to two decoupled secondorder equations (15) and (16) if one employs the conformal transformation and redefinition of scalar appropriately after choosing (3), leading to a canonical scalar action with the Starobinsky potential in the Einstein frame. In the scalartensor theory approach, one assigns the perturbed Ricci scalar to an independent scalar φ Instead, it does not have the trace of metric perturbation h
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