Gravitational Waves in Viable Modified Gravity Theories

We review our recent work [1] on gravitational waves in viable f(R) models. We concentrate on the exponential gravity and Starobinsky models. We show that in both cases, the mass of the scalar mode is order of 10⁻³³eV when it propagates in vacuum. In the presence of matter density, such as galaxy, the scalar mode can be heavy. In particular, it becomes almost infinity so that the scalar mode of gravitational wave for the exponential model disappears like the ACDM, whereas it can be as low as 10⁻²⁴eV in the Starobinsky model, corresponding to the lowest frequency of 10⁻⁹ Hz, which may be detected by the current and future gravitational wave probes in space.