Testing gravity theories using tensor perturbations

Primordial gravitational waves constitute a promising probe of the very early Universe and the laws of gravity. We study in this work changes to tensor-mode perturbations (TMPs) that can arise in various proposed modified gravity (MG) theories. These include additional friction effects, nonstandard dispersion relations involving a massive graviton, a modified speed, and a small-scale modification. We introduce a physically motivated parameterization of these effects and use current available data to obtain exclusion regions in the parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on tensor-mode MG parameters as constrained by future experiments COrE, Stage-IV and PIXIE. For a fiducial value of the tensor-to-scalar ratio $r=0.01$, we find that an additional friction of $3.5\sim4.5\%$ compared to GR will be detected at $3$-$\sigma$ by these experiments, while a decrease in friction will be more difficult to detect. The speed of gravitational waves needs to be by $5\sim15\%$ different from the speed of light for detection. We find that the minimum detectable graviton mass is about $7.8\sim9.7\times 10^{-33}$ eV, which is of the same order of magnitude as the graviton mass that allows massive gravity theories to produce cosmic acceleration. Finally, we study TMPs in MG during inflation using our parameterization. We find that the tensor spectral index is related to $r$ and the friction parameter $\nu_0$ by $n_T=-3\nu_0-r/8$. Assuming that the friction parameter is unchanged throughout the history of the Universe and is much larger than $r$, future experiments will be able to distinguish this MG consistency relation from the standard inflation one, and thus can be used as a further test of MG. In summary, TMPs and cosmic-microwave-background B-mode polarization provide a complementary avenue to test gravity theories. (Abridged)