Dr Ryo Namba (Kavli IPMU, University of Tokyo)
A fully non-linear massive gravity was recently constructed by de Rham, Gabadadze and Tolley (dRGT), removing the unwanted extra degree of freedom condemned by ghost instability, known as Boulware-Deser (BD) ghost. It was, however, soon found that homogeneous and isotropic solutions with accelerated expansion in this theory suffers new-type ghost instabilities at the non-linear level. The bigravity theories as an extension of the dRGT massive gravity promote the non-dynamical fiducial metric in the dRGT theory to a dynamical quantity. The class of these theories with each matter sector coupling to only one of the physical and fiducial metrics preserves the structure that guarantees the absence of the BD ghost, and it has been shown to have some parameter space for cosmological solutions. While these solutions are stable against perturbations for the graviton mass greater than the Hubble expansion rate, a linear analysis exhibits ghosts for the scalar graviton in the opposite regime, indicating an instability in the early universe. We extend the analysis including non-linear effects from self interactions of the scalar graviton. We study the stability of the non-linear solutions, exploring the possibility to evade the instability at both early and late times.