Scalar perturbations in massive gravity in the presence of matter

The de Rham-Gabadadze-Tolley (dRGT) theory provides a consistent massive extension of general relativity, but stable self-accelerating solutions within it have been elusive. The quasi-dilaton extension of the dRGT theory allows for such solutions by introducing an additional scalar field with a global rescaling symmetry. In this talk, I will discuss scalar perturbations in the extended quasi-dilaton theory in the presence of matter. I will first briefly introduce the theory and the self-accelerating background evolution where the quasi-dilaton (in the presence of a massive graviton) can act as an effective cosmological constant. I will next discuss the general calculation of scalar perturbations without restricting to any choice of gauge. I will then choose a particular form for matter where a unitary gauge for matter fields is most convenient to work in and present the kinetic matrix calculation for all propagating scalar degrees of freedom. I will show that the conditions for positive eigenvalues can be satisfied, and the theory can thus remain ghost-free on the self-accelerating solution in the presence of matter. Lastly, I will briefly discuss the linear growth of structure in this theory, that the next talk will describe in more detail.