Speaker
Description
General relativity propagates only two degrees of freedom (DOFs), and Lovelock's theorem strongly constrains possible alternatives. A natural way to explore modified gravity is to relax temporal diffeomorphism invariance while preserving spatial covariance. Such spatially covariant gravity theories, however, generically propagate an additional scalar mode. We will discuss three complementary constructions that remove this unwanted mode while retaining the two DOFs of general relativity. The first starts from a general spatially covariant Lagrangian and derives, through Hamiltonian constraint analysis, the degeneracy and consistency conditions needed to eliminate the scalar DOF. The second works directly at the Hamiltonian level, where auxiliary constraints are introduced as part of the definition of the theory to restrict the phase-space dynamics. The third uses a perturbative Lagrangian approach, expanding the action around a cosmological background and fixing the coefficient functions order by order so that scalar perturbations are absent. These constructions provide explicit modified gravity theories beyond general relativity without introducing extra DOFs and sharpen the question of the uniqueness of general relativity.