Phase space structure of symmetric teleparallel theory of gravity

Abstract The ‘generalized symmetric teleparallel gravity’ (GSTG) does not admit diffeomorphic invariance, since the auxiliary field as well as the shift vector act as non-propagating dynamical variables carrying 1/2 degrees of freedom each. We show that in a minisuperspace model, which is devoid of the shift vector, the problem is alleviated for locally Lorentz invariant GSTG theory, and diffeomorphic invariance is established at least for one connection. However, the eerie structure of the Hamiltonian constructed even in the background of spatially flat isotropic and homogeneous Robertson–Walker space-time, can not be maneuvered. In contrast, the other two spatially flat connections containing an arbitrary time dependent function, doesʼnt admit non-linear extension to ‘symmetric teleparallel equivalent to general relativity’ (STEGR). We therefore construct the phase-space structure with three different spatially flat connections for the ‘Lorentz invariant’ linear-scalar–vector–tensor GSTG action. Diffeomorphic invariance is established and the associated Hamiltonians are found to be well behaved for all the three cases.