Vulnerability of f(Q) gravity theory and a possible resolution

Abstract: Both the generalized teleparallel theories of gravity suffer from some serious problems. The strong coupling issue appearing as a consequence of extra degrees of freedom in the generalized metric teleparallel gravity' theory, prompted to considergeneralized symmetric teleparallel gravity' theory (GSTG). Unfortunately, recent perturbative analysis in the background of maximally symmetric space-time revealed that GSTG also suffers from the strong coupling issue and the ghost degrees of freedom. It has also been cognised that GSTG does not admit diffeomorphic invariance in general. Lately, it has been shown that except for the first, the other two connections associated with spatially flat Robertson-Walker metric do not even admit GSTG, while the first connection leads to an eerie Hamiltonian upon ensuing Dirac-Bergmann constraint analysis. Here we show that the only existing non-flat connection is also not viable in the same sense. Thus GSTG happens to be jeopardized. These problems do not showup in $f(R,Q)$ theory of gravity. Modified Dirac-Bergmann constraint analysis is deployed to formulate the phase-space structure. Quantization, probabilistic interpretation and semi-classical approximation connote that such a theory is well behaved in the context of early inflation, which has also been studied.