Cosmological perturbation theory in f (Q, T) gravity

We developed the cosmological linear theory of perturbations for f(Q, T) gravity, which is an extension of symmetric teleparallel gravity, with Q the non-metricity and T the trace of the stress-energy tensor. By considering an ansatz of f(Q, T) = f(1)(Q) + f(2)(T), which has been broadly studied in the literature and the coincident gauge where the connection vanishes, we got equations consistent with f(Q) gravity when f(T) = 0. In the case of the tensor perturbations, the propagation of gravitational waves was found to be identical to f(Q), as expected. For scalar perturbations, outside the limit f(T) = 0, we got that the coupling between Q and T in the Lagrangian produces a coupling between the perturbation of the density and the pressure. This coupling is preserved when considering the weak coupling limit between Q and T. On the other hand, in the strong coupling limit with a generic function of the form f(2)(T) = alpha T + beta T-2, the perturbative equations are heavily driven by the f(2)(T) derivatives when beta not equal 0. However, when beta = 0, the perturbative equations are identical to the weak coupling limit even though this case is a non-minimally coupling one. The presence of T in the Lagrangian breaks the equation of the conservation of energy, which in turn breaks the standard rho' + 3H(rho + p) = 0 relation. We also derived a coupled system of differential equations between delta, the density contrast and v in the H << k limit and with negligible time derivative of the scalar perturbation potentials, which will be useful in future studies to see whether this class of theories constitute a good alternative to dark matter. These results might also enable to test f(Q, T) gravity with CMB and standard siren data that will help to determine if these models can reduce the Hubble constant tension and if they can constitute an alternative to the Lambda CDM model.

Automated summary

We developed the cosmological linear theory of perturbations for f(Q, T) gravity and analyzed the coupling between Q and T as well as the properties related to scalar and tensor perturbations. Our analysis suggests that f(Q, T) gravity could serve as a good alternative to dark matter in certain cases, and we provided a method for further studying this theory.