http://arxiv.org/abs/2111.04205
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. The presence of $T$ in the Lagrangian breaks the equation of the conservation of energy, which in turn breaks the standard $\rho’ + 3\mathcal{H} (\rho+p) = 0$ relation. We also derived a coupled system of differential equations between $\delta$, the density contrast and $v$ in the quasi-static limit, which will be useful in future studies to see whether this class of theories constitute a good alternative to dark matter. These results will also enable to test $f(Q,T)$ gravity with CMB data that will determine if these models can reduce the Hubble constant tension.
A. Nájera and A. Fajardo
Tue, 9 Nov 21
64/102
Comments: 10 pages
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