Constraining Weyl type f(Q,T) gravity with Big Bang Nucleosynthesis

The Weyl type $f(Q,T)$ modified gravity theory is an extension of the $f(Q)$ and $f(Q,T)$ type theories, where $T$ is the trace of the matter energy-momentum tensor, and the scalar non-metricity $Q$ is represented in its standard Weyl form, and it is fully determined by a vector field ${\omega }_{\mu }$. The theory can give a good description of the observational data, and of the evolution of the late-time Universe, including a geometric explanation of the dark energy. In this work we investigate the Big Bang Nucleosynthesis (BBN) constraints on several Weyl type $f(Q,T)$ gravity models. In particular, we consider the corrections that Weyl type $f(Q,T)$ terms induce on the freeze-out temperature ${\mathcal{T}}_f$, as compared to the standard $\mathrm{\Lambda }$CDM results. We analyze in detail three distinct cosmological models, corresponding to specific choices of the functional form of $f(Q,T)$. The first model has a simple linear additive structure in $Q$ and $T$, the second model is multiplicative in $Q$ and $T$, while the third is additive in $T$ and the exponential of $Q$. For each $f(Q,T)$ we consider first the cosmological evolution in the radiation dominated era, and then we impose the observational bound on $\mid \delta {\mathcal{T}}_f\mathrm{/}{\mathcal{T}}_f\mid$ to obtain constraints on the model parameters from the primordial abundances of the light elements such as helium-4, deuterium and lithium-7. The abundances of helium-4 and deuterium agree with theoretical predictions, however, the lithium problem, even slightly alleviated, still persists for the considered Weyl type $f(Q,T)$ models. Generally, these models satisfy the BBN constraints, and thus they represent viable cosmologies describing the entire dynamical time scale of the evolution of the Universe.