The Weyl-type modified gravity theory is an extension of the $f(Q)$ and $f(Q,T)$ theories, where $T$ is the trace of the matter energy-momentum tensor, and the scalar nonmetricity $Q$ is represented in its standard Weyl form, which is fully determined by a vector field ${\omega }_{\mu }$. The theory provides a solid explanation of the observational data and the evolution of the late-time Universe, offering 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. We analyze in detail three distinct cosmological models, each corresponding to a specific choice of the functional form of $f(Q,T)$. The first model adopts 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 $f(Q,T)$ model, we consider first the cosmological evolution in the radiation dominated era, and then we determine the constraints on the model parameters from the primordial abundances of the light element, 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 timescale of the evolution of the Universe.

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• Alternative gravity theories
• Big bang nucleosynthesis
• Evolution of the Universe