Can the cosmological \(^{7}{\mathrm{Li}}\) problem be solved in the Weyl-type \(f(Q,T)\) modified gravity theory?

One of the most powerful evidence for the Big Bang theory is the prediction of the primordial abundances of the elements by the Big Bang Nucleosynthesis (BBN) theory. The BBN theory in its standard formulation is a parameter-free theory, with the precise knowledge of the baryon-to-photon ratio of the Universe, obtained from studies of the anisotropies of cosmic microwave background radiation. The theoretical abundances of light elements during primordial nucleosynthesis and those determined from observations are in good agreement throughout a range of nine orders of magnitude. However, there is still a significant difference of the ⁷Li abundance, overestimated by a factor of ∼ 2.5 when calculated theoretically. In the present work we will consider the nucleosynthesis process in the framework of the Weyl-type f(Q,T) theory, a modified gravity theory representing an extension of the f(Q) and f(Q,T) type theories, obtained under the assumption that the scalar non-metricity Q of the space-time is expressed in its standard Weyl form. Hence, the nonmetricity of the spacetime is fully determined by a vector field \(w^{\mu }\). The theory can give a good description of the observational data, and of the evolution of the late-time Universe. We show that in some parameter ranges the Lithium abundance can be explained, and these ranges have a relatively weak dependence on the initial value of the Weyl vector.