Palatini formulation of the conformally invariant $$f\left( R,L_m\right) $$ gravity theory

Abstract We investigate the field equations of conformally invariant models gravity with curvature-matter coupling, constructed in Weyl geometry, using Palatini formalism. consider case which Lagrangian is given by sum square scalar, strength associated to vector, and a geometry-matter coupling term, from matter scalar. After substituting scalar terms its Riemannian counterpart, quadratic action defined Riemann geometry involves nonminimal between Ricci Lagrangian. For sake generality, more general Lagrangian, vector nonminimally coupled an arbitrary function also considered. By varying independently respect metric connection, independent connection can be expressed as Levi-Civita auxiliary scalar- vector-dependent metric, related physical means conformal transformation. The are obtained both formulations. cosmological implications investigated for three distinct corresponding different forms functions. A comparison standard $$\Lambda $$ Λ CDM model performed, we find that type give acceptable description observations.