braneworld cosmology with a non-minimally coupled scalar field and palatini bulk gravity

We study a five-dimensional braneworld cosmology in the palatini formalism, where a bulk scalar field couples non-minimally to the ricci scalar. the bulk contains a delta-function brane with z2 symmetry that confines standard matter fields. we derive generalized field equations and obtain the effective friedmann and raychaudhuri equations on the brane, which display key differences from the metric formulation. non-minimal coupling of palatini ricci scalar and scalar field corrections significantly modify both early- and late-time dynamics: in the high-energy regime, the non-minimal coupling reshapes the effective scalar potential, altering slow-roll parameters and the duration of inflation—negative couplings flatten the slope and enhance inflation, while positive couplings steepen it, with further modulation from the bulk cosmological constant. to test the viability of the model, we constrained its parameter space using the planck 2018 datasets to obtain the observationally viable ranges for the model’s parameter. at low energies, the system approaches scalar-dominated or vacuum de sitter solutions, where the effective newton constant and cosmological constant emerge from the interplay of brane tension, scalar potential, and bulk contributions. this structure naturally realizes a generalized randall–sundrum fine-tuning and supports late-time acceleration.