Exact vacuum FLRW solutions in q-deformed Brans-Dicke cosmology

Abstract

We study a q-deformed extension of Brans-Dicke (BD) gravity in a spatially flat Friedmann-Lema & icirc;tre-Robertson-Walker space-time. The deformation enters through a coupling function that modifies the effective gravitational strength and leads to generalized Friedmann equations. In the matter-free sector, we obtain exact analytic solutions for the scale factor and the BD scalar field, and recast the scalar contribution as an effective fluid. We show that the corresponding equation-of-state parameter and the deceleration parameter are constants and depend only on the BD coupling omega and the deformation function, allowing the scalar sector to mimic radiation-, matter-, or dark-energy-like behavior for a restricted region of parameter space.