Scalar-Field Singularities and Cyclic Cosmology in Brans-Dicke Theory

Abstract

We investigate a Brans-Dicke cosmological model with a scalar-field potential and derive an analytical solution for a power-law ansatz for the scalar field. The resulting cosmological evolution terminates in a scalar-field singularity at which the scalar field diverges and the effective gravitational coupling tends to zero, while the scale factor remains finite and the energy density and pressure diverge. We then explore a heuristic interpretation of this behaviour in which the rapid decrease of the effective gravitational coupling near the singularity could be associated with accelerated black-hole evaporation. We phenomenologically postulate a transition to a subsequent cosmological branch, although a smooth transition preserving the same scalar-field potential on both branches has not been obtained within the ansatz considered. The physical mechanism underlying such a transition therefore remains unknown. Finally, we discuss possible, highly speculative connections between this scenario and the Little Red Dots observed by the James Webb Space Telescope. These connections are not predictions of the present model but motivate further investigation of the possible implications of scalar-field singularities for cyclic cosmological scenarios.