A Weyl geometric scalar field approach to the dark sector

TL;DR

This paper investigates the dark sector using Weyl geometric scalar tensor theory, incorporating non-standard scalar field contributions to model galactic dynamics and cosmology, including a potential bouncing universe scenario.

Contribution

It introduces a novel scalar field Lagrangian within Weyl geometry that combines MOND-inspired and second-order terms, bridging galactic and cosmological models.

Findings

Successful modeling of galactic dynamics with MOND-like behavior

Discussion of transition to Einstein gravity and scalar cosmology

Tentative proposal of a bouncing cosmological model

Abstract

This paper explores the dark sector (dark matter and dark energy) from the perspective of Weyl geometric scalar tensor theory (integrable Weyl geometry). In order to account for the galactic dynamics successfully modelled by MOND ("modified Newtonian dynamics"), the non-minimally coupled scalar field considered here has a Lagrangian with two non-conventional contributions in addition to a standard kinetic term: one is inspired by Bekenstein/Milgrom's RAQUAL ("relativistic a-quadratic Lagrangian") from 1983, the other one by a second order term introduced in cosmological studies by Novello et al. in 1993. {\bf See, however, the error warning below}. We consider the transition to the Einstein gravity on one hand and to scalar field cosmology in the FRW framework on the other. A bouncing cosmological model is tentatively discussed at the end.