Scalar--Tensor Theories of Gravity with \PHI Dependent Masses

TL;DR

The paper investigates generalized scalar--tensor gravity with a scalar field $\Phi$ that induces $\Phi$-dependent particle masses, focusing on a two-sector (visible and dark) realization motivated by string theory. It derives the Einstein-frame action with two couplings $\beta_I,\beta_V$ and shows how a conformal frame can render visible masses constant while dark-sector masses vary as $m_n(\Phi) \propto \Phi^{\sigma}$, leading to non-conservation of $T^{\mu\nu}$ and violations of the equivalence principle. The authors identify new phenomena, including non-geodesic dark-matter trajectories, potential effects on galactic halos, and a dark-entropy production during the matter era, and they constrain model parameters using nucleosynthesis, cosmological age, and gauge-coupling variation, finding very strong bounds, especially from electromagnetic coupling constancy. They show that string-theory predictions (dilaton coupling to photons) impose bounds on $\omega$ and combinations of couplings that can be many orders of magnitude stronger than standard post-Newtonian or nucleosynthesis limits, effectively requiring a stabilized dilaton to remain viable. The work highlights that while a two-sector Φ-dependent mass scenario can be natural in effective string theories, observational constraints strongly favor either a single-sector (equivalent to standard scalar--tensor gravity) or a theory with a mechanism that fixes the dilaton after inflation; moduli may circumvent some of these bounds since they may not couple to the electromagnetic sector.

Abstract

We study new physical phenomena and constraints in generalized scalar--tensor theories of gravity with $Φ$--dependent masses. We investigate a scenario (which can arise in string theories) with two types of $Φ$--dependent masses which could correspond to visible and dark matter sectors. The parameters of this theory are constrained from post--Newtonian bounds, primordial nucleosynthesis and the age of the Universe. We present a perfect fluid formalism for the dark matter sector with variable masses and find an entropy increase effect during the matter era and, in principle, a measurable effect on the motion of the halo of spiral galaxies. For the case of string effective theories, the constancy of gauge couplings provide new bounds which are orders of magnitude stronger than the previous ones.