Screening Modifications of Gravity through Disformally Coupled Fields
Tomi S. Koivisto, David F. Mota, Miguel Zumalacarregui
TL;DR
The paper investigates a non-conformal, disformal coupling between a canonical scalar field and matter as a viable modification of gravity. It formulates the disformal framework with $\bar{g}_{\mu\nu} = C(\phi) g_{\mu\nu} + D(\phi) \phi_{,\mu} \phi_{,\nu}$, derives the coupled-energy exchange $\nabla_\mu T^{\mu\nu}_m = -Q \phi^{,\nu}$ and the scalar-field equation in terms of $\mathcal{M}^{\mu\nu}$, $\mathcal{Q}_{\mu\nu}$, and $X$, with stability requiring $\frac{D p}{C-2DX} \ll 1$ in non-relativistic regimes. An explicit cosmological model with exponential couplings shows that a purely disformal interaction to dark matter can trigger late-time acceleration when $D\dot{\phi}^2$ grows to order unity, producing a de Sitter phase with a DM equation of state approaching $-1$ and a background evolution that can fit observations comparably to $\Lambda$CDM, though perturbations may enhance structure growth. Linear perturbation analysis reveals an effective gravitational strength $G_{\rm eff}$ on subhorizon scales, with $\frac{G_{\rm eff}}{G} - 1 = \frac{Q_0^2}{4\pi G \rho^2}$, which can lead to tension with large-scale structure unless $D(\phi)$ is tuned or the field propagates in the disformal metric. The paper also introduces a disformal screening mechanism whereby couplings to visible matter are suppressed in dense environments, rendering local gravity tests compatible while preserving cosmological dynamics, and discusses observational signatures and possible refinements to mitigate perturbative growth.
Abstract
It is shown that extensions to General Relativity, which introduce a strongly coupled scalar field, can be viable if the interaction has a non-conformal form. Such disformal coupling depends upon the gradients of the scalar field. Thus, if the field is locally static and smooth, the coupling becomes invisible in the solar system: this is the disformal screening mechanism. A cosmological model is considered where the disformal coupling triggers the onset of accelerated expansion after a scaling matter era, giving a good fit to a wide range of observational data. Moreover, the interaction leaves signatures in the formation of large-scale structure that can be used to probe such couplings.