Cosmological attractors to general relativity and spontaneous scalarization with disformal coupling

Abstract

The canonical scalar-tensor theory model which exhibits spontaneous scalarization in the strong-gravity regime of neutron stars has long been known to predict a cosmological evolution for the scalar field which generically results in severe violations of present-day Solar System constraints on deviations from general relativity. We study if this tension can be alleviated by generalizing this model to include a disformal coupling between the scalar field $\phi$ and matter, where the Jordan frame metric ${\tilde{g}}_{\mu \nu }$ is related to the Einstein frame one $g_{\mu \nu }$ by ${\tilde{g}}_{\mu \nu }=A(\phi {)}^2(g_{\mu \nu }+\Lambda {\partial }_{\mu }\phi {\partial }_{\nu }\phi )$. We find that this broader theory admits a late-time attractor mechanism towards general relativity. However, the existence of this attractor requires a value of disformal scale of the order $\Lambda \gtrsim H_0^{-2}$, where $H_0$ is the Hubble parameter of today, which is much larger than the scale relevant for spontaneous scalarization of neutron stars $\Lambda \sim R_s^2$ with $R_s(\sim 10^{-22}{H}_0^{-1})$ being the typical radius of these stars. The large values of $\Lambda$ necessary for the attractor mechanism (i) suppress spontaneous scalarization altogether inside neutron stars and (ii) induce ghost instabilities on scalar field fluctuations, thus preventing a resolution of the tension. We argue that the problem arises because our disformal coupling involves a dimensionful parameter.

(v1) 10 pages, 2 figures. (v2) typos corrected. (v3) 11 pages, new references, matches published version

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Cited by in corpus (4)

• Invertible disformal transformations with higher derivatives
• Multi-scalar Gauss-Bonnet gravity -- hairy black holes and scalarization
• Stars disformally coupled to a shift-symmetric scalar field
• Cosmology in theories with spontaneous scalarization of neutron stars