Cosmological attractors to general relativity and spontaneous scalarization with disformal coupling

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 φ and matter, where the Jordan frame metric gμν is related to the Einstein frame one gμν by gμν=A(φ)2(gμν+Λ∂μφ∂νφ). 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 ΛH0-2, where H0 is the Hubble parameter of today, which is much larger than the scale relevant for spontaneous scalarization of neutron stars Λ∼Rs2 with Rs(∼10-22H0-1) being the typical radius of these stars. The large values of Λ 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.