Cosmology in theories with spontaneous scalarization of neutron stars

In a model of spontaneous scalarization of neutron stars proposed by Damour and Esposito-Farese, a general relativistic branch becomes unstable to trigger tachyonic growth of a scalar field φ toward a scalarized branch. Applying this scenario to cosmology, there is fatal tachyonic instability of φ during inflation and matter dominance being incompatible with solar-system constraints on today's field value φ0. In the presence of a four-point coupling g2φ2χ2/2 between φ and an inflaton field χ, it was argued by Anson et al. that a positive mass squared heavier than the square of a Hubble expansion rate leads to the exponential suppression of φ during inflation and that φ0 can remain small even with the growth of φ after the radiation-dominated epoch. For several inflaton potentials approximated as V(χ)=m2χ2/2 about the potential minimum, we study the dynamics of φ during reheating as well as other cosmological epochs in detail. For certain ranges of the coupling g, the homogeneous field φ can be amplified by parametric resonance during a coherent oscillation of the inflaton. Incorporating the backreaction of created particles under a Hartree approximation, the maximum values of φ reached during preheating are significantly smaller than those obtained without the backreaction. We also find that the minimum values of g consistent with solar system bounds on φ at the end of reheating are of order 10-5 and hence there is a wide range of acceptable values of g. Thus, the scenario proposed by Anson et al. naturally leads to the viable cosmological evolution of φ consistent with local gravity constraints, without modifying the property of scalarized neutron stars.