Cosmology in theories with spontaneous scalarization of neutron stars

In a model of spontaneous scalarization neutron stars proposed by Damour and Esposito-Farese, general relativistic branch becomes unstable to trigger tachyonic growth scalar field $\ensuremath{\phi}$ toward scalarized branch. Applying this scenario cosmology, there is fatal instability during inflation matter dominance being incompatible with solar-system constraints on today's value ${\ensuremath{\phi}}_{0}$. the presence four-point coupling ${g}^{2}{\ensuremath{\phi}}^{2}{\ensuremath{\chi}}^{2}/2$ between an inflaton $\ensuremath{\chi}$, it was argued Anson et al. that positive mass squared heavier than square Hubble expansion rate leads exponential suppression ${\ensuremath{\phi}}_{0}$ can remain small even after radiation-dominated epoch. For several potentials approximated as $V(\ensuremath{\chi})={m}^{2}{\ensuremath{\chi}}^{2}/2$ about potential minimum, we study dynamics reheating well other cosmological epochs in detail. certain ranges $g$, homogeneous be amplified parametric resonance coherent oscillation inflaton. Incorporating backreaction created particles under Hartree approximation, maximum values reached preheating are significantly smaller those obtained without backreaction. We also find minimum $g$ consistent solar system bounds at end order ${10}^{\ensuremath{-}5}$ hence wide range acceptable $g$. Thus, naturally viable evolution local gravity constraints, modifying property stars.