Expressions for linearized perturbations in a massive-scalar-field-dominated cosmological model

A spatially flat cosmological model dominated by a massive scalar (or pseudoscalar) field ($\Phi$) with the scalar field potential $V\left(\Phi \right)=m^2{(\Phi -{\Phi }^{\mathrm{}\left(2\right)\mathrm{}})}^2$ (where ${\Phi }^{\mathrm{}\left(2\right)\mathrm{}}$ is the value of the scalar field at which the potential vanishes), in the limit in which the length scale corresponding to the scalar field mass $m$ is very much smaller than length scales of cosmological interest (and, in particular, the length scale set by the Hubble parameter), is a tractable approximation of the macrophysics of both the late-time axion-dominated scenario as well as the early-time "reheating" subscenario of the inflation picture. Extending techniques we have previously developed, we derive solutions of the synchronous-gauge relativistic linear perturbation equations which govern the evolution of spatial irregularities, about a spatially homogeneous and isotropic background, in this model.