Non ScaleInvariant Isocurvature Perturbations Produced in the PowerLaw Inflation
Abstract
We present a careful analysis of non scaleinvariant insocurvature perturbation produced in the powerlaw inflation. We first derive the exact form of the twopoint function for a massless scalar field φ in a powerlaw background, a (t) ∝ t^{1+n} (n≫1). For generality, we allow the scalar field to have a small nonminimal coupling to gravity, ~ ξφ^{2} R (ξ≪1). We then regard φ as an axionlike field whose quantum fluctuation gives rise to an isocurvature perturbation with its amplitude proportional to a trigonometric function of φ. As a concrete example, we consider the case when φ is a Majoron and the baryon density fluctuation is produced in proportion to sin (φ/f) where f is the symmetry breaking scale. We find the resulting spectrum of the (baryon) isocurvature perturbation depends very much on the sign of n*, where 1/n* = 1/n + ξ. For n* > 0, corresponding to an infrared unstable scalar field, the spectrum is white noise on large scales and almost scaleinvariant on small scales. On the other hand, for n* < 0, corresponding to an infrared stable scalar field, the spectrum is almost scaleinvariant on all the scales.
 Publication:

Modern Physics Letters A
 Pub Date:
 1991
 DOI:
 10.1142/S0217732391003432
 Bibcode:
 1991MPLA....6.2935S