The Density Perturbation in the Chaotic Inflation with Non-Minimal Coupling

Abstract

Centeny thtkawa institute for lr;lzeoretical ]Physics Kyoto Univezsiby, L[ii 611 (Received February 2e, ]991) We formulate a method to rigorously evaluate the density perturbation amplitude in infiation moclels with non-canonical gravity, As a specific example but which contains essential features of non:canonical models, the density perturbation in theAi chaotic inflation model with non-minimal coupling caipZ is carefully investigated in terms of the Hamiltonian formalism for constrained systems. We utilize a particular cunforrnai transformation under which the original system with a nen-minimally coupled scalar field is transfornied into one with a minimal coupling and derive a recluced Hamiltonian for scalar-type perturbations (which describe density perturbations) in which only the dynamical degrees of freedom are contained. We then evaluate the amplitude of density perturbations arising from vacuum fluctuations of the system. We find the amplitude in the confor-mally transformecl metric exactly agrees with that in the original metric. Thus the result obtained in the previous papers by a rather crude approach is confirmed in a more rigorous manner; i.e., the constraint on A is weakened if e is large, gl. Introduction After a decade of extensive studies on inflationary universe models, it has now become widely known that in order to reconcile the smallness of the density perturba-tion in an inflation model it is necesSary to assume an unnaturally srpall coupling constant (or mass parameter) for an infiaton field. For example, in the case of chaotic inflation withAi potential,i) the observed isotropy of the cosmic microwave background constrains