Induced-gravity inflation and the density perturbation spectrum

Recent experimental determinations of the spectral index describing the scalar mode spectrum of density perturbations encourage comparison with predictions from models of the very early universe. Unhke extended inflation, Induced-gravity Inflation predicts a power spectrum with 0.98 _< ns _< 1.00, in close agreement with the experimental measurements. An exciting test for models of the very early universe stems from recent measurements of the power spectrum of density perturbations, as seen in the cosmic microwave background radiation. The scalar spectrum, modeled as 79(k) oc k ns [1], functions as a test for models like infation, independently of the familiar test based on the magnitude of the fluctuations. As pointed out by Andrew Liddle and David Lyth [2], extended inflation predicts a spectral index (ns) which is tilted too far away from the Harrison-Zel'dovich (scale-invariant) spectrum (ns = 1.00), and hence cannot match the recent Cosmic Background Explorer (COBE) determination. In this Letter, the predictions from a cousin-model of extended inflation, Induced-gravity Inflation, are compared with the experimental values. Unlike extended inflation, Induced-gravity Inflation predicts a spectral index in quite close agreement with recent experimental values. Like extended inflation [ 3 ], Induced-gravity Inflation (IgI) [4-6] incorporates a Generalized Einstein Theory (GET) gravity sector. Yet unlike extended inl E-mail dkmser@husc harvard edu flation, IgI incorporates only one scalar boson to get all the work of inflation done: the scalar field which couples to the Ricci scalar in Brans-Dicke-like fashion is the same field whose potential, V(~b), drives inflation. This is the crucial difference as far as ns is concerned: by adopting a potential which leads to a second order phase transition (unlike the first order phase transition incorporated in extended inflation), IgI can escape two related problems of extended inflation (discussed below) and lead to an acceptable spectrum of perturbations. Much of the formalism developed in the literature for calculating ns assumes an Einsteinian gravitational background [7]; hence it cannot be applied in a straightforward manner to IgI, because of its GET gravity sector. Furthermore, as discussed in [8], the usual strategy of applying a conformal transformation to bring IgI into the canonical Einstein-Hilbert gravitational form [9] may prove problematic when studying the spectrum of perturbations, stemming from ambiguities with semiclassical quantization in the various frames. Therefore, in this Letter, we will restrict attention to the "physical" or "Jordan" frame, in which the nonminimal ~b2R coupling is explicit. 0370-2693/94/$07.00 @ 1994 Elsevxer Scmnce B V All rights reserved SSDI 0370-2693 (94) 01252-0 24 D.I. Katser / Physws Letters B 340 (1994) 23-28 The action for IgI is given by: S = d4xv/-L-g -~wR ~dp.ud ~' V(d~) + LM ,