arXiv:gr-qc/0402071v1 16 Feb 2004 December 10, 2018 15:1 WSPC/Trim Size: 9.75in x 6.5in for Proceedings main PRE-INFLATIONARY PERTURBATIONS SPECTRUM GIOVANNI IMPONENTE Dipartimento di Fisica, Universit´ a “Federico II”, Napoli and INFN – Napoli – Italy ICRA – International Center for Relativistic Astrophysics E-mail: imponente@icra.it GIOVANNI MONTANI Dipartimento di Fisica – G9 Universit´ a “La Sapienza”, Roma – Italy ICRA – International Center for Relativistic Astrophysics E-mail: montani@icra.it In the framework of a flat FLRW model we derive an inflationary regime in which the scalar field, laying on the plateau of its potential, admits a linear time dependence and remains close to a constant value. The behaviour of inhomogeneous perturbations is determined on the background metric in agreement to the “slow-rolling” approximation. We show that the inhomogeneous scales which before inflation were not much greater then the physical horizon, conserve their spectrum (almost) unaltered after the de Sitter phase. 1. Introduction The Standard Cosmological Model (SCM) finds many confirmations in the picture of the actual Universe 1 , but its shortcomings to describe very early stages of evo- lution appear as soon as the so-called horizon and flatness paradoxes are taken into account 2,3,4 . The Inflationary Paradigm (IP) has acquired progressively an increasing interest, because it provides a natural explanation for such paradoxes 2,3,4 ; the IP success relies overall on the consistent and simultaneous treatment of many different as- pects of the cosmological puzzle. The capability to generate a Harrison–Zeldovich Spectrum (HZS) for the density perturbations outstands among these, and in fact the IP predicts it from the quantum fluctuations of the scalar field during the de Sitter phase. This picture is well-grounded, but has to face the delicate point regarding the mech- anism by which the quantum inhomogeneities approach a classical limit 5 . The quantum origin of the perturbations is also supported by the exponential suppres- sion of the ultra-relativistic inhomogeneities during the de Sitter phase 6 . In this work we show the existence of an inflationary regime allowing a classical origin for the HZS. In fact we deal with perturbations of the scalar field φ which, if described by a HZS before inflation, survive to the Universe exponential expansion; 1