Possible origin of CMB temperature fluctuations: Vacuum fluctuations of Kaluza-Klein and string states during inflationary era

Abstract

We point out that the temperature fluctuations of cosmic microwave background (CMB) can be generated in a way that is different from the one usually assumed in slow-roll inflation. Our mechanism is based on vacuum fluctuations of fields which are at rest at the bottom of the potential, such as Kaluza-Klein modes or string excited states. When there are a large number (typically of order \(N\sim 10^{14}\)) of fields with small mass in unit of Hubble parameter during the inflationary era, this effect can give significant contributions to the CMB temperature fluctuations. This number \(N\) makes it possible to enhance scalar perturbation relative to tensor perturbation. Comparison with the observed amplitudes suggests that models with string scale of order \(10^{-5}\) of 4D Planck scale are favorable.