Quantum fluctuations at the Planck scale

Abstract

The recently measured cutoff, kmin=4.34±0.50/rcmb (with rcmb the comoving distance to the last scattering surface), in the fluctuation spectrum of the cosmic microwave background, appears to disfavor slow-roll inflation and the associated transition of modes across the horizon. We show in this Letter that kmin instead corresponds to the first mode emerging out of the Planck domain into the semi-classical universe. The required scalar-field potential is exponential, though not inflationary, and satisfies the zero active mass condition, ρϕ+3pϕ=0. Quite revealingly, the observed amplitude of the temperature anisotropies requires the quantum fluctuations in ϕ to have classicalized at ∼3.5×1015 GeV, consistent with the energy scale in grand unified theories. Such scalar-field potentials are often associated with Kaluza–Klein cosmologies, string theory and even supergravity.