Quantum Fluctuations at the Planck Scale

Abstract

The recently measured cutoff, k_min=[4.34(+/-)0.50]/r_cmb (with r_cmb 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 k_min 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, rho_phi+3p_phi=0. Quite revealingly, the observed amplitude of the temperature anisotropies requires the quantum fluctuations in phi to have classicalized at ~3.5x10^15 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.