Quantum fluctuations at the Planck scale

Abstract

Abstract The recently measured cutoff, $$k_\mathrm{min}=4.34\pm 0.50/r_{\mathrm{cmb}}$$ kmin=4.34±0.50/rcmb (with $$r_{\mathrm{cmb}}$$ 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 $$k_{\mathrm{min}}$$ 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, $$\rho _\phi +3p_\phi =0$$ ρϕ+3pϕ=0 . Quite revealingly, the observed amplitude of the temperature anisotropies requires the quantum fluctuations in $$\phi $$ ϕ to have classicalized at $$\sim 3.5\times 10^{15}$$ ∼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.