The Lightest Field in Physics: Mass and Excursion Required of a Scalar That Rolls at the Observed Vacuum Density

If the observed vacuum density is the potential energy of a rolling scalar field rather than a true constant, the field is tightly constrained. This paper solves the quadratic potential V = m^2 phi^2/2 at the observed density of 2.52 x 10^-47 GeV^4 for masses around the Hubble scale. A mass of one hbar H0, 0.00 x 10^-33 eV, requires a field value of about two reduced Planck masses and gives a slow-roll parameter of about 0.49; masses ten times larger fail slow roll outright, while flatter potentials are bought only with larger field excursions. The computation maps the narrow window in which scalar-field dark energy can imitate a vacuum. It is a computation from stated assumptions, not a measurement.