Structure Formation with a Self-Tuning Scalar Field

A scalar field with an exponential potential has the particular property that it is attracted into a solution in which its energy scales as the dominant component (radiation or matter) of the Universe, contributing a fixed fraction of the total energy density. We study the growth of perturbations in a cold dark matter dominated $\ensuremath{\Omega}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ universe with this extra field, with an initial flat spectrum of adiabatic fluctuations. The observational constraints from structure formation are satisfied as well, or better, than in other models, with a contribution to the energy density from the scalar field ${\ensuremath{\Omega}}_{\ensuremath{\varphi}}\ensuremath{\sim}0.1$ which is small enough to be consistent with entry into the attractor prior to nucleosynthesis.