We investigate constraints on scalar dark matter (DM) by analyzing the Lyman-α forest, which probes structure formation at medium and small scales, and also by studying its cosmological consequences at high and low redshift. For scalar DM that constitutes more than 30% of the total DM density, we obtain a lower limit m10-21 eV for the mass of scalar DM. This implies an upper limit on the initial field displacement (or the decay constant for an axion-like field) of Ï 1016 GeV. We also derive limits on the energy scale of cosmic inflation and establish an upper bound on the tensor-to-scalar ratio of r<10-3 in the presence of scalar DM. Furthermore, we show that there is very little room for ultralight scalar DM to solve the "small-scale crisis" of cold DM without spoiling the Lyman-α forest results. The constraints presented in this paper can be used for testing generic theories that contain light scalar fields.
