  Line intensity mapping (LIM) is emerging as a powerful technique to map the
cosmic large-scale structure and to probe cosmology over a wide range of
redshifts and spatial scales. We perform Fisher forecasts to determine the
optimal design of wide-field ground-based mm-wavelength LIM surveys for
constraining properties of neutrinos and light relics. We consider measuring
the auto-power spectra of several CO rotational lines (from J=2-1 to J=6-5) and
the [CII] fine-structure line in the redshift range of $0.25<z<12$. We study
the constraints with and without interloper lines as a source of noise in our
analysis, and for several one- and multi-parameter extensions of $\Lambda$CDM.
We show that LIM surveys deployable this decade, in combination with existing
CMB (primary) data, could achieve order of magnitude improvements over Planck
constraints on $N_{\rm eff}$ and $M_\nu$. Compared to next-generation CMB and
galaxy surveys, a LIM experiment of this scale could achieve bounds that are a
factor of $\sim3$ better than those forecasted for surveys such as EUCLID
(galaxy clustering), and potentially exceed the constraining power of CMB-S4 by
a factor of $\sim1.5$ and $\sim3$ for $N_{\rm eff}$ and $M_\nu$, respectively.
We show that the forecasted constraints are not substantially affected when
enlarging the parameter space, and additionally demonstrate that such a survey
could also be used to measure $\Lambda$CDM parameters and the dark energy
equation of state exquisitely well.
