  Line intensity mapping (LIM) provides a unique and powerful means to probe
cosmic structures by measuring the aggregate line emission from all galaxies
across redshift. The method is complementary to conventional galaxy redshift
surveys that are object-based and demand exquisite point-source sensitivity.
The Tomographic Ionized-carbon Mapping Experiment (TIME) will measure the star
formation rate (SFR) during cosmic reionization by observing the redshifted
[CII] 158$\mu$m line ($6 \lesssim z \lesssim 9$) in the LIM regime. TIME will
simultaneously study the abundance of molecular gas during the era of peak star
formation by observing the rotational CO lines emitted by galaxies at $0.5
\lesssim z \lesssim 2$. We present the modeling framework that predicts the
constraining power of TIME on a number of observables, including the line
luminosity function, and the auto- and cross-correlation power spectra,
including synergies with external galaxy tracers. Based on an optimized survey
strategy and fiducial model parameters informed by existing observations, we
forecast constraints on physical quantities relevant to reionization and galaxy
evolution, such as the escape fraction of ionizing photons during reionization,
the faint-end slope of the galaxy luminosity function at high redshift, and the
cosmic molecular gas density at cosmic noon. We discuss how these constraints
can advance our understanding of cosmological galaxy evolution at the two
distinct cosmic epochs for TIME, starting in 2021, and how they could be
improved in future phases of the experiment.
