  A class of optical transients known as Luminous Red Novae (LRNe) have
recently been associated with mass ejections from binary stars undergoing
common-envelope evolution. We use the population synthesis code COMPAS to
explore the impact of a range of assumptions about the physics of
common-envelope evolution on the properties of LRNe. In particular, we
investigate the influence of various models for the energetics of LRNe on the
expected event rate and light curve characteristics, and compare with the
existing sample. We find that the Galactic rate of LRNe is $\sim 0.2$
yr$^{-1}$, in agreement with the observed rate. In our models, the luminosity
function of Galactic LRNe covers multiple decades in luminosity and is
dominated by signals from stellar mergers, consistent with observational
constraints from iPTF and the Galactic sample of LRNe. We discuss how
observations of the brightest LRNe may provide indirect evidence for the
existence of massive ($> 40$ M$_\odot$) red supergiants. Such LRNe could be
markers along the evolutionary pathway leading to the formation of double
compact objects. We make predictions for the population of LRNe observable in
future transient surveys with the Large Synoptic Survey Telescope and the
Zwicky Transient Facility. In all plausible circumstances, we predict a
selection-limited observable population dominated by bright, long-duration
events caused by common envelope ejections. We show that the Large Synoptic
Survey Telescope will observe $20$--$750$ LRNe per year, quickly constraining
the luminosity function of LRNe and probing the physics of common-envelope
events.
