  Bursty star formation -- a key prediction for high-redshift galaxies from
cosmological simulations explicitly resolving stellar feedback in the
interstellar medium -- has recently been observed to prevail among galaxies at
redshift $z \gtrsim 6$. Line intensity mapping (LIM) of the 158 $\mu$m [C II]
line as a star formation rate indicator offers unique opportunities to
tomographically constrain cosmic star formation at high redshift, as an
alternative to observations of individually detected galaxies. To understand
effects of bursty star formation on [C II] LIM, which remain unexplored in
previous studies, we present an analytic modeling framework for high-$z$ galaxy
formation and [C II] LIM signals that accounts for bursty star formation
histories induced by delayed supernova feedback. We use it to explore and
characterize how bursty star formation can impact and thus complicate the
interpretation of the [C II] luminosity function and power spectrum. Our simple
analytic model indicates that bursty star formation is most important for low
halo masses, and in the power spectrum it can create a substantial excess in
the large-scale clustering term. This distortion results in a power spectrum
shape which cannot be explained by invoking a mass-independent scatter. We
conclude that burstiness must be accounted for when modeling and analyzing [C
II] datasets from the early universe, and that in the extreme, the signature of
burstiness may be detectable with first-generation experiments such as TIME,
CONCERTO, and CCAT-DSS.
