  (Abridged) Star and planet formation theories predict an evolution in the
density, temperature, and velocity structure as the envelope collapses and
forms an accretion disk. The aim of this work is to model the evolution of the
molecular excitation, line profiles, and related observables during low-mass
star formation. Specifically, the signatures of disks during the deeply
embedded stage are investigated. Semi-analytic 2D axisymmetric models have been
used to describe the evolution of the density, stellar mass, and luminosity
from the pre-stellar to the T-Tauri phase. A full radiative transfer
calculation is carried out to accurately determine the time-dependent dust
temperatures and CO abundance structure. We present non-LTE near-IR, FIR, and
submm lines of CO have been simulated at a number of time steps. In contrast to
the dust temperature, the CO excitation temperature derived from submm/FIR
lines does not vary during the protostellar evolution, consistent with C18O
observations obtained with Herschel and from ground-based telescopes. The
near-IR spectra provide complementary information to the submm lines by probing
not only the cold outer envelope but also the warm inner region. The near-IR
high-J (>8) absorption lines are particularly sensitive to the physical
structure of the inner few AU, which does show evolution. High signal-to-noise
ratio subarcsec resolution data with ALMA are needed to detect the presence of
small rotationally supported disks during the Stage 0 phase and various
diagnostics are discussed.
