(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.
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