  We study the dynamics of cold molecular gas in two main-sequence galaxies at
cosmic noon (zC-488879 at $z\simeq1.47$ and zC-400569 at $z\simeq2.24$) using
new high-resolution ALMA observations of multiple $^{12}$CO transitions. For
zC-400569 we also re-analyze high-quality H$\alpha$ data from the SINS/zC-SINF
survey. We find that (1) Both galaxies have regularly rotating CO disks and
their rotation curves are flat out to $\sim$8 kpc contrary to previous results
pointing to outer declines in the rotation speed $V_{\rm rot}$; (2) The
intrinsic velocity dispersions are low ($\sigma_{\rm CO}\lesssim15$ km/s for CO
and $\sigma_{\rm H\alpha}\lesssim37$ km/s for H$\alpha$) and imply $V_{\rm
rot}/\sigma_{\rm CO}\gtrsim17-22$ yielding no significant pressure support; (3)
Mass models using HST images display a severe disk-halo degeneracy: models with
inner baryon dominance and models with "cuspy" dark matter halos can fit the
rotation curves equally well due to the uncertainties on stellar and gas
masses; (4) Milgromian dynamics (MOND) can successfully fit the rotation curves
with the same acceleration scale $a_0$ measured at $z\simeq0$. The question of
the amount and distribution of dark matter in high-$z$ galaxies remains
unsettled due to the limited spatial extent of the available kinematic data; we
discuss the suitability of various emission lines to trace extended rotation
curves at high $z$. Nevertheless, the properties of these two high-$z$ galaxies
(high $V_{\rm rot}/\sigma_{\rm V}$ ratios, inner rotation curve shapes,
bulge-to-total mass ratios) are remarkably similar to those of massive spirals
at $z\simeq0$, suggesting weak dynamical evolution over more than 10 Gyr of the
Universe's lifetime.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology