  We study the geometries generated by two-dimensional causal dynamical
triangulations (CDT) coupled to $d$ massless scalar fields. Using methods
similar to those used to study four-dimensional CDT we show that there exists a
$c=1$ "barrier", analogous to the $c=1$ barrier encountered in non-critical
string theory, only the CDT transition is easier to be detected numerically.
For $d\leq 1$ we observe time-translation invariance and geometries entirely
governed by quantum fluctuations around the uniform toroidal topology put in by
hand. For $d>1$ the effective average geometry is no longer toroidal but
"semiclassical" and spherical with Hausdorff dimension $d_H = 3$. In the $d>1$
sector we study the time dependence of the semiclassical spatial volume
distribution and show that the observed behavior is described an effective
mini-superspace action analogous to the actions found in the de Sitter phase of
three- and four-dimensional pure CDT simulations and in the three-dimensional
CDT-like Ho\v{r}ava-Lifshitz models.

General Relativity and Quantum Cosmology;High Energy Physics - Lattice;High Energy Physics - Theory