  We investigate the impact of spatial topology in 3+1 dimensional causal
dynamical triangulations (CDT) by performing numerical simulations with
toroidal spatial topology instead of the previously used spherical topology. In
the case of spherical spatial topology we observed in the so-called phase C an
average spatial volume distribution n(t) which after a suitable time
redefinition could be identified as the spatial volume distribution of the
four-sphere. Imposing toroidal spatial topology we find that the average
spatial volume distribution n(t) is constant. By measuring the covariance
matrix of spatial volume fluctuations we determine the form of the effective
action. The difference compared to the spherical case is that the effective
potential has changed such that it allows a constant average n(t). This is what
we observe and this is what one would expect from a minisuperspace GR action
where only the scale factor is kept as dynamical variable. Although no
background geometry is put in by hand, the full quantum theory of CDT is also
with toroidal spatial toplogy able to identify a classical background geometry
around which there are well defined quantum fluctuations.
