  The four dimensional Causal Dynamical Triangulations (CDT) approach to
quantum gravity is already more than ten years old theory with numerous
unprecedented predictions such as non-trivial phase structure of gravitational
field and dimensional running. Here, we discuss possible empirical consequences
of CDT derived based on the two features of the approach mentioned above. A
possibility of using both astrophysical and cosmological observations to test
CDT is discussed. We show that scenarios which can be ruled out at the
empirical level exist.
