The laws of nature that emerge from string theory are in essence discrete: they contain no continuous parameters.  The possible laws correspond to the possible topologies of spacetime.  I will first explain what quantum gravity is, and why it is essential for interpreting measurements of the polarization of the cosmic microwave background (CMB). I will then develop the connection between discrete laws and topology, and show how we have exploited this connection to systematically enumerate inflationary cosmologies in string theory.  The brightness of the primordial gravitational wave signal in the CMB is controlled by integers that count the number of holes in the spacetime.