Can semi-classical gravity describe the beginning of the universe?

Could the universe have arisen as a quantum fluctuation? In other words, could spacetime have “tunneled” into existence out of nothing? That is the premise of the best known theories of initial conditions, namely the no-boundary and tunneling proposals. To understand these theories, we must understand the path integral approach to gravity, which in the past has been hampered by a number of technical issues. I will describe recent progress in defining and calculating gravitational path integrals, and will discuss the consequences for a semi-classical description of the beginning of the universe.