There are various proposals as to what initial state can give rise to an inflationary cosmology. The
two most popular ones are the no boundary (Hartle-Hawking) and the tunneling (Vilenkin)
proposals. Both of them explain only part of the observations and lead to some paradoxes. I will
review these proposals and I will propose a novel initial state (wavefunction) of the universe which
in the far past has asymptotically AdS boundary conditions. In the semiclassical limit it is a
Euclidean wormhole solution that can give rise to an expanding universe upon analytic continuation
to Lorentzian signature. This proposal evades some of the issues that plagued the no boundary
and the tunneling proposals. Moreover, the asymptotic AdS conditions in the Euclidean past could
in principle allow for the description of inflationary cosmologies and their perturbations within the
context of holography, leading to microscopic models.