In the first part of the talk I will consider the one loop quantum backreaction from a non-minimally coupled massless scalar field in homogeneous (inflationary) cosmological backgrounds. I will discuss in particular under what conditions the backreaction can become big. Next, I will consider two non-local phenomenological models of backreaction, and how that there is a class of nonlocal cosmologies consistent with many observations starting with a Universe with a negative cosmological term. These models are particularly attractive for string theory, since stable low energy string theory vacua have negative energy.

Utrecht University