  The indeterminism of quantum mechanics generally permits the independent
specification of both an initial and a final condition on the state. Quantum
pre-and-post-selection of states opens up a new, experimentally testable,
sector of quantum mechanics, when combined with statistical averages of
identical weak measurements. In this paper I apply the theory of weak quantum
measurements combined with pre-and-post-selection to cosmology. Here,
pre-selection means specifying the wave function of the universe or, in a
popular semi-classical approximation, the initial quantum state of a subset of
quantum fields propagating in a classical back-ground spacetime. The novel
feature is post-selection: the additional specification of a condition on the
quantum state in the far future. I discuss "natural" final conditions, and show
how they may lead to potentially large and observable effects at the present
cosmological epoch. I also discuss how pre-and-post-selected quantum contrast
to the expectation value of the stress-energy-momentum tensor, resolving a
vigorous debate from the 1970's. The paper thus provides a framework for
computing large-scale cosmological effects arising from this new sector of
quantum mechanics. A simple experimental test is proposed.
