A covariant and gauge invariant formulation of the cosmological backreaction

Using our recent proposal for defining gauge invariant averages we give a general-covariant formulation of the so-called cosmological backreaction. Our effective covariant equations allow us to describe in explicitly gauge invariant form the way classical or quantum inhomogeneities affect the average evolution of our Universe.

Towards an S-matrix Description of Gravitational Collapse

Extending our previous results on trans-Planckian ($Gs gg hbar$) scattering of light particles in quantum string-gravity we present a calculation of the corresponding S-matrix from the region of large impact parameters ($b gg Gsqrt{s}>lambda_s$) down to the regime where classical gravitational collapse is expected to occur. By solving the semiclassical equations of a previously introduced effective-action approximation, we find that the perturbative expansion around the leading eikonal result diverges at a critical value $b = b_c = O(Gsqrt{s})$, signalling the onset of a new (black-hole related?) regime. We then discuss the main features of our explicitly unitary S-matrix -- and of the associated effective metric -- down to (and in the vicinity of) $b = b_c$, and present some ideas and results on its extension all the way to the $ b to 0$ region. We find that for $b<b_c$ the physical field solutions are complex-valued and the S-matrix shows additional absorption, related to a new production mechanism. The field solutions themselves are, surprisingly, everywhere regular, suggesting a quantum-tunneling -- rather than a singular-geometry -- situation.