Seminar of Theory of Relativity and Gravitation

We present a new perspective on QFT on quantum cosmological space-times. Naively, the semiclassical limit of a quantum space-time can be taken by averaging the gravitational operators on a semiclassical state of geometry. The result is an effective classical metric (which in general does not obey Einstein equation). We show that, once quantum matter is taken into account, a new possibility arises: the dynamics of matter on quantum space-time can be equivalently described by standard QFT on a classical space-time, whose geometry is encoded in a so-called "dressed metric", a classical metric which is different than the naive semiclassical one. Such matter-dependent dressed metric can be thought of as the metric "seen" by the matter field.We explore this interpretation and its consequences in various instances, such as scalar field on quantum cosmological space-times, addressing the question of observable effects on the propagation of matter. Indeed, since the dressed metric depends on the matter, Lorentz-violating phenomena are expected (such as deformation of dispersion relations). We prove that for massless field on FRW quantum spacetime [1] no violation takes place; we then address the massive case [2], and show that an isotropy-breaking is present, since the dressed metric depends on the direction of propagation of the mode of the field.References:[1] A. Ashtekar, W. Kaminski, J. Lewandowski - "Quantum field theory on a cosmological, quantum space-time", Phys. Rev. D 79, 064030 (2009)[2] A. Dapor, J. Lewandowski - "Isotropy-Breaking in Quantum Cosmology", arXiv:1211.0161