Institute for Mathematics, Astrophysics and Particle Physics, Radboud University
We consider cosmological scalar perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field, and present a formulation designed to preserve covariance. The perturbations are described in terms of Mukhanov-Sasaki gauge invariants, linear perturbative constraints, and variables canonically conjugate to them. This set is completed into a canonical one for the entire system, including the homogeneous degrees of freedom. We find the global Hamiltonian constraint of the model, and explain how to quantize the system respecting covariance. In particular, we use a hybrid quantization approach in the framework of Loop Quantum Cosmology. Employing a Born-Oppenheimer ansatz that separates the perturbations from the homogeneous geometry, we derive a Schrödinger equation for the cosmological perturbations. Moreover, we obtain the effective equations that are naturally associated with the Mukhanov-Sasaki variables. They provide the master equation to compute quantum geometry corrections to the power spectrum of primordial scalar perturbations.
2015 November 10, 10:30
Faculdade de CiÍncias da Universidade de Lisboa (C6.2.51)
Campo Grande, 1749-016 Lisboa