Separate universes in loop quantum cosmology: framework and applications

I present a streamlined review of how the separate universe approach to cosmological perturbation theory can be used to study the dynamics of long-wavelength scalar perturbations in loop quantum cosmology, and then use it to calculate how long-wavelength curvature perturbations evolve across the loop quantum cosmology bounce assuming a constant equation of state. A similar calculation is possible for tensor modes using results from a complementary approach to cosmological perturbation theory in loop quantum cosmology based on an effective Hamiltonian constraint. An interesting result is that the tensor-to-scalar ratio can be suppressed or amplified by quantum gravity effects during the bounce, depending on the equation of state of the matter field dominating the dynamics. In particular, if the equation of state lies between -1/3 and 1, the value of the tensor-to-scalar ratio will be suppressed during the bounce, in some cases significantly