Two Fluid Quantum Bouncing Cosmology I: Theoretical Model
Bouncing cosmologies offer an alternative to inflation by resolving the initial singularity through a contracting phase followed by a bounce into expansion. In many such models, the contracting phase is dominated by a single matter component, typically pressureless dust, which leads to an almost scale-invariant spectrum of scalar cosmological perturbations with a slight blue tilt, so that generating the observed red-tilted spectrum within this framework was challenging. In this work, we consider a more realistic scenario in which the contracting phase includes both matter and radiation, as required on physical grounds. We show that the presence of radiation can naturally induce a red tilt in the spectrum of curvature perturbations seeded by quantum vacuum fluctuations in the remote past of the contraction. Since the perturbations of the two fluids are coupled via gravity, vacuum initial conditions must be carefully defined. We demonstrate that, without fine-tuning, the resulting entropy perturbations are subdominant with respect to curvature perturbations. This suggests that a minimal two-component bounce model, involving only ordinary matter and radiation, can connect to the standard expanding cosmology with observationally viable initial conditions.