Abstract
In the matter bounce scenario, a dust-dominatedcontracting space-time generates scale-invariantperturbations that, assuming a nonsingularbouncing cosmology, propagate to the expandingbranch and set appropriate initial conditionsfor the radiation-dominated era. Since thisscenario depends on the presence of a bounce,it seems appropriate to consider it in thecontext of loop quantum cosmology where a bouncinguniverse naturally arises. For a pressurelesscollapsing universe in loop quantum cosmology, thepredicted power spectrum of the scalar perturbationsafter the bounce is scale-invariant and the tensorto scalar ratio is negligibly small. A slight redtilt can be given to the scale-invariance ofthe scalar perturbations by a scalar field whoseequation of state is P = −ϵρ, whereϵ is a small positive number. Then, thepower spectrum for tensor perturbations is alsoalmost scale-invariant with the same red tilt asthe scalar perturbations, and the tensor to scalarratio is expected to be r ≈ 9 × 10−4.Finally, for the predicted amplitude of the scalarperturbations to agree with observations, the criticaldensity in loop quantum cosmology must be of the orderρc ∼ 10−9ρPl.
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