We investigate a particular type of classical nonsingular bouncing cosmology, which results from general relativity if we allow for degenerate metrics. The simplest model has a matter content with a constant equation-of-state parameter and we get the modified Hubble diagrams for both the luminosity distance and the angular diameter distance. Based on these results, we present a Gedankenexperiment to determine the length scale of the spacetime defect which has replaced the big bang singularity. A possibly more realistic model has an equation-of-state parameter which is different before and after the bounce. This last model also provides an upper bound on the defect length scale. PACS numbers: 04.20.Cv, 98.80.Bp, 98.80.Jk Keywords: general relativity, big bang theory, mathematical and relativistic aspects of cosmology *

Many studies have been carried out since T.Padmanabhan proposed that the cosmic acceleration can be understood from the perspective that spacetime dynamics is an emergent phenomenon. Motivated by such a new paradigm, we firstly study the de Sitter universe from emergence of space. After that we investigate the universes in general cases and then narrow down our discussions into one of them with a detailed discussion of the possibility in describing our real universe classically. Furthermore, a constraint on Ht and a estimated value ofΩ Λ (caused by ρ vac ) can be derived from our model, the comparison with experiments is also presented. The results show the validity of our model.

We derive the equations of motion for scalar metric perturbations in a particular nonsingular bouncing cosmology, where the big bang singularity is replaced by a spacetime defect. The adiabatic perturbation solution is obtained for nonrelativistic hydrodynamic matter. We get the same result by working with conformal coordinates. This last method is also valid for vector and tensor metric perturbations, and selected results are presented. PACS numbers: 04.20.Cv, 98.80.Bp, 98.80.Jk Keywords: general relativity, big bang theory, mathematical and relativistic aspects of cosmology *

We obtain the geodesics for the simplest possible stealth defect which has a flat spacetime. We, then, discuss the lensing properties of such a defect, and the corresponding image formation. Similar lensing properties can be expected to hold for curved-spacetime stealth defects.

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