Friedmann-like cosmological models without singularity

The singular big bang is replaced by a nonsingular big bounce, before which the universe was contracting.

“Accordingly, the singular big bang is replaced by a nonsingular big bounce, before which the universe was contracting (Kuchowicz 1978;Garcia de Andrade 2001;Popławski 2010cPopławski , 2011a)).”

In the comoving frame, the Einstein field Equation (6) for the FLRW metric becomes the Friedmann equations (10) and (11).

“In the comoving frame of reference, in which the four-velocity u i of the cosmological spin fluid satisfies u 0 =1 and u α =0 (α denotes spatial indices), the Einstein field Equation (6) for this metric becomes the Friedmann equations (the cosmological constant is negligible in the early universe; Kuchowicz 1978;Gasperini 1986;Brechet et al. 2008;Popławski 2010cPopławski , 2011a)):”

If the spin orientation of particles in a spin fluid is random, then the last term on the right-hand side of Equation (6) vanishes after averaging, and the Einstein-Cartan equations for such a spin fluid are equivalent to the Einstein equations for a perfect fluid with effective energy density and pressure.

“If the spin orientation of particles in a spin fluid is random, then the last term on the right-hand side of Equation (6) vanishes after averaging.Thus, the Einstein-Cartan equations for such a spin fluid are equivalent to the Einstein equations for a perfect fluid with the effective energy density  k s 4 2 and the effective pressure k p s 4 2 (Hehl et al. 1974;Kuchowicz 1978;Gasperini 1986;Bre”

The universe is therefore oscillatory: its scale factor oscillates between the minimum and maximum scale factors.

“The universe is therefore oscillatory: its scale factor oscillates between the minimum and maximum scale factors (Kuchowicz 1978).”