Newtonian cosmology with a quantum bounce

Abstract

It has been known for some time that the cosmological Friedmann equation deduced from general relativity can also be obtained within the Newtonian framework under certain assumptions. We use this result together with quantum corrections to the Newtonian potentials to derive a set a of quantum corrected Friedmann equations. We examine the behavior of the solutions of these modified cosmological equations paying special attention to the sign of the quantum corrections. We find different quantum effects crucially depending on this sign. One such a solution displays a qualitative resemblance to other quantum models like Loop quantum gravity or non-commutative geometry.

Viscous Cosmologies

“…Even with constant velocities in the co-moving frame, there will be a non-zero effect of the bulk viscosity given by (18). We agree here with Murphy [21] who mentioned this result without an explicit derivation.…”

“…The other problem in the early universe is the choice of the inflationary scenario at the beginning of the universe. Many solutions for both problems have been suggested including scalar fields [11] and higher order gravity [12][13][14] for the inflationary mechanism and versions of quantum gravity [15][16][17] or quantum corrected cosmology [18] for the first problem.…”

Coulomb law in the nonuniform Euler–Heisenberg theory

“…Here corrections proportional to h have been calculated and confirmed [9,10]. They have applications in quantum corrections to the Schwarzschild metric and cosmology [11,12].…”

Einstein-Cartan Cosmologies

“…This suggests that the Hubble parameter can have a local minimum, a sign of a bouncing universe. Such forms appear in theories such as Loop Quantum Cosmology models [63], Generalized Uncertainty Principle approaches [64] or quantum corrections in Newtonian Cosmology [65].…”