2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140632A non-singular cosmology is derived in modified gravity (MOG) with a varying gravitational coupling strength $G(t)=G_Nξ(t)$. Assuming that the curvature $k$, the cosmological constant $Λ$ and $ρ$ vanish at $t=0$, we obtain a non-singular universe with a negative pressure, $p_G < 0$. Quantum fluctuations at $t\sim 0$ produce creation of pairs of particles from the vacuum explaining the origin of matter. The universe expands for $t\to \infty$ according to the standard radiation and matter dominated solutions. The arrow of time reverses at $t=0$ always pointing in the direction of increasing entropy ${\cal S}$ and the entropy is at a minimum value at $t=0$, solving the conundrum of the Second Law of Thermodynamics. The Hubble radius $H^{-1}(t)$ is infinite at $t=0$ removing the curvature and particle horizons. The negative pressure $p_G$ generated by the scalar field $ξ$ at $t\sim 0$ can produce quantum spontaneous creation of particles explaining the origin of matter and radiation.10 pages, no figures, Latex file. Revised version of paperGeneral Relativity and Quantum Cosmologytext