  A non-singular cosmology is derived in modified gravity (MOG) with a varying
gravitational coupling strength $G(t)=G_N\xi(t)$. Assuming that the curvature
$k$, the cosmological constant $\Lambda$ and $\rho$ 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 $\xi$ at $t\sim 0$ can produce
quantum spontaneous creation of particles explaining the origin of matter and
radiation.
