New estimates of the deceleration parameter in weak gravity

Abstract

We consider weak gravity at accelerations $\alpha<a_H$ when Rindler and cosmological horizon collude at $R_H=c/H$, where $c$ is the velocity of light and $H$ is the Hubble parameter. This is manifest in reduced inertia $m$, below the value $m_0$ in Newtonian gravity. Striking evidence for a sharp transition to weak gravity is found in galaxy rotation curves. Their sensitivity to the cosmological background is expressed by correlations to the deceleration parameter $q=1-(4\pi a_0/cH)^{2}$ and $q=-1/2 -3 (\Omega_b/\sqrt{2}\sqrt{\pi})^{1/2}$, where $a_0$ is Milgrom's scale in the baryonic Tully-Fisher relation of spiral galaxies and $\Omega_b$ is the baryonic matter density. The Planck value $\Omega_b=0.048$ with $H\simeq 73$ km s$^{-1}$ Mpc$^{-1}$ shows $q\simeq-0.85$. Future surveys may determine $Q_0=\left.dq(z)/dz\right|_{z=0}$ to provide a direct test for dynamical dark energy ($Q_0>2.5$) versus $\Lambda$CDM ($Q_0<1$).