New estimates of the deceleration parameter in weak gravity

We consider weak gravity at accelerations $α<a_H$ 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 $q=1-(4πa_0/cH)^{2}$ and $q=-1/2 -3 (Ω_b/\sqrt{2}\sqrtπ)^{1/2}$, where $a_0$ is Milgrom's scale in the baryonic Tully-Fisher relation of spiral galaxies and $Ω_b$ is the baryonic matter density. The Planck value $Ω_b=0.048$ 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 $Λ$CDM ($Q_0<1$).

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