On the radial acceleration relation for galaxies in a wide range of redshifts

Abstract: The thermal history of the Universe is introduced within the Debye Gravitational Theory (DGT), a thermodynamic theory of induced gravity, and allows to obtain the evolution of systems with the redshift. DGT reproduce the ESO VLT observations, showing falling outer rotation curves for galaxies at redshift above 0.77. A scaling law is observed in the radial acceleration relation (RAR) of galaxies. For accelerations smaller than $\sim 10^{-10}ms^{-1}$ the observed acceleration $g_{obs}$ decreases more slowly than acceleration generated by the baryonic mass $g_{bar}$, following always the relation $g_{obs} \sim \sqrt{g_{bar}}$. The RAR does not care about the specific properties of the galaxy, the relation exists in nearby high-mass elliptical and low-mass spheroidal galaxies. In this paper, through a straightforward analysis, we show that according to DGT, the RAR scaling law observed in nearby galaxies is broken, when are considered distant galaxies. The extreme case happen for galaxies at redshift above 0.77, because according to DGT, the galaxies have declining rotation curves, and the rotation velocity falling faster than the Keplerian-law curve. Then in this case $g_{obs}$ decreases more faster than $g_{bar}$, this means that $g_{obs}$ is systematically lower than $g_{bar}$. We show that DGT prediction for the RAR of galaxies at high redshift is in agreement from those obtained from the falling rotation curves observed by VLT telescope.