On the rotation curves of galaxies at low and high redshifts
The thermal history of the Universe is included in the Debye Gravitational Theory (DGT) to describe the speed of rotation of the galaxies. The DGT incorporate the temperature of Debye in the entropic gravitational theory. According to the DGT, the expression of the rotation of the galaxies is not a continuous function of the redshift, there is a discontinuity at $\sim 0.77$. According to their redshift, the galaxies form two groups. (a) Those with redshift above 0.77 with declining rotation curves like $R^{\beta}$ with $\beta \leq -0.5$ (Newtonian regime). (b) Those with redshift below 0.77 with rising rotation curves like $R^{\beta}$ with $\beta \geq 0$ (Mondian regime). At $z\sim 0.77 $ an extra boost (Dirac delta-like twisting force) led the galaxies to spin very fast.This scenario is consistent with a mysterious entity such as the dark energy and that at $z\sim 0.77 $, in addition to accelerating the expansion, boosted the rotation of the galaxies again, inducing a transition between the Newtonian regime to the Mondian regime. It is possible to check that the characteristics on galaxy rotations provided by the DGT for a broad range of redshift from $z\sim 4$ to $z=0$ are in agreement with the observations. We believe that the change in the form of rotation of galaxies at $z\sim 0.77$ is new evidence for the hypothesis of dark energy.