  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.
