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"radius_1" Depiction, Acceleration Scenario, multiple plots

RADIUS_1 DEPICTION

The next figure in the following post describes the case wherein the universe is expanding at an accelerating rate in the present era. Note that the Hubble parameter curve does not intersect t=1 at a reasonable point and that there are few points of multiple intersection.By the way, the equations for the derivative curves were found by using the **Mathematica** website that features a free utility that finds derivatives. Of course, the first derivative represents the speed of expansion and the second derivative stands for the acceleration or deceleration.Graphically, this scenario displays less symmetry and does not much illustrate Noether's theorem. Remember, these equations are semi-theoretical as well as based on phenomenology. So, being theoretical in part, they should be potentially able to respect Noether's theorem.

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