The slowing of expansion in the matter dominated era

On all the graphs of the inflation of the universe, the era dominated by matter is slowing the rate of expansion. With an intuitive explanation (for all you science communicators out there) could you tell me if the deceleration was = to the gravitational rate of deceleration? What did the deceleration start at? Where did it bottom out? And last but not least Is the rate of acceleration occurring at the inverse of the deceleration of gravity? I would welcome as many nuanced explanations as possible from as many sources as possible. A single answer, no matter how well written, can include all viewpoints.

• When you refer to deceleration of gravity in this context, please tell me you don't mean $9.8 m/s^2$. Jan 9 at 19:35
• Wow, no. I mean does the slowing expansion in the matter era prior to the acceleration of the dark energy era relate to the gravitational potential between all the mass in that era. Was all the mass of the matter era gravitationally bound before the beginning of acceleration? Jan 9 at 22:08
• Could you add a reference? (I'm thinking it might be Davis & Lineweaver, but I don't recollect them using quite the same verbal terminology--which I, a layperson, rely on. Their articles often include the phrase "Expanding Confusion", and often differentiate expansion of the Hubble Sphere from the overall expansion.) Jan 9 at 23:37

Cosmic expansion decelerates due to the mutual gravitational attraction of all of the universe's matter. This is quite a simple concept. If you place a bunch of matter at rest, it will collapse under its gravity. If you instead give it an initial expansion kick, the expansion will gradually slow over time.

By the way, while my description uses only the everyday Newtonian intuition for gravity, that is completely valid. Newtonian gravity predicts exactly the correct cosmic expansion dynamics in a matter dominated universe..

Jason Verreault sked: "could you tell me if the deceleration was = to the gravitational rate of deceleration?"

Yes, it was and still is, the present acceleration is also gravitational and force free.

Jason Verreault sked: "What did the deceleration start at?"

If there was inflation right after that, and if there was a big bang singularity right from the start, ending at the time below when the accelerated era began:

Jason Verreault sked: "Where did it bottom out?"

When ä=0 at a≈0.61 and t≈7.7 Gyr after the big bang, see here.

• So mass became gravitationally unbound after dark energy 'dominated' the universe? Jan 10 at 5:18
• Did you mean 0.61? Jan 10 at 6:52
• In there was inflation right after that Did you mean “If…”? And inflation right after what? Jan 10 at 6:54
• @Jason Verreault asked: "So mass became gravitationally unbound after dark energy 'dominated' the universe?" - The masses still attract each other, that's why the Hubble parameter was and is always shrinking, though asymptotically converging to a finite value in the infinite future. Jan 10 at 20:14
• @Ghoster wrote: "Did you mean a=0.61?" - Yes, "a=6.1" was a typo, and the "in" should also be an "if", so if there was inflation then right after inflation, the exact transiston depending on the model how fast the inflation field decays, but since we can't test such models and don't know for sure if there even was an inflation era I don't have the details. Jan 10 at 20:17