Final answer:
The universe initially expanded rapidly, then decelerated due to gravitational attractions between galaxies, and later started to accelerate again as dark energy became the dominant force.
Step-by-step explanation:
The relationship between the expansion rate and the age of the universe is that after an initial phase of rapid expansion known as inflation, the expansion rate began to decelerate because galaxies were closer together and their mutual gravitational attraction was strong.
However, as time went on and galaxies moved farther apart, gravity's influence weakened and dark energy began to dominate, causing the rate of expansion to accelerate once again. This shifting dynamic is evident through various observational evidences, including measurements of nearby galaxies, abundances of light elements like deuterium, helium, and lithium, the distribution and motion of dark matter, supernovae observations, galaxy formation in the early universe, and the Cosmic Microwave Background (CMB).