"The acceleration provides the replacement for gravity"
and how does this acceleration keep things on the ground?
what accelerates the "flat earth"?
off the point: that quote is semantically orouborus, it eats its own tail, because in reativity acceleration and gravity are synonymus, the basis of it appears logically sound and it fits observation, therefore the relativity model appears a good model for predicting how things are.
space appears curved cus matter and energy are equivelent- they aren't seperate entitys - one is denser i.e condensed. and because matter, synonymous with condesed energy, appears attractive at all directions in space-time(4 dimensional; 3 space; 1 time) making it "curve". that is called gravity. the fact relativity fits observation more so than other models, i rate it more probable than the flat earth theory of acceleration.
my opinion of gravity: it is not a "force" it is how matter, condensed energy, behaves because of the interaction of the 4 dimensions we find ourselves in.
p.s people who accuse me of being, or claim to be, a round earther are deluded, because the current model states explicitly that it is spherical, not just round.