Cosmic Growth and Expansion Conjoined

Cosmological measurements of both the expansion history and growth history have matured, and the two together provide an important test of general relativity. We consider their joint evolutionary track, showing that this has advantages in distinguishing cosmologies relative to considering them individually or at isolated redshifts. In particular, the joint comparison relaxes the shape degeneracy that makes $f\sigma_8(z)$ curves difficult to separate from the overall growth amplitude. The conjoined method further helps visualization of which combinations of redshift ranges provide the clearest discrimination. We examine standard dark energy cosmologies, modified gravity, and "stuttering" growth, each showing distinct signatures.