In order to better understand the equivalence between gravitational forces of rotatingbodies and rotating frames, I use the Einstein-Infeld-Hoffman equation to develop a cosmological appropriate integral for such study. I find that the ΛCDM model of cosmology along with General Relativity (GR) are enough to get a near equivalence between rotational frames and gravity. Then using this integral and asserting an interpretation of Mach’s Principle (MP), I examine what might need to change from the standard ΛCDM cosmology to make a perfect equivalence. One topic developed and tested is a modified ΛCDM cosmology with a time varying gravitational coupling. This model is compared with supernova distance modulus data against ΛCDM. I find that in some cases this modified cosmology can statistically outperform ΛCDM.