With the recent emergence of the fact that $\Omega_{M}(t_0)$ is apparently less than one, standard cosmology now faces two particularly unpalatable alternatives: either there exists another source of energy to precisely bring $\Omega_{tot}(t_0)$ back to one, or else the spatial curvature $k$ of the universe is non-zero. In the standard Einstein-Friedmann cosmology neither of these options is achievable without a fine tuning of the early universe above and beyond that already provided by inflation; and, moreover, if inflation is correct, the large value inferred for $1-\Omega_{M}(t_0)$ would then entail after generations of work, and after an almost 20 year long conviction that $\Omega_{M}(t_0)=1$, that the cosmology community apparently does not have all that clear an idea as to the primary content of the universe. Given the severity of this situation, it is legitimate to ask if the problem lies not in unknown astrophysics, but rather in the assumed validity of standard gravity itself, with all of the problems which cosmology currently faces being readily traceable to one single source, namely the Einstein-Friedmann cosmological evolution equations themselves. In order to address this question we present a general, model independent analysis of the recently detected apparent cosmic repulsion, and discuss its potential implications for gravitational theory. In particular, we show that a non-flat negatively spatially curved universe acts like a diverging refractive medium, to thus naturally cause galaxies to accelerate away from each other. Additionally, we show that even though such a negatively spatially curved universe is not natural in standard gravity, it does nonetheless have a natural origin within conformal gravity, a fully covariant candidate alternative to standard gravity. In conformal cosmology the flatness, horizon, universe age, cosmological constant, and cosmic repulsion problems are all resolved, and no need is found for dark matter. (References: astro-ph/9803135; astro-ph/9804335, Phys Rev D58, 103511, 1998.)