Can modern cosmological observations be reconciled with a general-relativistic Universe without an anti-gravitating energy source? Usually, the answer to this question by cosmologists is in the negative, and it is commonly believed that the observed excess dimming of light from supernovae relative to the predictions of the Milne model is evidence for dark energy. In this talk I will illustrate why this intuition does not generally hold once the symmetries of the Friedman-Lemaitre-Robertson-Walker metric are broken. This opens up an avenue of research into general-relativistic space-time solutions without dark energy that may be competitive cosmological models. I will discuss the geometrical constraints that such space-times must necessarily satisfy in order to conform with cosmological observations.