How do the heavens "blaze forth" the death of Julius Caesar?

On the eve of the Ides of March, a thunderstorm is occurring. This, given in Shakespeare's stage direction, is the only objective evidence, coincidental as it might be, that the gods are producing an omen that some great or terrible event is to occur. The other things—Calpurnia's report that a lioness has given birth in the streets, that graves have opened up, and that there has been a great battle in heaven causing blood to rain down on the capital—could all simply be someone's hallucinations. In antiquity, people genuinely believed in omens and that the heavens would, as Calpurnia says, "blaze forth the death of princes."
The ambiguity with which all these elements of the supernatural are presented, in my view, simply enhances the power and the universal meanings in Shakespeare's drama. In Julius Caesar the "blazing forth" of lightning, graves opening, and battles in the sky, just like the Soothsayer's prescience about the Ides of March, are both real and unreal. They are, at the very least, symbolic of the power, both creative and destructive, of man's imagination and expressive of an indissoluble link among God (or to the ancient Romans, the gods), nature, and humanity.