over time. Today, despite the hard evidence of the background radiation, many researchers still find it hard to accept the idea that the universe was created in a state of infinite density and zero volume. How could it ever get out of such a state?

Almost nobody doubts there was a period in the early universe when it was extremely hot and dense; in fact, WMAP and other measures of the cosmic microwave background provide unmistakable proof. There have been numerous other attempts to account for this radiation, but none of them can explain why its temperature is very nearly the same in all directions. Thus, for want of a better explanation most cosmologists accept that it is the remnant of a primeval fireball.

The debate has to do with the Big Bang singularity itself. Could there be a way of accounting for all observed cosmological results without having the mathematics of the theory go haywire some 13.7 billion years in the past? Could the initial creation of matter be explained by a known physical process, rather than just by fiat?

In the late 1960s, Hawking and Penrose demonstrated that just as black holes must have final singularities, the standard Big Bang must have had an initial singularity. The theorems they proved assumed that the universe contained material of typical density and pressure and that its dynamics could be modeled through ordinary general relativity. Most physicists have accepted these conditions as reasonable and have resigned themselves to a universe of indeterminate origin.

In recent decades, however, researchers have sought ways around this knotty issue. One such proposal was put forth, interestingly enough, by Hawking himself. At a 1981 conference organized by the Vatican, he suggested that space-time has no boundary. By substituting “imaginary time” (mathematically, real time multiplied by the square root of negative one) for real time, Hawking found that he could transform the Big Bang singularity into a smooth surface— akin to Earth’s South Pole. Just as Antarctic explorers don’t fall off

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