What came before the Big Bang?

Robert Brandenberger, a physicist at McGill University who was not involved in the study, said the new paper “sets a new standard of rigor for the analysis” of the mathematics of the beginning of time. In some cases, what at first appears to be a singularity—a point in spacetime where mathematical descriptions lose their meaning—may actually be an illusion.

A Taxonomy of Singularities

The central issue Geshnizjani, Ling and Quintin face is whether there is a point before inflation at which the laws of gravity break down at a singularity. The simplest example of a mathematical singularity is what happens to the function 1/x HOW x approaches zero. The function takes a number x as input, and outputs another number. like x gets smaller and smaller, 1/x becomes larger and larger, approaching infinity. whether x is zero, the function is no longer well defined: it cannot be relied upon as a description of reality.

Sometimes, however, mathematicians can overcome a singularity. For example, consider the prime meridian, which passes through Greenwich, England, at zero longitude. If you had a function of 1/length, it would run amok at Greenwich. But there’s really nothing physically special about the suburbs of London: You can easily redefine the zero longitude to pass through another place on Earth, and then your function will behave perfectly normally when you approach the Royal Observatory in Greenwich.

Something similar happens at the limit of mathematical models of black holes. The equations describing non-rotating spherical black holes, worked out by physicist Karl Schwarzschild in 1916, have a term whose denominator goes to zero at the black hole’s event horizon—the surface surrounding a black hole beyond which nothing cannot escape. This led physicists to believe that the event horizon was a physical singularity. But eight years later, astronomer Arthur Eddington showed that if a different set of coordinates is used, the singularity disappears. Like the prime meridian, the event horizon is an illusion: a mathematical object called a coordinate singularity, which arises only because of the choice of coordinates.

In contrast, at the center of a black hole, the density and curvature go to infinity in a way that cannot be eliminated using a different coordinate system. The laws of general relativity begin to sputter. This is called a curvature singularity. This implies that something is happening that is beyond the ability of current physical and mathematical theories to describe.