Gravitational waves confirm mathematical prediction of inflationary big bang

In a dramatic announcement on March 16, 2014, a team of astronomers led by John Kovac of the Harvard-Smithsonian Center for Astrophysics said that they have detected gravitational waves, confirming predictions made by mathematical physicists Alan Guth, Andrei Linde and others in the 1970s and 1980s.

Gravitational waves from inflation, with their distinctive twisting pattern, in the polarization of the cosmic microwave background radiation.

MIT physicist/cosmologist Max Tegmark assessed the discovery in these terms: “I think that if this stays true, it will go down as one of the greatest discoveries in the history of science.”

Similarly, Marc Kamionkowski of Johns Hopkins University, who in 1997 predicted that these gravitational waves should be found under the inflation hypothesis, said, “This is huge. … It’s not every day that you wake up and find out something completely new about the early universe. To me this is as Nobel Prize–worthy as it gets.”


The big bang cosmology, as currently understood, had its origins in the mathematics of Einstein’s 1915 general theory of relativity, which suggested that the space-time fabric of the universe was expanding, and thus that the universe originally began in a “singularity,” now termed the big bang.

The big bang received substantial confirmation in 1964 when Arno Penzias and Robert Wilson, two radio astronomers in New Jersey, found that a low-level noise was coming from the cosmos in all directions. Physicists at nearby Princeton University, led by Robert Dicke, immediately recognized that their experimental results neatly fit the “black body” spectrum of the primordial echo of the universe 300,000 years after the big bang, earlier predicted purely on mathematical grounds. At about the same time, other theoretical calculations showed that the big bang would have produced a universe that is roughly 75% hydrogen, 25% helium, with traces of He-3 and Li-7, also exactly as observed [Guth1997, pg. 101-103].

Nonetheless, many puzzles remained in the overall big bang scenario. For example, why, if the universe originated in a big bang 13.8 billion years ago (the currently accepted age), does the universe look so similar from one part of the sky to another? After all, there has not been enough time since the big bang for any light or other medium to have communicated any information between these two portions of the universe.

These and other mysteries were dramatically explained by the inflation hypothesis, originally discovered in 1979 by Alan Guth and later developed by numerous other researchers, including Stanford physicist Andrei Linde and Princeton University physicist Paul Steinhart.

The inflation hypothesis is that in the first tiny fraction of a second (approximately 10-36 second) after the big bang, the space-time fabric of the universe underwent an enormous expansion, by at least 30 orders of magnitude. This expansion “stretched out” the wrinkles and non-uniformities of the very early universe to a level roughly what we see today. Inflation is just one phase of the early big-bang cosmology: a more complete chronology is available from this Wikipedia article.


In recent decades, inflation has come under attack by some in the physics/cosmology community, mainly because various formulations of inflation require dubious “ad hoc” parameters and assumptions to be viable. For example, highly improbable conditions are required for the inflation process to be initiated, and so many outcomes are possible that it is difficult to make any firm observational predictions from the theory.

Paul Steinhardt of Princeton University (who, as noted above, was one of the pioneers of inflation) has emerged as a vocal detractor in recent years: “We thought that inflation predicted a smooth, flat universe. Instead, it predicts every possibility an infinite number of times. We’re back to square one.” Similarly, Sean Carroll of CalTech explains, “Inflation is still the dominant paradigm, but we’ve become a lot less convinced that it’s obviously true. … If you pick a universe out of a hat, it’s not going to be one that starts with inflation.” [Gefter2012].

All researchers, whether or not they still believe the inflation scenario, agree that inflation is sorely in need of additional experimental testing and confirmation.

The BICEP2 results

Against this background, the newly announced results of the Background Imaging of Cosmic Extragalactic Polarization 2 (BICEP2) experiment are dramatic indeed. The BICEP2 is basically a giant superconducting thermometer, built from 250 chip-sized polarization detectors, constructed at the Amundsen-Scott South Pole Station. It looks for polarizations (twists) in the cosmic microwave background, which are evidence of gravitational waves generated during the inflation era, as predicted by earlier mathematical calculations. The measured polarization values are completely consistent with the leading inflation scenario.

Along this line, the BICEP2 researchers reported reported an r value of 0.16 plus or minus 0.05, which indicates that inflation began at 10-36 second after the big bang. This rules out several competing inflation models, but it fits very well with the most commonly used inflation model, which predicts r = 0.15.

Researchers emphasize that in spite of the excitement, we must be patient until the current results are confirmed. But several other experiments, using different approaches and experimental facilities, are close on the heels of the BICEP2 experiment, and thus we should know soon if the BICEP2 results are confirmed. If they are confirmed, the discovery will almost certainly be rewarded by a Nobel Prize, possibly for Guth and also for Kovac. The recipient(s) will join a distinguished list of Nobel laureates who have done work in big bang cosmology, including Penzias and Wilson (1978), Mather and Smoot (2006), and Perlmutter, Schmidt and Riess (2011).

The unreasonable effectiveness of mathematics

In Tegmark’s recent book Our Mathematical Universe, he comments at length on how and why it is “that we humans can successfully predict so much about our cosmos with mathematics.” Now with the BICEP2 results, “here we go again”, confirming the unreasonable effectiveness of mathematics, as Wigner so memorably described it.

In his book, Tegmark offers a provocative explanation to explain this effectiveness, particularly in the context of physics, cosmology and inflation: the universe appears to be well-explained by mathematics, because, in brief, the universe is mathematics. In other words, the universe (actually the multiverse) is nothing more or less than the set of all logically consistent mathematical structures and their relations. We live in one universe that appears mysteriously congenial to life, but that is only because if it weren’t congenial, we wouldn’t be here to talk about it (i.e., the Anthropic Principle).

In this regard, the latest experimental results for inflation arguably can be seen as the first bit of (indirect) experimental evidence for the existence of the multiverse: we are just one spoke in an infinite and eternally bifurcating system of universes, springing from the inflation process, not to mention other levels of the multiverse, as sketched by Tegmark and others.

Nonetheless, difficult questions remain. How can one discuss the “probability” of our universe existing as we see it unless one can define, in a rigorous sense, a probability measure on the space of all universes in the multiverse? After all, it doesn’t make much sense to say that we are one of an infinite collection of habitable universes in an even larger ensemble of all universes.

As we recently noted in another Math Drudge blog, all of this also underscores the emerging need for constructive dialogue between philosophers and science. As big bang cosmologist Joseph Silk notes,

Drawing the line between philosophy and physics has never been easy. Perhaps it is time to stop trying. The interface is ripe for exploration.

[Added 31 Mar 2014:] The gravitational wave announcement continues to “make waves,” so to speak, in the physics community, since it once again brings to the fore the issue of the multiverse. This Scientific American article highlights some of these issues.

[Added 11 Jun 2014:] Researchers are now questioning the BICEP2 experimental results themselves. In particular, some researchers at U.C. Berkeley and at New York University are now arguing that the “twisting patterns” found by the BICEP2 team could more easily be explained by dust in the Milky Way. When this dust is accounted for, the BICEP2 signal attributed to gravitational waves “either vanishes or is greatly diminished.” See this Scientific American report for further details.

Comments are closed.