#### String theory, fine tuning and the multiverse

String theory is the name for the theory of mathematical physics which proposes that physical reality is based on exceedingly small “strings” and “branes,” embedded in 10- or 11-dimensional space. String theory has been proposed as the long-sought “theory of everything,” because it appears to unite relativity and quantum theory, and also because it is so “beautiful.”

Yet in spite of decades of effort, by thousands of brilliant mathematical physicists, the field has yet to produce specific experimentally testable predictions. What’s more, hopes that string theory would result in a single crisp physical theory, pinning down unique laws and fundamental constants, have been dashed. Instead, the theory admits a huge number of different options, by one reckoning numbering more than 10^{500}, which is often called the “string theory multiverse.”

A number of leading string theorists and other physicists view the huge number of different multiverse options as an advantage. They argue that this may offer a solution to the long-standing paradox of why the universe appears so freakishly fine-tuned for life. They reason that we should not be surprised to live in an extraordinarily life-friendly universe, because given 10^{500} possible multiverse designs, inevitably at least one (ours) beats the enormous odds and is favorable to life.

However, the string theory/multiverse hypothesis also has numerous detractors. Sabine Hossenfelder, in her 2018 book Lost in Math: How Beauty Leads Physics Astray, laments the fact that physicists have for so long pursued string theory, supersymmetry and other theories that lack solid underpinning in empirical science, just because they are considered “beautiful.” Similarly, physicist Lee Smolin, writing in his 2006 book The Trouble With Physics, declares,

A scientific theory that makes no predictions and therefore is not subject to experiment can never fail, but such a theory can never succeed either, as long as science stands for knowledge gained from rational argument borne out by evidence.

#### New paper on string theory and the multiverse

On 25 June 2018, a team of prominent string theorists led by Cumrun Vafa of Harvard University released a new paper that fundamentally questions the whole notion of a string theory-based multiverse with 10^{500} or more variations. If their results are confirmed by other physicists and experimental evidence, they could seriously challenge string theory and/or our entire conception of modern physics and cosmology.

The Vafa result and its implications are explained in detail in a very nice Quanta article by Natalie Wolchover. Here is a brief summary:

The main result of the Vafa team paper implies that as the universe expands, the vacuum energy density of empty space must decrease at least as fast as the rate given by a certain formula. The rule appears to hold in most string theory-based universal models, but it violates two bedrocks of modern cosmology: the accelerating expansion of the universe due to dark energy and the hypothesized “inflation” epoch of the first second after the big bang.

In particular, Vafa and his colleagues argue that “de Sitter universes,” with stable, constant and positive amounts of vacuum energy density, simply are not possible under rather general assumptions of string theory. Such universes in general, and ours in particular, would reside in the “swampland” of string theory because they are not mathematically consistent. And yet here we are…

Just as significantly, the Vafa team result draws into question the widely accepted “inflation” epoch of the very early universe, when the universe is thought to have expanded by a factor of roughly 10^{30} or more. The trouble is, Vafa’s result implies that the “inflaton field” of energy that drove inflation must have declined too quickly to have formed a smooth and flat universe like the one we reside in.

String theorists and other physicists are divided about the Vafa team result. Eva Silverstein of Stanford University, a leader in efforts to construct string theory-based models of inflation, believes the result is likely false, as does her husband Shamit Kachru, co-author of the 2003 KKLT paper that is the basis of string theory-based models of de Sitter universes. But others, such as Hirosi Ooguri of the California Institute of Technology, are inclined to believe the Vafa result, since other “swampland” conjectures have withstood challenges and are now on a very solid theoretical footing.

#### Potential explanations and experimental tests

One possible way out is that the accelerating expansion of the universe is not due to an ever-present positive dark energy, as currently believed, but instead is due to quintessence, a hypothesized energy source that gradually decreases over tens of billions of years. If the quintessence hypothesis is true, it could revolutionize physics and cosmology.

The quintessence hypothesis will be tested in several new experiments currently underway, and some others scheduled for the future, which will analyze more carefully whether the accelerating expansion of the universe is constant or variable. One of these experiments is the Dark Energy Survey, currently underway, which analyzes the clumpiness of galaxies. The initial results so far, released in August 2017, find the universe is 74% dark energy and 21% dark matter, with everything else (stars, galaxies, planets and us) in the remaining 5%, all of which is pretty much consistent with our current understanding so far.

Another related experiment is the Wide Field Infared Survey Telescope (WFIRST) system, which is specifically designed to study dark energy and infrared astrophysics. The Euclid telescope, currently in development, will investigate even more accurately the relationship between distance and redshift that is at the heart of modern cosmology.

As mentioned above, the theory of cosmic inflation is also challenged by the Vafa team result. Along this line experimental systems such as the Simons Observatory will search for signatures and other evidence of cosmic inflation. This evidence will be scrutinized carefully, though, in the wake of the widely hailed 2014 announcement of evidence for inflation that subsequently bit the dust, so to speak, in the sense that the results were explained by dust in the Milky Way.

#### High stakes

However these results turn out, they are likely to have earthshaking implications for the fields of mathematical physics, experimental physics and cosmology.

If Vafa’s results are confirmed as correct, and the dark energy explanation for the accelerating expansion of the universe and the inflation epoch of the early universe are reaffirmed by experimental evidence, then this may spell doom for string theory.

Either way, Vafa’s conjecture has certainly roused the physics community like few other developments of recent years. Vafa explains,

Raising the question is what we should be doing. And finding evidence for or against it — that’s how we make progress.

[This appeared in the Math Scholar blog.]