Thread by @WKCosmo

I have a new paper in PRL this week:

journals.aps.org/prl/abstract/1…

The paper sounds a little chewy ("consistent with the existence of a tachyonic instability" WTF?) but it is actually a very simple little argument. Let me step you through it. 1/

Here's an arXiv link: arxiv.org/abs/1811.11698

TL;DR: The string multiverse is really hard to get rid of. 2/

We all know string theory has lots of extra dimensions, right? These need to be folded up, or "compactified", in order to make a universe (like ours) that appears lower-dimensional. 3/

Turns out there are a *lot* of ways to do this. It is estimated that there are around 10^(500) different compactifications of string theory. 4/

Each of these stable states corresponds to a way to construct *empty space* in string theory, called a "vacuum state". (Turns out that "nothing" is a really complicated thing). 5/

But there is a longstanding problem with this picture: Every vacuum state that has actually been solved for and written down has turned out to have *negative* energy in the vacuum, i.e. a negative Cosmological Constant. This is called "anti de Sitter space". 6/

The universe we live in does not have a negative cosmological constant, as far as we can tell. 7/

Around a fifteen years ago, a solution was proposed, called "KKLT" after the first initials of its authors, Kachru, Kallosh, Linde, and Trivedi. 8/
arxiv.org/abs/hep-th/030…

The KKLT mechanism consisted of a very particular way to stack up a bunch of higher-dimensional surfaces, or "branes", just so that the negative energy of the string vacuum state would be canceled out, or "uplifted" to a positive energy. 9/

Kind of ugly and inelegant, but it saved string theory from making a grossly wrong prediction, so it nonetheless became very influential. It now has 2651 citations. 10/

KKLT also automatically leads to the idea of a "string multiverse", in which there are innumerably many stable states of string theory with large vacuum energies. 11/

Each of these stable states expands exponentially quickly -- this is inflation. 12/

So the string multiverse is expanding exponentially quickly in all directions, creating infinitely many separate universes, each with different laws of physics, corresponding do different vacuum states. 13/

Lots of people (including me) are not very fond of this outcome. 14/

This changed last year, when Vafa and collaborators came up with a radical idea: suppose all of the vacua of string theory have negative energy because positive-energy vacua are *forbidden*. 15/
arxiv.org/abs/1806.08362

This is called the "de Sitter Swampland Conjecture". 16/

This means (for example) that KKLT is wrong. This has generated ... just a bit of controversy. 17/

The different set of possible states of string theory can be modeled as a ball rolling around in a complicated, higher-dimensional "landscape" of peaks and valleys, where each valley corresponds to one of these 10^(500) stable states of the theory. 18/

Written in the langauge of the landscape, the Swampland Conjecture says that none of the valleys on this complicated surface can have positive energy. 19/

Anything with positive energy has to be someplace on a steep hillside: the Swampland Conjecture can be written mathematically as a lower bound on the slope of the potential surface in the landscape. 20/

Any "flat spots", where the ball rolling around on the landscape can come to rest, must have negative energy. 21/

This applies to cosmological inflation, which makes things difficult because inflation requires a *nearly* flat spot on the potential with positive energy in order to work. 22/

If there are no flat spots with positive vacuum energy, there is no inflation and therefore no eternal inflation, and no string multiverse. The Swampland Conjecture kills the Multiverse! 23/

Eh. Not so fast. It turns out that the Swampland conjecture also kills known physics, such as the Higgs boson. 24/

Remember that the Higgs boson give mass to the particles of the Standard Model by "spontaneous symmetry breaking". 25/

It's like a ball on a hill again: when it's at the top of the hill, all particles are massless. When it rolls to the bottom of the hill, other particles acquire mass. 26/

But the top of the hill for the Higgs boson is a flat spot with *positive* vacuum energy. This is forbidden by the Swampland Conjecture, which should apply to all scalar fields, including the Higgs. 27/

So by getting rid of the multiverse, we have also gotten rid of known physics like the Higgs boson. Merde! 28/

In order to fix this (and other more technical issues), Vafa and collaborators proposed a fix, called the "refined" swampland conjecture: 29/
arxiv.org/abs/1810.05506

This says that, ok, you can have a flat spot with positive vacuum energy, as long as it's *unstable*, i.e. a hilltop and not a valley. This makes things like the Higgs potential ok. 30/

Which brings us to my little paper. 31/

The thing is that *any* flat spot on a scalar potential with postive vacuum energy can in principle drive cosmological inflation. 32/

If it's a hilltop, the period of cosmological inflation will not last forever, because the field will inevitably roll off the top of the hill toward a stable state (a valley). So maybe we're ok. 33/

This still keeps us safe from eternal inflation and the string multiverse, right? Not so fast. 34/

There are two effects: the classical effect of the field rolling down the hill, which stops inflation, and quantum fluctuations, which can push the field back up to the top of the hill. 35/

The first process happens exponentially quickly. But as long as we're inflating, the universe is expanding also exponentially quickly. 36/

If the exponential expansion beats the exponentially fast decay, then the inflation wins and we again have eternal inflation and a multiverse. 37/

What I show in this paper is that if we satisfy the refined Swampland Conjecture, then indeed inflation can win over the decay, and we get the string multiverse back. 38/

And if it can happen, given the 10^(500) options in the string landscape, then someplace, it *will* happen. The multiverse is no longer ruled out: it is for all practical purposes, inevitable. 39/

This means that, as soon as we fix up the Swampland Conjecture so it doesn't trivially rule out known physics like the Higgs, we inevitably get an unwelcome passenger: the string multiverse! 40/

This is important because it looked like the Swampland Conjecture was likely to free us from the multiverse and associated awful stuff like the Anthropic Principle. Not so, we're still stuck with it. Sorry. 41/41