Inspired by "if a metastable de Sitter space lasting for cosmological durations really is impossible in string theory, then dark energy needs to be explained in some other way, e.g. via quintessence" in one of my previous questions.

Suppose a metastable de Sitter vacua lasting for cosmological durations really is impossible in string theory. Then it sounds like our universe should have moved from a false vacuum to the current vacuum at some point in the past, possibly several times. This changes the laws of physics, and I'm sure such a grand shift in the laws of physics can also explain such problems as baryon asymmetry, the Hubble tension, etc.

The problem with this of course is that at least some of the laws of physics still seem to hold in the very distant past - for example supernovae at cosmological distances look like supernovae in the local universe - so even if the laws of physics have changed, they can't possibly have changed by that much.

Hence the following, closely-related questions:

  • If the universe had undergone a false vacuum decay in the past, how would we know? What would such a universe look like, to a modern observer?
  • Is it possible that a false vacuum decay changes only some laws of physics, with the others staying the same? For example, can a false vacuum decay modify the equations of GR, but leave E&M unchanged?
  • Is it possible that a false vacuum decay changes the laws of physics only slightly? For example, can a false vacuum decay change the speed of light from $3 \times 10^{8} m/s$ to $2.9 \times 10^{8} m/s$, and leave all other properties (such as the constancy of the speed of light in all reference frames) unchanged?

PS: This question uses quite a bit of jargon. If anyone's interested in this, here's some non-technical background. In string cosmology, there is one "law of physics" (string theory) in the high-energy limit, but that "law of physics" can adopt any of multiple different forms in the low-energy limit. Each of those forms would correspond to its own universe (called "vacuum"; plural "vacua"), and our universe today corresponds to one of them. There are about $10^{500}$ of these universes, and most of them are metastable (hence they are "false" vacua). It is in principle possible for these universes to "quantum tunnel" to a "lower-energy" universe. Such an event would change the laws of physics and have dramatic consequences. This question asks about just how dramatic those consequences are.


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In the eternal inflation paradigm as I understand it, there is an eternally inflating de Sitter universe, in which scattered bubbles of flat space nucleate via vacuum decay. Those bubbles expand less slowly than their parent, and so they are true islands. They can't see each other, and all matter within them only formed after the nucleation event, so they can't see anything from the eternally inflating parent either. If this applied to our universe, then the universe would look like it does. There is no way to directly observe anything from the preceding false vacuum, it only existed long before the cosmic microwave background came into being, and the only way to infer that a vacuum decay occurred is through some indirect theoretical means.

On the other hand, if you have a model of inflation in which bubbles of true vacuum can come into contact with each other, then the regions of contact would manifest as enormous domain walls extending right across our Hubble volume, i.e. something we don't see.

You ask if vacuum decay could change the laws of gravity but not other forces, or if it could have very small effects, like slightly modifying the speed of light. Regarding gravity, that is something which ought to be universal across different vacua; unless one includes the effects of fields other than the metric, e.g. a dilaton might produce a "fifth force" modifying gravity. Regarding a change in the speed of light, if the photon picked up a small mass that could happen, I suppose via the condensation of an electrically charged Higgs-like field. If you take string theory's "swampland conjectures" seriously, they might place constraints on how light a massive photon-like particle could be.

Since you pose the question in the context of string theory, I would like to say that vacuum decay in string theory is very poorly understood. Even in field theory, vacuum decay is arguably poorly understood. Coleman and de Luccia's model remains the main way to think about it, but people are still tweaking it today.

As for string theory, they can't even agree whether de Sitter space exists in string theory. The original "landscape" models of 2003, were constructed in supergravity, i.e. an approximation to string theory, and especially since 2018, there has been a heated debate as to whether those approximations are valid, or whether they are destabilized by effects from the full theory. As far as I can see, this debate has not been resolved, five years later.

This doesn't just affect modeling of dark-energy accelerated expansion, it even affects the viability of inflation. Again as far as I know, inflation in string theory is mostly studied via supergravity approximations, not by fully stringy methods. And as for modeling the budding multiverse of eternal inflation, the models (mostly from Susskind and collaborators) are something even further removed from actual string theory, often little more than a branching graph or a grid of cells being stochastically subdivided. These "models" are used for statistical reasoning and say nothing about the actual mechanics of vacuum decay.

There are more sophisticated models of vacuum change in string theory. There's the work on topology change in the Calabi-Yau space that Brian Greene and others did. There's Bousso and Polchinski's idea that an anthropically friendly cosmological constant might be produced by a cascade of vacuum decays in which there are quantum jumps in the amount of closed-string flux winding around the compact dimensions. But I think it's not at all clear how to embed these examples, into a rigorous multi-vacuum formalism that is truly stringy. String theorists are much better at doing perturbation theory around a single vacuum. Unifying all the vacua into a single formalism would be deeply nonperturbative, and I can't think of any proposals from after the mid-1990s (though surely I have overlooked something).


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