Is There Evidence Of A Multiverse?

If we live in an inflationary multiverse, other universes are moving away from us faster than the speed of light. There would be no way to send or receive a signal from one of those other universes, which puts the prospect of testing it in fairly dire straits.

Not every cosmologist agrees with that. Laura Mersini-Houghton and Rich Holman not only claim that the multiverse is in the realm of testable physics but that they have a model that makes a series of predictions. Some of which, at least they claim, are confirmed in the Planck and CMB data.

Their proposal uses a lot of quantum cosmology and high energy physics. I’ve tried to explain it in a way that’s understandable but presented so as not to lose any important subtleties. I’ve left some detail as end notes, connected to certain parts of the text. I’ve written it this way to avoid breaking the general flow of the article but it will be important to read these for a more complete understanding of the model. 

In their approach, they use a particular model for the landscape of string theory discovered by Fredrik Denef and Michael Douglas, Houghton and Holman imagine that the wave function of the universe “spreads out” across the entire landscape* and with the distribution of vacua energies on that space it behaves very similarly to a condensed matter system.**

Once universes make the quantum-to-classical transition and decoherence kicks in, a bath of very weakly coupled quantum fluctuations in other sectors of the landscape induce a measurement on that system. Those fluctuations have energies***

Mersini-Houghton and Holman sum over all the energies of these fluctuations to calculate the backreaction effect on the geometry of our universe.

It does that by perturbing the scale factor and the moduli (a set of scalar fields). They add this term to the Wheeler-DeWitt equation and reduce it to something called the "Master equation". Only when Lambda is larger will there be a corresponding solution to the Master equation that describes a really existing world. 

Solving the Master equation should give us the probability for the distribution for vacua on that landscape. Laura Mersini-Houghton calls this the "superselection principle" because it purports to tell us what sector of the landscape we occupy without relying on anthropic reasoning. 

The Master equation also doesn't have a Hamiltonian constraint like the Wheeler-DeWitt equation and therefore there is a fundamental time parameter in the model, which exhibits time-symmetry. Internal time is defined using the scale factor and so in their model, they are able to reverse the arrow of time. 

The backreaction effect of superhorizon wavelength fluctuations breaks the entanglement among universes, which leaves a correction to the inflationary potential. So that during the inflationary epoch, the backreaction term is negative. Here's the more interesting part, that creates gravitational instabilities, that contribute to the Newtonian gravitational potential, to counteract the cosmological constant. 

The authors then construct the effective density matrix**** for our patch of the landscape and use that to obtain values for observables in the CMB. 

- A cold spot results from the modified Newtonian potential. Since the modification is negative, it results in a suppression of the amplitude of perturbations and a hole in the sky, which shows up as a void. They predicted one should appear 8 billion light-years away of about 12 degrees in the sky. 

- A modified Newtonian potential also results in a modified Friedman equation. In this case, Mersini-Houghton and Holman add a non-local term to the equation F(b, V) where b is the SUSY breaking scale and V is the vacuum energy.

This obviously affects the expansion of the universe and structure formation. Which leaves another void at the ‘quadruple’ scale and this is how I interpret Eq. (4) and Eq. (5) in the paper "Birth of the Universe from the Multiverse"

In all seriousness though, I don’t think either of these can claims can hold up to serious scrutiny. The effective potential that results from the entanglement between universes is also dependent on the inflationary potential, a free parameter. Wholly without the landscape you could pick a potential for inflation that is the same as the effective potential in their paper.

- Assuming inflation started at the GUT scale, and since the expansion has an added term which depends on the SUSY breaking scale, the new term must be small enough so to not do violence to the smoothing out of our universe by inflation. This means the

Where Mp is the Planck mass. This means that supersymmetric particles won’t be found at the LHC. 

- Temperature variations in the CMB are not random. There are "lumps" which are slightly warmer or cooler than the surrounding temperatures, which are aligned with each other in a preferred direction. Something now known as the "axis of evil".

- The 'bulk flow' an observation that suggested that large clusters of galaxies were being pulled away from us by something outside our local universe. The suggestion here is that another universe is gravitationally 'tugging' on our own. This prediction was dealt a serious blow in paper thirteen of the Planck series, who ruled it as being "not statistically significant".

Of this one, I’m not too sure. My understanding is that a 'bulk flow' should always appear when the CMB frame does not coincide with the expansion frame of the universe. Although there are at least around 10 papers on arXiv strongly disfavoring a model with a large bulk flow.

I am somewhat worried that none of these predictions are derived from first principles. They make various assumptions about quantum mechanics and appear to involve a very realist interpretation of the landscape and the wave function, at least in the language with which it’s presented.

There is one last thing that I ought to mention. There is a paper on the arXiv by William H. Kinney***** which studies the entanglement between universes and purports to find no evidence of other universes. The conclusion section of his paper "Limits on Entanglement Effects in theString Landscape from Planck and BICEP/Keck Data" is very detailed.

He rules out two models of inflation, the original exponential potential that Mersini-Houghton, Holman and Takahashi consider in their 2008 paper "Cosmological Avatars of the Landscape. II. CMB and LSS Signatures" and something called a Starobinsky inflationary potential. The first of these is "entirely ruled out by the data", due to the overproduction of a type of fluctuation called a 'tensor mode'. The second is actually a good fit for the data but that fit is spoiled if entanglement is added.****** I'll leave it to the reader to consult the conclusion section of his paper for more.

Endnotes

* Archil Kobakhidze and Laura Mersini-Houghton in their original paper "Birth of the Universe from the Landscape of String Theory" use a simplified model, they don't use the entire landscape of all vacuum solutions with an initial 3-geometry, in their calculations. Instead, they restrict their argument to a minisuperspace, which includes only supersymmetric (SUSY) vacuum solutions with a vacuum potential, zero vacuum energy and with a metric describing an initial spatially flat and homogenous 3-geometry.

In another paper "Can we predict Lambda for the non-SUSY sector of the Landscape" they apply the same selection principle to the non-SUSY sector of the landscape, these two sectors are assumed to be disconnected.

As far as I can understand the model, specifically in a 2008 paper Laura Mersini-Houghton and Rich Holman "Why the Universe started in a low entropy state" are far less subtle, the vacuum energy is determined by the SUSY breaking scale, and therefore it's this sector of the landscape that produces classical universes with an early inflationary epoch, like ours.

So we might take as our boundary condition for quantum cosmology, that 'the wave function is restricted to this minisuperspace and does not leak into other sectors of the landscape'.

** The wave function of the universe behaves like an electron travelling through a piece of wire.

*** This equation is an equation for the total energy of the system, E = -KE + PE.

**** a density matrix is similar to a wave function, except that it describes quantum amplitudes even with ignorance of classical states. This is the right notion for describing a system with statistical uncertainty, a "pure" wave function always has zero entropy because it is in some specific state. But a density matrix can have a greater entropy which you can calculate using "von Neumann entropy", Wikipedia has a good proof of this on their page.

***** I hear that apparently Laura Mersini-Houghton and Rich Holam tried to have the paper removed from the arXiv, claiming that they were not added as authors, though they are thanked in the acknowledgement section of the paper.

****** Sabine Hossenfelder wrote a post on this paper on her blog Backreaction.