## Monday, February 3, 2014

### Does the multiverse explain the cosmological constant?

At the end of the last post on falsifiability, I mentioned the possibility that the multiverse hypothesis might provide an explanation for the famous cosmological constant problem. Today I'm going to try to elaborate a little on that argument and why I find it unconvincing.

Limitations of space and time mean that I cannot possibly start this post as I would like to, with an explanation of what the cosmological problem is, and why it is so hard to resolve it. Readers who would like to learn a bit more about this could try reading this, this, this or this (arranged in roughly descending order of accessibility to the non-expert). For my purposes I will have to simply summarise the problem by saying that our models of the history of the Universe contain a parameter $\rho_\Lambda$ – which is related to the vacuum energy density and sometimes called the dark energy density – whose expected value, according to our current understanding of quantum field theory, should be at least $10^{-64}$ (in units of the Planck scale energy) and quite possibly as large as 1, but whose actual value, deduced from our reconstruction of the history of the Universe, is approximately $1.5\times10^{-123}$. (As ever with this blog, the mathematics may not display correctly in RSS readers, so you might have to click through.)

This enormous discrepancy between theory and observation, of somewhere between 60 and 120 orders of magnitude, has for a long time been one of the outstanding problems – not to say embarrassments – of high energy theory. Many very smart people have tried many ingenious ways of solving it, but it turns out to be a very hard problem indeed. Sections 2 and 3 of this review by Raphael Bousso provide some sense of the various attempts that have been made at explanation and how they have failed (though this review is unfortunately also at a fairly technical level).

This is where the multiverse and the anthropic argument comes in. In this very famous paper back in 1987, Steven Weinberg used the hypothesis of a multiverse consisting of causally separated universes which have different values of $\rho_\Lambda$ to explain why we might be living in a universe with a very small $\rho_\Lambda$, and to predict that if this were true, $\rho_\Lambda$ in our universe would nevertheless be large enough to measure, with a value a few times larger than the energy density of matter, $\rho_m$. This was particularly important because the value of $\rho_\Lambda$ had not at that time been conclusively measured, and many theorists were working under the assumption that the cosmological constant problem would be solved by some theoretical advance which would demonstrate why it had to be exactly zero, rather than some exceedingly small but non-zero number.

Weinberg's prediction is generally regarded as having been successful. In 1998, observations of distant supernovae indicated that $\rho_\Lambda$ was in fact non-zero, and in the subsequent decade-and-a-half increasingly precise cosmological measurements, especially of the CMB, have confirmed its value to be a little more than three times that of $\rho_m$.

This has been viewed as strong evidence in favour of the multiverse hypothesis in general and in particular for string theory, which provides a potential mechanism for the realisation of this multiverse. Indeed in the absence of any other observational evidence for the multiverse (perhaps even in principle), and the ongoing lack of experimental lack of experimental evidence for other predictions of string theory, Weinberg's anthropic prediction of the value of the cosmological constant is often regarded as the most important reason for believing that these theories are part of the correct description of the world. For instance, to provide just three arbitrarily chosen examples, Sean Carroll argues this here, Max Tegmark here, and Raphael Bousso in the review linked to above.

I have a problem with this argument, and it is not a purely philosophical one. (The philosophical objection is loosely the one made here.) Instead I disagree that Weinberg's argument still correctly predicts the value of $\rho_\Lambda$. This is partly because Weinberg's argument, though brilliant, relied upon a few assumptions about the theory in which the multiverse was to be realised, and theory has subsequently developed not to support these assumptions but to negate them. And it is partly because, even given these assumptions, the argument gives the wrong value when applied to cosmological observations from 2014 rather than 1987. Both theory and observation have moved away from the anthropic multiverse.