Pop Goes the Universe

Last year Scientific American published a controversial article titled "Pop goes the Universe", the three authors Anna Ljjas, Paul Steinhardt and Abraham Leob are skeptics of inflationary cosmology and they gave roughly three arguments for their position which they claim are made sharper by the Planck 2015 data. That was then followed with a letter signed by 33 physicists who study cosmology, denouncing the article that had been published.

Originally I didn't want to write this post, the whole business of signing a letter denouncing the article instead of writing to the editor makes me feel uneasy. It reminds me of when a hundred Nazi scientists were called on to denounce Einstein, had he been wrong, you would have only needed one. Science media should be an open space where people are allowed to hear about controversies in physics. Inflation is not a well established scientific theory like the Big Bang or evolution, and some very highly respected theoretical physicists are in real doubt.

Inflation probably is the correct theory, it's the best worked out model to date but I still have some worries about it. Some of the arguments used in favour of inflation aren't very convincing. For one, inflation is supposed to explain the observed large scale homogeneity and isotropy in the universe and it does. But virtually everyone agrees it re-introduces the same problem by assuming an even more homogeneous finely tuned initial patch at the start of the universe, $P= e^{S}$ where $S =1/\Lambda$ in fact its orders of magnitude worse.

Inflation was also postulated to solve the horizon problem, and this is the best argument for inflation. Everywhere across the CMB the temperature is ~2.7K including in regions that haven’t yet had time to interact with one another but inflation allows you to start the universe off at much smaller size (so that distant regions have time to interact) and then expand those regions exponentially far, away from each other. There’s nothing wrong with this as an explanation but it’s also possible that the universe didn’t begin at the Big Bang, so that different regions have had time to interact in a previous cycle or aeon of the universe’s evolution, though it’s not clear how to make this alternative to inflation consistent with the low entropy condition at the Big Bang. 

Second the known relation between the mass density of the universe and it's critical density, $\Omega _{tot} \equiv \frac{\rho _{tot}}{\rho _{c}}$ when you extrapolate the Friedman equations back into the past it’s initial value is already very close to one.  We know that the curvature density parameter increases with time in the standard model, so that it must be smaller in the past. The exact numbers don't matter but this essentially is the "flatness problem" because cosmologists expect the initial value of the curvature density prameter to increase with time under the standard model and inflation is supposed to reduce it to something compatible with observation, and it does so by decreasing our coomoving horizon. 

In principle there’s no reason why the universe should start off with a value of curvature density close to one, if it started out with something much higher inflation would probably give you the wrong answer. Even if we insist it did start out at one, we’re already assuming flatness not explaining it but fortunately, this albeit quasi-solution that inflation offers comes at only a small price, minimally its ontology postulates the existence of a vacuum potential as a function of a scalar field, with a sufficiently high positive energy density, and although it can’t be observed, in works in classical gravity, so one doesn’t have to assume too much about the early universe.

Thirdly inflation predicts a statistical distribution of adiabatic, non-gaussian and nearly scale invariant anistropies in the universe, primordial quantum fluctuations that plant seeds of early galaxy formation. Which we can measure and inflation can be modelled to fit the data, although this is not a natural outcome of every inflationary model, it depends on the equation of state which has to be small, (it also has to be constant for various Hubble expansion terms) and the number of e-folds. You can adjust the energy density curve in the theory to fit virtually any observation you want, though the simplest model of inflation actually suffices to explain these observations naturally and well, but this match with the data is then spoiled by the lack of significant gravitational wave detection $(r ~ 0.15 - 0.4)$ in the CMB.

These waves are ripples in the fabric of spacetime which are caused by the exponential stretching of space during the inflationary epoch, and we'd expect to find a higher ratio of tensor to scalar fluctuations, if the simplest version of the theory is correct.

In this sense inflation like the standard model has to be tuned to fit in with observation, but not only is the probability of the density fluctuations low on inflation around $10^{-15}$ according to Steinhardt but more temperature variations would result in more stars and galaxies, and likely more observers. So that appealing to the anthropic principle doesn’t make our observations more natural given inflation. 

None of these arguments for inflation are any kind of silver bullet, but none of these are the focus of the article by Steinhardt et al. Instead Steinhardt traditionally presented three problems for inflation, which he thinks have now been given support by Planck. These roughly line up with three parts to any inflationary model, those are (a) the inflationary potential which determines a family of classical trajectories and (b) the initial conditions which determine a subset of trajectories and (c) the measure which assigns a weight to each trajectory. 

The simplest model of inflation would involve only the simplest version of all three postulates, but such a model is in high friction with data from the Cosmic Microwave Background Radiation, the Planck satellite which measured the CMB, a relic from when matter decoupled from radiation, they found temperature anisotropy variations are scale invariant to 0.01 of a per cent. This and the lack of significant gravitational wave detection $r < 0.1$ is incompatible with such models.

Sometimes this is misleadingly described as "evidence for a multiverse" or eternal inflation because proponents of the idea are forced to retreat and consider more complicated mechanisms for the decay of the inflaton field. The authors argue for example that the data favoured only complicated single field inflation (because a property called "non-Guassianity" is small), and models with a plateau, other models like power law potentials or chaltic inflation are now no longer allowed by Planck. They call this restriction the "unlikeliness problem" because plateau models produce less inflation and require more parameters than alternative models. Moreover it justifies focusing on the plot between $r$ the ratio of tensor to scalar fluctuations and $n_{s}$ the scalar spectral index. Since this is a sharper way to evaluate single field inflation.

Not only do these more complicated models need extraordinary fine tuning, both in the potential they artificially construct (although other cosmologists would argue that it’s different for plateau rather than hill top models), but also in the initial entropy of the Big Bang which the theory, by itself cannot explain. Steinhardt et al argue that Planck 2015 makes this even worse because the energy density in such models needs to 12 orders of magnitude less than the simplest version, which quantitatively translates to an initial smooth patch Hubble volume $10^{9}$ larger.

What worries me more than anything else about inflationary cosmology, is that by extrapolating speculative physics to vastly larger orders of magnitude, it's now led to an entire community of cosmologists arguing about domains well outside of our observable universe. I don't have any a priori problem with the existence of multiple universes but the idea of modern science decoupling from rigorous scrutiny and an emphasis on empirical evidence worries me. I don't know if there are other universes but unless a proposal is testable and falsifiable, it's not science.

Though there are some versions of the multiverse which may lead to observational consequences for our sector of it, things like bubble collisions with other baby universes or entanglement between the early universe and others leaving some mark on the inflaton's potential in our universe, so far no evidence has been found, despite the fact there have been genuine attempts to look for these signatures. If you're a proponent, you hardly need to worry about this, so long as you have an infinite multiverse, where anything that can happen will happen, you can explain away any null result as occurring in some sector.

There are a whole load of other reasons to be skeptical of eternal inflation, like the measure problem that I've talked about when I reviewed Lawrence Krauss' book "A Universe From Nothing". This essentially is the problem of how to assign the right probabilities to our observations given eternal inflation. The most natural measure, the volume measure makes our observable universe exponentially unlikely by a factor of at least $10^{-10^{55}}$ this is what Steinhardt calls uniquely the "multiverse problem", and its the last argument Steinhardt makes against inflation. Eternal inflation he argues is a natural consequence of cosmic inflation and the measure problem is the indispensable baggage that it carries. In fact the volume measure seems to favour simple models over the plateau favoured by Planck. Which arguably has made the problem even more difficult. 

I largely agree with what Steinhardt writes, it doesn’t seem to me that inflation solves all of the problems it’s postulated to solve, it’s an interesting model that agrees with the data but some scepticism is still warranted. Having said that I disagree with Steinhardt on one argument, I think the horizon problem in particular lends a lot of credibility to inflation. I’d still give it an above $0.5$ chance of being right. 

It may be worth mentioning the monopole problem that Andre Linde argued in 1983 was solved by inflation, if inflation occurred at the GUT era. Certain exotic topological defects, like magnetic monopoles or cosmic strings aren’t observed in our universe as often as one might have expected because inflation is supposed to "push them" beyond the observable horizon. I didn’t include this in the main body of text because there’s no empirical evidence for cosmic strings or magnetic monopoles.