New Year, New Universe?

Hello! This is Matt Johnson, and I was recently asked to write a brief guest post for FQXi about some of my recent work with Stephen Feeney, Daniel Mortlock, and Hiranya Peiris on observational tests of eternal inflation. To supplement some popular stories (e.g. Science) and blog posts (cosmic variance, backreaction) that describe this work (as well as the papers themselves), I thought I'd use this space to give some background on why thinking about eternal inflation is an interesting problem, give a realistic picture of what is theoretically and observationally possible to do, and paint a broad picture of our recent work.

I've been fascinated by the idea of eternal inflation (I'll describe what this is fully below, and you can also look at the article "When Universes Collide" for some of the background too) ever since my PhD advisor (and FQXi director) Anthony Aguirre as well as Tom Banks and Michael Dine got me thinking about it. I find it truly amazing that science could provide the tools to predict and search for evidence of such radical phenomena. Ever since, I suppose I've been spending a significant amount of time searching for other universes. Sound crazy? Maybe, but read on and perhaps I can convince you otherwise...

Perhaps one of the most speculative ideas in modern physics is that of the "multiverse." In this scenario, our observable universe is purported to be only a very small pocket embedded in a much larger cosmos. Outside of our pocket, the physical constants we view as fixed, and perhaps even the laws of physics themselves, could be different. In this picture, the pocket containing our observable universe was born from, and is embedded inside, some parent vacuum. What might we learn about these origins, and the possibility that we live in a multiverse?

This question has received a lot of attention in the past few years. Part of the reason is that eternal inflation, which gives rise to the multiverse described above, seems to follow fairly naturally from string theory. (You can read more about this in the article, "Tying Down the Multiverse with String.")

Two things are necessary to obtain eternal inflation from string theory: multiple metastable vacua and an effective four-dimensional positive cosmological constant. The multiple vacua correspond to the many ways that the 6 extra dimensions predicted by string theory can be compactified (and thus hidden from our view). Although they are classically stable, the size and shape of a compactification can be adjusted through quantum mechanical tunneling. In the four-dimensional picture, this corresponds to the formation of an expanding bubble inside of which things like the vacuum energy, masses of particles, strength of gravity, and perhaps other properties, are different. Since an effective four dimensional cosmological constant is necessary to explain the currently observed dark energy, and to source an inflation in the early universe, the second criteria is expected to be accommodated by string theory. When the formation and expansion of bubbles is outpaced by the expansion caused by the cosmological constant, the bubbles do not meet on average, and the original (inflating) spacetime is never completely eaten up: this epoch of inflation is eternal.

Each undisturbed bubble contains a homogenous open universe, which if there is a secondary epoch of inflation, could be consistent with our observable universe. Some of the properties of our parent vacuum could be imprinted in the density fluctuations produced during this secondary epoch of inflation (even allowing us to probe the dimensionality of our parent vacuum, as described in this paper by Graham, Harnik & Rajendran Phys.Rev.D82:063524,2010), providing one observational check on the theory of eternal inflation. However, these effects are typically on very large scales, where there is a large theoretical error (due to cosmic variance), and are therefore difficult to distinguish from the standard picture. Another possibility comes from the fact that although the bubbles do not merge completely, any given bubble will undergo many collisions with other bubbles. Each collision perturbs the bubble interior, giving rise to inhomogeneities. If any of these collisions affected the observable portion of our bubble interior, the resulting inhomogeneities are imprinted on the cosmic microwave background, opening up the exciting possibility of directly observing the dynamics of eternal inflation.

Even this is still quite difficult, since the signal from a bubble collision must make it through the second epoch of inflation I mentioned above. The longer inflation lasts inside our bubble, the weaker the signal. In addition, since we only have causal access to a small portion of our bubble interior, we only see a subset of all the collisions. To expect to have a collision in our past, the (exponentially suppressed!) probability of bubble formation in our parent vacuum must be balanced against the ratio of energy scales in our parent vacuum and the secondary epoch of inflation inside of our bubble. Assessing if these criteria can be met requires a detailed theory (say of a set of string theory compactifications), which at the moment we do not have.

However, in the space of possible theories, there are cases where bubble collisions are potentially observable and expected to be there. We can therefore focus on constraining, and possibly verifying, those theories which give rise to signatures that are observable with current and future technology. Although it is certainly possible (and perhaps very likely) that we live in an unfortunate region of theory space where there are no signatures to be found, the significance of a definitive detection of other bubble universes is hard to understate. This outlook shifts the questions being asked from "what is the best fundamental theory and what does it predict?" to things like: Given the set of possibly observable collisions, what type of signatures would they leave? How would we go about detecting the signatures of a potentially observable bubble collision in the CMB?

The latest installment in trying to answer these questions, which I will describe in the remainder of this blog post, can be found in a pair of papers I wrote with Stephen Feeney, Daniel Mortlock, and Hiranya Peiris (arXiv:1012.1995v2 & arXiv:1012.3667v1. Important previous work on these questions includes papers by Chang, Kleban, and Levi as well as Czech, Kleban, Larjo, Levi, and Sigurdson, and some of the work I've done with Aguirre, Shomer, and Tysanner. Building on this previous work, we outlined a generic set of signatures of bubble collisions in the temperature fluctuations of the CMB, and designed an algorithm that targets these signatures, which we then applied to the WMAP 7-year data release.

First, let's talk about the generic signatures we might expect for a bubble collision. The spherical (and Lorentz boost) symmetry of two colliding bubbles implies that a collision will have circular symmetry on the CMB sky. The fact that a collision affects only a portion of the bubble interior, together with this circular symmetry, implies that the temperature pattern will be confined to a disc. Depending on how the collision propagates through our bubble interior, the temperature and its derivatives need not be constant across the boundary of the disc. Finally, the inhomogeneities produced by the collision are stretched by inflation, implying that the temperature modulation will be very broad inside the disc. The signature is therefore a circular hot or cold spot, with a possible temperature discontinuity along its edge, which we specify using a five parameter phenomenological model.

Of course, there are lots of hot and cold spots in the CMB, so how does one identify a bubble collision? Finding and explaining "weird" features in the CMB data is in general a dangerous business. For example, do the fluctuations spelling out Stephen Hawking's initials really need an explanation? To avoid such pitfalls, our methods are as close to a blind analysis of the full sky data as possible. An optimal search algorithm would consist of taking the full sky data, and asking if the addition of an arbitrary number of bubble collisions at arbitrary locations on the sky provides a better fit to the data than the standard picture of purely Gaussian fluctuations. Unfortunately, this is computationally impossible, and so we have designed a method to segment the sky into regions which have bubble collision-like fluctuations, which are then analyzed further.

This first step of segmenting the sky is accomplished using wavelet analysis. Wavelets provide information about the position and angular scale of features in the CMB data. Comparing the strength of a signal in the data to the signals obtained from simulations with and without bubble collisions, we can locate the most promising features at a variety of angular scales. Within these "blobs," we then look for a circular temperature discontinuity. Finally, we determine if the addition of a collision is a better fit to the data than the standard hypothesis of Gaussian fluctuations using Bayesian model selection (the degree to which the bubble collision hypothesis is preferred is quantified through the "evidence ratio").

Using simulations of the CMB data with bubble collisions, we segment the parameter space of possible collision strength into regions in which our algorithm would: definitively detect a collision, would have some sensitivity to the presence of a collision, or would not be able to detect a collision. We control for systematics by applying our pipeline to a full simulation of the WMAP experiment, providing a set of realistic data containing no collision. We found that the presence of a detectable circular temperature discontinuity was the most distinguishing evidence for a bubble collision. Applying our algorithm to the WMAP 7 year data release, we find no evidence for circular temperature discontinuities. However, we identify four features which are consistent with being bubble collisions. These features all have best-fit parameters in the region of parameter space we are sensitive to, and yield evidence ratios consistent with similar simulated bubble collisions. However, in this region of parameter space the ability to make a definitive detection is strongly dependent on the level of experimental noise and the particular realization of the background Gaussian CMB fluctuations. We therefore cannot claim that we have detected bubble collisions, but also cannot rule out the possibility that these features are bubble collisions.

The good news is that our ability to detect bubble collisions will markedly improve with data from the Planck satellite. Better resolution and lower noise will improve every step of our analysis pipeline, and the much better polarization data can be used to find complementary signatures of bubble collisions (derived by Czech, Kleban, Larjo, Levi, and Sigurdson). We will be analyzing this data as soon as possible, which will hopefully remove the ambiguity in our results.

It's also important to emphasize that bubble collisions during eternal inflation are not the only way to get circular spots in the CMB. Some other hypotheses include

textures, primordial inhomogeneities, and kinks in the path of the field driving inflation. Our analysis pipeline can be applied to test these theories as well, and used to compare how well each hypothesis fits the data. This analysis will also shed light on the possible observability and distinguishability of bubble collisions. With any luck, in the coming year or two, we will have a more complete picture of what might be out there!