Tuesday, March 18, 2014

Twisting, Tumbling and Rapidly Expanding Space-Time

This is the sort of news that excites me.  It's when there's a huge revelation towards advances in science that shows some hard progress.  It's the sort of thing that, when I read it, makes me think humanity isn't entirely 120% doomed.  I mean, this coupled with the additional pleasant news that Fred Phelps won't likely be alive that much longer (fingers crossed for Pat Robertson to follow along next)...  it's like there is some reason to get up in the morning and not feel unbounded shame for being considered part of the species Homo Sapiens.  I'm talking about the news regarding the direct evidence of the Inflation hypothesis.

I will warn you, that as a science geek, I'm going to get a little involved here, but I'm going to avoid getting all too technical, as I am merely a geek, and not an actual student of astrophysics.  My level of understanding of the actual mathematics down to its nitty-gritty details is nowhere near that of someone who is actually in the field.  That said, I am more aiming to take it down to some level of detail in the interest of putting those details out in a way that should be somewhat understandable to a novice.

I will begin by explaining the need for the inflation hypothesis.  The directly observed fact that the universe is expanding leads us back to the extrapolation that if we think backwards in time, the universe would have been smaller, and in theory, you could follow it all the way back to the point where it has almost zero volume.  Of course, as far as our observations take us, it can only depend on the remnants of the universe that exist, and that means we can find things like the cosmic background radiation, and that will at most take us back to the point where the universe was large enough that it was no longer opaque, and radiation could actually be emitted and seen.  This much of the expansion of the universe is generally called the Big Bang Period, and it's the part of the overarching Big Bang Theory that can be considered confirmed fact.  Going further back to the Big Bang Singularity is a reasonable extrapolation and it includes a number of models for nucleosynthesis, existence of matter, etc., but didn't really have any strong direct evidence, though it has loads of indirect evidence.  Furthermore, anyone would tell you that the Big Bang by itself is incomplete in that it has a large array of loose ends that needed tying, and this is where a lot of conjectural models, inflation included, came up.

It can be a bit confusing that the word "theory" comes up here in models such as "M-Theory" and so on, but it should be noted that they are are not called "The Membrane Theory" or "The String Theory" in the way we call Einsteinian gravitation "The Theory of General Relativity" or evolution "The Theory of Evolution by Natural Selection"...  These former models are tagged with the word "theory" in the sense that they are theoretical foundations and mathematics for a collection of hypothetical models that can explain a number of things, but have no real evidence explicit to their models.  In this particular case, they are "theories" in the same way that "music theory" is a theory.  For a long time, inflation fit in this category.  It really wrapped up a lot of the questions about the Big Bang in a nice little bow, but beyond that, it didn't have much of anything going for it scientifically.

In particular, it was a solution to the horizon problem.  The cosmic background radiation is largely isotropic and homogeneous.  This is a problem because a singularity for the very beginnings of space and time is most likely to have engaged in its initial expansion by way of small quantum energy state fluctuations.  This alone works mathematically, but quantum mechanics is noisy by nature.  After all, it puts everything into a wave state, and that means a minimum amount of ripples here and there and everywhere even in the lowest energy state (i.e. Heisenberg's Uncertainty Principle).  Yet when we look at the cosmic background, there is no such unevenness.  The amount of fluctuation is only on the range of 1 thousandth of 1 percent. This is the sort of thing we expect for things like contained gases because energy transfer across matter in a contained vessel has time to reach equilibrium.  For the universe, this doesn't work because space and time are always expanding.  And in fact, it's expanding faster than the speed of light; which means that even radiative transfer of energy (which is limited to the speed of light) cannot provide causal contact for equilibrium.  This is really where inflation comes in because it proposes that there was a short period in the early universe (from ~10-35 to 10-32 seconds of age) where the universe grew at an exponential rate -- about a factor of 1050 times larger in that short expanse of time (some disagreement, but we know it has to be at minimum 1026 times).  In the same sense that sharply pulling on a wrinkled cloth will smooth it out, this is what happened to space time.  In addition, it also removes a lot of the curvature of space-time, which was another problem for the Big Bang by itself (the fact that the universe appears to be flat).

The fact that the curvature of the universe is so small as to appear flat and that the universe is largely homogeneous are predictions of inflation, but make for, at best, indirect evidence for the model.  After all, we can put forth more than one conjecture to address these problems.  However, we can get more specific to inflation by accounting for the fact that it alone posits this rapid expansion of space-time for a short period.  This sort of massive change in the geometry of space-time can't really be without any markers, and so one of the basic predictions is that inflation of this type (specifically, Linde's "new inflation") should yield a signature gravitational wave.  The observational evidence that the BICEP2 experiment has put out indicates exactly this.  Specifically, what it found was a type of polarization of the light emitted in the cosmic background radiation.

There's more than one type of polarization of light of course.  As we already know, the universe is pretty darn homogeneous, but there is still some variation (we exist because of that variation), and this means there is still fluctuations in the density of the plasma of the early universe.  Maps like the one below show where there is some tiny temperature variations in the CMB, and it's these differences that ultimately became stars, galaxies and planets.
This variation qualifies as a scalar field perturbation.  In this case, the scalar quantity that links to it is one of temperature, but the source field that caused it is given the name "inflaton" field only because we can't really pin down what its real nature and/or properties are without further observation.  Scalar fields, though, can only create E-mode polarizations.  That is to say, polarization with no curl component and only has a gradient component.  Tensor fields like gravitational fields produce both E-mode and B-mode polarizations, the latter of which are divergence-free and have only a curl component.

Of course, the difficult bit is differentiating between B-mode polarization that happened as a result of inflation in the early universe and B-mode polarization that happens due to gravitational phenomena afterwards.  We've directly observed both gravitational waves as well as B-mode polarization from gravitational lensing.  Moreover, a lot of B-mode polarization we observe is really modified E-mode.  The key we have to look for is the fact that inflation was expansion of all of space and time, just as the Big Bang itself is.  That means that the B-mode polarization we should be looking for should be everywhere in the cosmic background and exhibit the same sort of homogeneity (and likewise, the same order of lack thereof) as the cosmic background itself.  Since we are dealing both with a gravitational perturbation as well as a scalar perturbation (the aforementioned "inflaton" field), there needs to be a certain amount of energy that was expended in scalar perturbations and a fraction of it that went into gravitational or tensor field perturbations.  The ratio of the amplitudes of the wave fluctuations in scalar vs tensor fields is given by r = AT/AS (tensor amplitude divided by scalar amplitude).  As it so happens, there is an interplay between the size of the inflaton field density perturbations, the size of the gravitational wave perturbations, and the total amount of roll that the field goes through along its potential energy "hill".  The rolling is proportional to 10x the square root of r.  Meaning that r > 0.01 is enough for the inflation field to roll by more than the Planck scale (~1.22 x 1019 GeV).  If inflation only happened on this scale, though, there's probably not going to be any way to detect the signature gravitational wave any time soon.  There's enough gravitational lensing from distant stars and galaxies all over the place that the B-mode polarization "noise" would exceed the "signal."  There are various reasons that I can't completely elucidate that actually show it has to be much greater than this...  I can't elucidate them because I'm not well-versed enough in the literature to really explain it well.  In order for BICEP2 to really get a solid (i.e. statistically significant) bead on the primordial gravitational wave, r would have to be around 0.2, which is actually quite enormous.

In fact, that's exactly what it was...  well, with an error range of [-0.05..+0.07].  And with a significance of 5-sigma.  There was much ass, and lo, it was kicked.

This is strong direct evidence for the Big Bang all the way back to near the singularity and for inflation itself.  Now what should be made clear is that we're only at the point of getting closer to understanding the early universe, but we don't really have a clue what caused inflation or what caused it to stop (as such, inflation can't really be considered to have graduated to "theory" status).  We just now have very good reason to believe it happened.  While that sounds like I'm tempering the awesome news here, it's actually amazing in its own right to think that we can actually observe the remnants of something that happened when the universe was only 10-35 seconds old right now... 13.82 billion years later.  That is nothing, if not a powerful statement of just how amazing are the things we can do at the forefront of scientific understanding.  On the face of it, this is not something that is going to change your life in the here and now, but it's the sort of thing that advances the knowledge that humankind has going forward, and there will never be a way for that to be a meaningless endeavor.  It's one thing as part of the atheist community to put a lot of effort in swinging a club at the rubbish and dregs of humanity that religion likes to produce, but there is always something to be said for those who rake themselves from that rubbish and produce something of real value.  This is one of those times when the cream that has risen to the top deserves that sort of attention.  Clap your hands.