Thursday, 31 March 2016

Before the Big Bang Part I

This post will be the first in a series of posts dealing with what our best models of the pre-Planck cosmos are, what evidence supports them, what might falsify them, and what steps are being taken to make some progress. It was originally motivated by a forum post in which somebody reasonably scientifically literate asserted categorically that there was no way we could ever know what happened before the Big Bang and that all our models were unfalsifiable. While it's certainly true that such knowledge presents some extremely difficult challenges, our pre-Planck hypotheses, as with all hypotheses, have essential features that have predictable, testable consequences that we should in principle be able to observe. For example, you'll remember all the hoo-ha a couple of years ago about the BICEP2 results (I'll cover this in some detail later, in case anybody isn't familiar with it). Had they withstood scrutiny, they would have comprehensively falsified one of our best pre-Planck models, namely the Ekpyrotic, or 'brane-worlds' model. 

As it is, if this B-Mode polarisation in the CMBR is observed and we can rule out sources other than those arising from an inflationary period in the first Planck second, then brane-worlds will be dead in the water. Further, and given some other details, it's possible that eternal inflation can gain some traction, and that will definitively rule out the idea that the BB that marks the past-boundary of our local cosmic expanse constitutes the beginning, although there are still problems to be faced, such as those arising from the BGV theorem so beloved of  Craig and other apologists who don't understand it.

But I'm getting ahead of myself. I'll cover much of this later, including BGV theorem, but I should lay a little ground work.

Before that, I wish to make a linguistic distinction so that I can plough on without a probable derail. I use the term 'universe' to deal with the whole shebang, and the term 'cosmos' to deal with our local cosmic expanse. Definitionally, they're identical, and this is merely my own convention for dealing with the distinction, because it makes matters clearer. Indeed, I might as well firm up this distinction for later clarity.

There is a long-standing problem with the multiple ways the word 'universe' is employed, and it requires a little history:

For most of history, the word 'universe' simply meant 'that which is', and referred to what we can observe in the night sky. It wasn't actually thought to be that large, in universal terms (pardon the pun). Sure, it was always going to be huge, but it was thought that the entire universe was contained within just what we think of as our own galaxy. Indeed, almost all of what can be seen with the naked eye is contained within the Milky Way. Hubble, of course, changed all that in the 1930s, when he demonstrated that some of the things that had been historically observed were too far away to be part of our galaxy, and that it was all rushing away from us. Did the meaning of the word 'universe' change at that point? Of course not! It still meant 'that which is', but it now encompassed a good deal more in our perception, because our understanding of what is had expanded.

So now, we understand that our local cosmic expansion may not be the entirety of 'that which is'. Does that change the definition of the word 'universe'? of course not! The word still means 'that which is', but now it encompasses whatever (if anything) preceded or lies outside of our local cosmic expansion.

In short, there is, and can be, only one universe, because the universe is 'that which is' and encompasses all of existence. 

Now, I can hear the objections already, namely that physicists and cosmologists talk about 'other universes' and 'multiverse' all the time, so I should spend a moment addressing that. 

The first thing to note is that cosmologists and physicists, unlike evolutionary biologists, are not used to having their words dishonestly equivocated by propagandists.

The second is to note that when cosmologists and physicists write, they tend to write for other cosmologists and physicists and, as such, their language is a) geared toward an audience that understands what they mean when they use the word, based on context and b) often lazy. For an example of the latter, one need only look at how popular science authors treat the concept of entropy as disorder, with very little qualification of what they mean. More on that particular topic in a near-future post .   

Since even in the most basic definition of the word 'universe', one finds 'the entirety of time and space', and since it's far from clear that time began at the big bang, then the most that can be said is that our local cosmic expansion arose from the big bang, not the universe. Indeed, the standard big bang model doesn't even deal with the beginning of our local cosmic expansion, for reasons I shall be dealing with shortly.   

What all of the above should make clear is that our language is often insufficient to deal with the deep principles of what constitutes the universe, and how careful we have to be. This is not a failure of understanding, but a failure of language. It is precisely for this reason that I am such a pedantic twat, and why semantics, oft-maligned and dismissed as irrelevant, is so important. Semantics is the heart of communication and, in my opinion, any dismissal of an argument based on the idea that 'it's just semantics', is not just fallacious, but indicative of a failure to think critically. It is, to use a favourite football analogy, the equivalent of diving in the box.  
This is why I employ the distinction I do. I refer to that which arose from the big bang as the cosmos, and the universe as a whole as the universe, while recognising that this may be a distinction without a difference.

So, a little history of cosmology:

Let's start with the Big Bang itself, because it was very much a conjecture, albeit one that was rooted in good science. In fact, we weren't absolutely certain it WAS good science at the time, because it was rooted in General Relativity, which was a new theory then.

The Big Bang is, in a nutshell, the name we have for the fact that the cosmos is expanding. It isn't the beginning of anything in any more than the most theoretical sense. There also isn't a single Big Bang theory, despite popular contrivances to that effect. As a famous physicist once commented, when asked by an apologist 'were you there at the big bang', the correct response is 'yes, I am', because all extant theories have a Big Bang in them..

It stemmed from the work of Georges Lemaitre, who first proposed that the cosmos was expanding based on Einstein's General Theory of Relativity from 1915. This was also independently proposed by Alexander Friedmann. Einstein had actually noted that GR implied that the cosmos couldn't be static if the fundamental equations of GR were taken at face value, and he didn't like this implication, so he introduced a fudge factor into the equations, the so-called Lambda term, or cosmological constant. A lot has been said about this over the years by people who want to romanticise, but Einstein was correct in calling it a blunder, despite the fact that modern cosmology has reintroduced the term. We'll come to that again shortly. Suffice it to say that Einstein's motivation for introducing it was entirely unjustified, because it was only because he believed the universe to be static (often, and not to be, confused with 'steady state', another term I'll come back to) and eternal. Lemaitre, a Belgian cleric, followed the equations, and posited first an expanding cosmos, and then the idea that it had a beginning in the so-called 'cosmic egg' hypothesis. Lemaitre was also the first to derive what later became known as Hubble's Law, which tells us in essence that the further away something is, the more quickly it's receding from us.

All of this was prior to Hubble actually making his famous observations, first that there were galaxies outside our own (it had been thought that extra-galactic sources were actually dust clouds or nebulae inside our own galaxy; Hubble didn't just show that the cosmos is expanding, he showed that there was far more of it than we'd thought, as detailed above), then that they were all receding from us.

So, now we have our expanding universe, and the classic Big Bang theory, but we've got some problems:

First, there's the horizon problem, a very specific problem with the classic Big Bang, namely that, as we look around the cosmos, we measure the temperature to be pretty much the same in every direction (isotropic). You'll have seen the images from COBE (Cosmic Background Exporer) and WMAP (Wilkinson Microwave Anisotropy Probe), no doubt, and the more recent Planck images of the CMBR:

Beautiful hi-res image here

You'll see that there are differences in that image, between the blue and the red bits. As you'd expect, the blue bits are the coldest bits and the red bits are the hottest bits (note that this image doesn't deal with the temperature of space, because space can't really be said to have a temperature; this is the temperature of the radiation pervading space, a measure of how quickly particles are moving; a bit of an aside, but it may become important later). Anyhoo, it looks like the temperature varies a fair bit, until you realise what those differences represent. The actual temperature is about 3 Kelvin, or -270 degrees Celsius, 3 degrees from absolute zero, and those differences are tiny, representing no more than a few 10,000ths of a degree. This is minuscule, and the standard Big Bang can't account for it. The problem is that at no point during a standard expansion have the furthest reaches of the cosmos been sufficiently close together for them to have reached thermal equilibrium, because they were always so far apart that even light couldn't have traversed the distance in the time the cosmos had been around. This was known as the 'horizon problem', and was one of those embarrassing things that arises now and then that the relevant scientists don't talk about. More on this shortly.

Then there's the flatness problem, which is a problem concerning why we measure the cosmos to be flat (Euclidean) on large scales.

The universe can basically take three 'shapes' on large scales (possibility of equivocation here, as I'll be using the term 'shape' to describe the actual topology of the cosmos shortly, so be aware); Flat, open and closed. 

The easiest way to think of this is in terms of either triangles or parallel lines. If the universe has positive curvature (Ω>1), triangles will have internal angles adding up to greater than 180 degrees and parallel lines will converge (i.e. Euclid's fifth postulate does not hold). This is like a sphere (a torus is a possibility).

If it has negative curvature (Ω<1), triangles will have internal angles adding up to less than 180 degrees and parallel lines will diverge (i.e. Euclid's fifth postulate does not hold). This is like a saddle, or a Pringles potato chip. 

If the curvature is zero (Ω=1), the internal angles of a triangle add up to 180 degrees and parallel lines will remain parallel (i.e. Euclid's fifth postulate holds). This is like a flat thing.

Note that this is a 2D representation (both text and image) of a higher-dimensional principle.

So why is this a problem? Well, it's a fine-tuning problem to do with the energy-density of the cosmos. Note that fine-tuning here isn't open to apologetic manipulation, i.e. we're not talking about something that had to be fine-tuned by somebody twiddling knobs, it refers to specific parameters having to fall within a narrow range of values if the model in question is correct. In this instance, it means that the energy density of the cosmos has to be almost perfectly within a certain narrow range in order for the cosmos to be flat on large scales. In the above text, the energy density is the Omega term in the brackets. It's worth noting that, in the case of the universe being flat, the possibility is there for the cosmos to be infinite in extent.

Before I move on, a small clarification of what is meant by the terms 'expansion' and 'inflation', because they're not the same thing:

Expansion is simply the observed fact that everywhere we look, galaxies are receding from us, and the further away they are, the quicker they're receding (indeed, beyond a certain distance away, they're actually receding at greater than light speed, which we might naïvely think impossible, but it doesn't violate special relativity, because nothing's actually travelling through space at greater than c; I'll come back to this).

Inflation is a very specific idea, often confused with expansion. Inflation is a bolt-on, a fudge, if you like, designed to explain the 'horizon problem' dealt with above.It refers specifically to a period of very rapid inflation in the earliest moments of the cosmos, which is required to smooth everything out so that we see the degree of isotropy (sameness) that we observe.

So, we have our standard Big Bang model, which is rooted in observing that the cosmos is expanding. Wind it backwards, and it soon becomes clear that, at some point in the past, everything in the cosmos was much closer together. Then, in 1970, Hawking and Penrose presented a paper called The Singularities of Gravitational Collapse and Cosmology, which showed that, if General Relativity holds under the appropriate conditions, any cosmos that is spatially closed, or constitutes an object undergoing relativistic gravitational collapse, must end in a spacetime singularity. It's worth noting here what's actually meant by that term, because it's the source of much confusion, not least because the second word of it has two distinct definitions. The first is the popular conception, namely an area of infinite density and infinite curvature, physical in nature, while the second is a set of conditions that our physical theories are unable to describe. The condition described in Hawking and Penrose's paper is of the former type, and this is the idea that most people have of how the cosmos began, namely an expansion from this physical singularity. It's interesting to note that neither Hawking nor Penrose think that this describes our universe, not least because this type of singularity is actually an asymptote according to Quantum Mechanics, which means essentially that it's prohibited. Indeed, Hawking had this to say as far back as 1988:

"The final result was a joint paper by Penrose and myself in 1970, which at last proved that there must have been a big bang singularity provided only that general relativity is correct and the universe contains as much matter as we observe. There was a lot of opposition to our work, partly from the Russians because of their Marxist belief in scientific determinism, and partly from people who felt that the whole idea of singularities was repugnant and spoiled the beauty of Einstein’s theory. However, one cannot really argue with a mathematical theorem. So in the end our work became generally accepted and nowadays nearly everyone assumes that the universe started with a big bang singularity. It is perhaps ironic that, having changed my mind, I am now trying to convince other physicists that there was in fact no singularity at the beginning of the universe – as we shall see later, it can disappear once quantum effects are taken into account."

Now, this has some interesting implications, the first of which is what largely motivates the idea that time began at the Big Bang. It's an idea that stems again from relativity, and it's about the deep relationship between space and time and the equivalence principle (the idea that being immersed in a gravitational field and being accelerated are the same thing). It boils down to the fact that, at a singularity, because of the acceleration, time stops. I've mentioned before that this doesn't actually mean that time didn't exist before the singularity, only that the singularity didn't experience it (in much the same way that photons don't experience time, yet time still exists).

So, now that's out of the way, we can summarise the standard Big Bang model as the idea that spacetime arose from a physical singularity some 13.72 billion years ago. We're aware that there are some problems with it; the horizon and flatness problems discussed previously, and a couple of other issues, such as the coincidence problem, which is that the vacuum and matter densities appear to be roughly equal, and the smallness problem, which is that the Lambda term from General Relativity (the cosmological constant) is so small.

Then, in the 1980s, Alan Guth had an interesting idea, namely what if the cosmos had undergone a period of hyper-rapid inflation very early on? That would mean that the furthest constituents in the cosmos could have been sufficiently close together to equalise. This also solves a couple of other problems concerning the shape of space and the energy density of the cosmos. This inflation would have massively inflated space from a singular density, exponentially expanding to about the size of an atom or so (yeah, that huge! lol).

So what's inflation?

Inflation is simply the idea that, very early in the history of the cosmos, there was a period of extremely rapid expansion. During this period, quantum fluctuations occurred as normal but, because the cosmos was expanding at a ridiculous rate, these fluctuations were stretched out. It is this stretching of those fluctuations that we see as the tiny inhomogeneities we observe in the CMBR. Moreover, the details of the theory tell us that those inhomogeneities would have generated gravitational waves, and that those gravitational waves would a) fall within a certain range of the energy spectrum and b) polarise the photons in the CMBR in a certain mode, the so-called B-Mode polarisation that the BICEP2 experiment was thought to have identified.

Here's an image of the patch of the CMBR they were looking at with the polarisation indicated:

You can see the 'twisting' in a spiral formation around the hot spots. This was what they were looking at, as the photons were polarised (if you looked at them through a polarising filter, you'd have to tilt the filter to that angle in order to be able to see the photons) by the angles shown by the black lines. Unfortunately, the polarisation was discovered to be a result of dust, and once corrected, showed no sign of polarisation from primordial gravitational waves.

Here's Pulsar explaining:

"Here's the killer plot:

The black dots with error bars show the original BICEP/Keck results, the purple dots with error bars show the corrected results after subtracting the dust contribution found by Planck. The red line is the B-mode polarization that’s expected from gravitational lensing alone (so without primordial gravitational waves). Clearly, the new results show no hint of primordial gravitational waves, except for a slight (not statistically significant) excess signal around multipoles of order 200.

So for now, the champagne can be put back in the fridge. It's important to emphasize though that the BICEP experiment only looked at a small patch of the sky and at one particular frequency. We'll have to wait and see what the other ongoing experiments will reveal

One of the interesting things about inflationary theory, beyond the problems it solves, is that there is a broader theory dealing with how inflation occurs, and this broader theory has an implicit multiverse built in. The idea is that the fabric of the universe is constantly expanding, but different parts of the universe slow their expansion at different times, and this slowing causes little bubble universes to pinch off. That inflationary energy has to go somewhere, so it converts to the radiation that filled the early cosmos and became the seeds of later structure. This is well beyond the scope of current observation, though, and possibly inherently untestable, but the BICEP results, had they been confirmed, would have been taken by many to be strongly suggestive of a multiverse.

I should point out, regarding William Lane Craig's citation of BGV theorem as allegedly supporting his formulation of the Kalam, that Guth, for whom the G stands, does not think that, for example, time began at the Big Bang.

Here he is, comparing inflationary theory to the brane-worlds model, which will be up next:

"So far, it's been made to sound, I think for the purposes of simplifying things, that until the cyclic model, all scientists had believed that the big bang was the origin of time itself. That idea is certainly part of the classic theory of the big bang, but it's an idea which I think most cosmologists have not taken seriously in quite a while. That is, the idea that there's something that happened before what we call the big bang has been around for quite a number of years... In what I would regard as the conventional version of the inflationary theory, the Big Bang was also not in that theory the origin of everything but rather one had a very long period of this exponential expansion of the universe, which is what inflation means, and, at different points, different pieces of this inflating universe had stopped inflating and become what I sometimes call pocket universes."

He goes on to say:

"What we call the Big Bang was almost certainly not the actual origin of time in either of the theories that we’re talking about. … The main difference I think [between the inflationary theory and Neil and Paul's theory] is the answer to the question of what is it that made the universe large and smooth everything out. … The inflationary version of cosmology is not cyclic. … It goes on literally forever with new universes being created in other places. The inflationary prediction is that our region of the universe would become ultimately empty and void but meanwhile other universes would sprout out in other places in this multiverse."

Source, a radio interview with Guth and Neil Turok. 

Moreover, the theorem itself doesn't imply what Craig says it does. Here's the meat of the issue:

It stems from the work of Arvind Borde, Alan Guth and Alexander Vilenkin, and we can take a look at the abstract of the paper:

"Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating -- or just expanding sufficiently fast -- must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime."

Inflationary spacetimes are not past-complete - Borde, Guth & Vilenkin - Arxiv 2001

Note the bold bit. They don't say that the universe requires a beginning, or even anything remotely like it. They are saying that inflationary cosmology alone cannot explain some of the issues with the boundary conditions of the cosmos.

 That seems a good place to leave this post, because I'm going to move on to branes next, and that requires an awful lot of groundwork, including a potted history of SR, GR and the standard model of particle physics.