It’s now time to launch another thread, one that is somewhat overdue as a means of transporting posts from the old version of these forums to the new version, and one that covers a topic that will be of much utility value in the future.
But before revisiting that past material, I need to provide a little background, and a little history, to explain certain key concepts covered in my past posts.
Quite a few people have, by now, no doubt heard of string theory, which was originally launched as a means of solving some difficult problems in particle physics, by treating those particles as one-dimensional vibrating “strings”. String theory has long since expanded its remit from these beginnings, not least because cosmological physicists realised fairly quickly, that the mathematical tools of string theory could also be applied to problems in the field of cosmology, and thus began the earnest pursuit by physicists of string theory as a possible candidate “theory of everything”, because its findings could apply both to the small and the large scale, in the absence of a fully working theory of quantum gravity. Indeed, one of the hopes that physicists had for string theory, is that it would point them toward that longed-for fully working theory of quantum gravity, but I digress.
Given the early promise string theory offered when first launched, it’s not surprising that it became popular among cutting-edge physicists. As a corollary of this popularity, other frameworks in physics took something of a back seat, one of these being supergravity, but in one of those amusing twists of scientific history, some interesting developments arose, in no small part due to the popularity of string theory and its extensions.
One of those extensions took the form of asking the question, “if we’re going to extend particles into one dimensional entities, why stop there?” Cosmologists, for various reasons, started pushing this particular envelope quickly, and started investigating whether or not objects of two and more dimensions, analogous to strings, were  possible, and  consistent with known physics. The answer to both questions was quickly determined to be a resounding “yes”, and so, what has come to be known as braneworld theory was launched - a natural, if mathematically intense, extension of string theory.
Briefly, a brane (the word being a contraction of “membrane”) is any object that plays the role of a fundamental entity in physics, be it a unit of spacetime or a particle like entity. Prefixing the word “brane” with a number tells you how many dimensions the brane in particular has - 0-branes are point particles, 1-branes are strings, and then we have 2-branes (sheet like entities) and upward.
There are, however, some restrictions on what is possible with branes. One important restriction being that they have to behave in a manner consistent with mathematical entities known as manifolds, which are, in effect, a means of defining generalisations of geometrical spaces. However, while the requirement to be, in effect, a manifold, places some restrictions upon brane behaviour, manifolds are themselves flexible and powerful objects, sometimes imbued with additional rich structure, so for example manifolds can have topologies associated with them, and can also be capable of supporting calculus operations or linear algebra operations upon them.
One important aspect of manifolds, is that multi-dimensional manifolds can be compactified - namely, subject to various mathematical transformations that shrink extra space dimensions “out of sight”, so to speak, while leaving the three familiar space dimensions macroscopically visible.
This ability to compactifty manifolds makes them eminently suitable as environments for string theory or M-theory operations, and one particular class of manifolds, namely Calabi-Yau manifolds, play a pivotal role in more recent string theory and M-theory work.
Now, it’s at this point that we encounter the twist of history I briefly alluded to above. This arises from the fact that physicists had an embarrassment of riches arising from 10-dimensional string theory - they had no less than five variations on the theme, all of which were internally consistent, and capable of modelling the universe as we know it, but with no means of determining which of those five variations was the one applicable to the observable universe. No test, either mathematical or empirical, existed to distinguish between the five.
It’s at this point that supergravity, or its more developed form, M-theory, made a resurgence. Courtesy of the fact that it was found that those five 10-dimensional string theory models were subsets of one, overarching, 11-dimensional M-theory model.
It was at this point that two physicists working in this framework, Paul Steinhardt & Neil Turok, made an interesting discovery. Namely, that it was possible to build 10-dimensional branes out of Calabi-Yau manifolds, have them move freely in a larger 11-dimensional space, and then work out what happens when two such branes collide.
This turned out to be a particularly elegant means of instantiating a universe such as the one we observe ourselves to inhabit. Elegant because it solved two major problems arising from standard Big Bang cosmology - namely, how to deal with the “singularity problem”, and how to supply energy to the newly instantiated universe, facilitating matter synthesis. In the case of the singularity problem, that quite simply vanished, and an exchange of energy between the colliding branes and the newly instantiated universe (itself residing in a new, causally disconnected brane after the collision) solved the initial energy input problem.
There’s another elegant feature to this work, however. Namely, that it provides a testable prediction.
One of the consequences of the braneworld collision envisaged by Steinhardt & Turok, is that primordial gravitational waves are sent rippling through the newly instantiated universe at the start. Each of these primordial gravitational waves has a wavelength. But the fun part is, these wavelengths conform to a pattern, known as a power spectrum.
To construct a power spectrum, you plot wavelength on the x-axis of a graph, and amplitude (or frequency of occurrence, which is a proxy for amplitude thanks to wave superposition) on the y axis. The resulting graph is a power spectrum for the waves being observed, and power spectra for light sources are wonderfully informative about the behaviour of those light sources.
If your graph is a flat straight line, then your measuring instruments are receiving waves of all wavelengths in equal quantity. If on the other hand, the graph is a sloping line or a curve, then that power spectrum is biased in favour of specific wavelengths, which tells you that some interesting processes are taking place.
This is where Steinhardt & Turok score highly at this point, because their braneworld collision model predicts that the power spectrum for primordial gravitational waves will be biased in favour of short wavelengths. This prediction is one of the main motivating factors behind the recent rush to build working gravitational wave detectors by scientists - precisely to test that prediction.
Of course, there’s much work to be done first, such as learning how to discriminate between primordial gravitational waves, and gravitational waves of more recent origin, such as those arising from black hole mergers. But once the requisite groundwork has been completed, that prediction will be tested, and if that predicted power spectrum is found in the data, Steinhardt & Turok pick up a Nobel Prize.
From this point on, I’ll not only be providing as complete an exposition of the papers in question as I can, but some interesting ramifications that arise from this braneworld collision model being found to be applicable to the instantiation of our observable universe. Life will become very interesting indeed when I cover those ramifications. Watch this space!