What goes into making a cosmological model? Here is a presentation (that was part of my Ph.D. dissertation) that I have reproduced and embedded here to describe what actually goes into the making of a cosmological model. After describing some general properties, I describe specifically a early-universe model that contains a viscous fluid and a magnetic field.
The background mathematics can be found in this old presentation of mine here:
A recent lecture and a series of interviews has been posted online where cosmologist George F.R. Ellis discusses the issue of fine-tuning in biology at considerable length and in considerable detail. Of course, the larger theme here is that to discuss and understand things like Darwinian evolution properly, one needs to have an understanding of the underlying physics, as it is laws of physics that allow life to emerge and for Darwinian evolution to occur in the first place. Here are the lectures:
A big part of my research involves dynamical systems theory. A lot of people don’t know what this is, at least, they don’t have a very good idea. It has not helped that the vast majority of Canadian university physics programs have deemphasized classical mechanics and differential equations, but that is an another story!
Anyways, here are some notes describing what they are and how they work.
Since I expect the concept of gravitational waves to once become very popular in the next few days, I wrote some quick notes on them, I.e., where they come from. They are handwritten, as I didn’t have time to LaTeX them, but, hopefully, they’ll be useful to interested readers!
Also note that, gravitational waves are not necessarily evidence of inflation. I wrote a paper a few years ago, describing a anisotropic early universe that had an epoch of plane waves that isotropized to our present-day universe. It can be seen here. It was subsequently published in Physical Review D.
Anyways, here are the notes (Interested readers should see the classic texts by Misner, Thorne, Wheeler, Landau and Lifshitz, or Stephani for more details).
One of my earliest works was deriving equations which themselves were forms of Einstein’s field equations that described the state of the early universe, which may have had dominant viscous effects. I was delighted to learn that these equations were published in Springer’s Handbook of Spacetime Cosmology textbook.
Here is a snapshot of the textbook page citing these equations:
Our new paper was accepted for publication in Physical Review D. The goal of the paper was to calculate the probability that a multiverse could emerge from a more general background spacetime, in this case, Bianchi Type I coupled to a chaotic inflaton potential. Basically, we found that a multiverse being generated from such a scenario has a small probability of occurring. Further, the fine-tuning problem that the multiverse / eternal inflation is supposed to solve doesn’t actually occur, because fine-tuning is still required of the geometry of the background spacetime, the initial conditions, and most importantly, the amount of anisotropy.