In the video below, I explain how to derive Kaluza Klein action which occurs from generalizing the Einstein-Hilbert action to five dimensions. The grand implication of this is that gravity and electromagnetism are unified!
Our new article was recently published in The Journal of Geometry and Physics. It is shown that under certain conditions, The Einstein Field Equations have the same form as a fold bifurcation seen in Dynamical Systems theory, showing even a deeper connection between General Relativity and Dynamical Systems theory! (You can click the image below […]
Here is a link to my lectures on nonlinear dynamical systems given at York University during the Winter semester of 2017. These lectures start off with manifold theory, and end with examples in biology, game theory, and general relativity/cosmology.
In the final two lectures of my differential equations class , I discussed how Dynamical Systems theory can be used to understand and describe the dynamics of cosmological solutions to Einstein’s field equations. Videos and lecture notes posted below: Lecture Notes:
New #cosmology paper: https://arxiv.org/pdf/1609.01310.pdf Using a dynamical systems approach to provide a unifying framework for the AdS, Minkowski, and de Sitter universes. #physics #mathematics #science
I have a talk today at Perimeter Institute: here are the slides. I basically showed that even a stochastic multiverse must be generated by precise initial conditions!
Most people when talking about cosmology typically talk about the universe in one context, that is, as a particular solution to the Einstein field equations. Part of my research in mathematical cosmology is to try to determine whether the present-day universe which we observe to be very close to spatially flat and homogeneous, and very […]
I tried to derive a general Einstein field equation for an arbitrary FLRW cosmology. That is, one that can handle any of the possible spatial curvatures: hyperbolic, spherical, or flat. Deriving the equation was easy, solving it was not! It ends up being a nonlinear, second-order ODE, with singularities at a=0, which turns out to […]
My new paper has now been published in Annalen der Physik, which is a great honour, because 100 years ago, Einstein’s General Theory of Relativity was also published in the same journal. This paper describes a method by which one is able to determine whether a given spatially flat cosmological model produces finite-time singularities, and […]
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 […]