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Cosmology General Relativity Mathematics Physics Science

New Article Published in Journal of Geometry and Physics

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 […]

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Cosmology General Relativity Mathematics Physics Science

Dynamical Systems in Cosmology Lectures

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:

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Cosmology General Relativity Mathematics Physics Science

Attempts at a General Einstein Equation for an Arbitrary FLRW Cosmology

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 […]

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Cosmology General Relativity Mathematics Physics Science

New paper published on cosmological singularities

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 […]

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Cosmology General Relativity Mathematics Physics Science

Making a Cosmological Model

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 […]

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Cosmology education General Relativity Mathematics Physics Science

Equations Published in a Cosmology Textbook

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 […]

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Cosmology General Relativity Mathematics Physics Science Statistics Uncategorized

New Paper on Stochastic Eternal Inflation

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 […]

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Cosmology education Mathematics Physics Science

On The Acausality of Heat Propagation

In many physics and chemistry courses, one is typically taught that heat propagates according to the heat equation, which is a parabolic partial differential equation: , where is the thermal diffusivity and is material dependent. Note also, we are considering the one-dimensional case for simplicity. Now, let be a solution to this problem, which represents […]

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Cosmology General Relativity Mathematics Physics Science

Black Holes, Black Holes Everywhere

Nowadays, one cannot watch a popular science tv show, read a popular science book, take an astrophysics class without hearing about black holes. The problem is that very few people discuss this topic appropriately. This is further evidenced that these same people also claim that the universe’s expansion is governed by the Friedmann equation as […]

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Cosmology Lectures on the Web

Here are some links  to some excellent cosmology lectures on YouTube. The videos actually teach you cosmology, as you would see it in a university/college setting. They do require some knowledge of General Relativity, but one in principle, can get away by knowing what a metric tensor is, Christoffel symbols are, and the various Riemann […]