### Fluid Dynamics for Cosmology

In a previous post I derived the first of Friedmann's equations but the equation cannot be solved unless we know how the density of the universe changes over time. In cosmology the Roberston-Walker metric is formulated with fixed coordinates for fundamental particles which do not vary with time. We can therefore assume that the matter and radiation which fills the universe is describable as an ideal fluid. The evolution of the density is going to depend on the pressure present in the universe, which depends on the material which fills the cosmos. The assumption I make is that there is a unique pressure for every density. This is the simplest assumption because under this condition pressure does not contribute any additional force.

This is the equation of state and gives us enough to solve the equation once we derive it. Consider the first law of thermodynamics

This applies to an expanding volume, V the energy of this volume is given by

The change in energy of the system then requires us to use the product from differential calculus

If we assume this process is adiabatic such that TdS equals zero then plug dE/dt back into the equation, taking dV as

Rearrange the equation slightly and you should get

I've substatued a for radius, as this is the form found in text books, the terms in the brackets form the most essential part of the equation. The first of these terms corresponds to the density, (mass per volume) which decreases as the universe expands. The second term has to do with energy, as the universe increases in size, pressure of the material has done work, which transfers into potential energy. This equation and the earlier derived Friedman equation are all we need to describe the evolution of the universe but it will be helpful for is to derive an equation for acceleration, the second Friedmann equation. Which will follow in an up coming post.

### Margaret Thatcher's Legacy for Britain

The following is an adaptation of my thoughts at UCL's Conservative Society some months ago concerning the issue of the Conservative Parties vote of no confidence that lead to the resignation of Margaret Thatcher, her legacy for Britain and why she's so undeserving hated by the hard left.

When one enters parliament through members lobby there are four prime ministers commemorated and immortalized in statue form. The first of these figures, David Lloyd George seeded the beginnings of the welfare state, the second Winston Churchill served his tenure protecting us from physical annihilation during the Second World War, the third, Clement Attlee nationalized the health service and sought to drive Britain down the road of socialism and the fourth, the late Baroness Thatcher brought great economic revolution at the end of the Cold War.

It's been said of British politics that these last two figures though diametrically opposed were the only elections that ever really mattered. B…

### Can inflation be eternal into the past?

Back in 2003 a paper appeared on the arXiv titled "Inflationary spacetimes are not past complete" that was published by Arvind Borde, Alan Guth and Alexander Vilenkin which has had considerable amounts of attention online. The theorem is rather uninteresting but simple and doesn't require a very complicated understanding of math. So I thought I'd explain the result here.

It's purpose is to demonstrate that inflationary models are geodesically incomplete into the past which they take as "synonymous to a beginning" but Vilenkin stresses that the theorem can be extended to non inflationary models so long as the condition of the theorem that the average rate of expansion is never below zero is met. These models too then are incomplete into the past. Consider the metric for an FRW universe with an exponential expansion

Where the scale factor is

Since the eternal inflation model is a "steady state cosmology" the mass density and the Hubble paramet…

### 'Don't boo Labour, vote Conservative!' #ImWithHer

"My pitch is very simple, I'm Theresa May and I believe I'm the best person to be Prime Minister"

In an election one doesn't always get the option of voting for their primary candidate, for me that's been the case here. Originally I had supported Michael Gove and then Andrea Leadsom for leadership of the Conservative party but on June 8th we're expected to choose between Theresa May and Jeremy Corbyn. Whatever you think of the two personally, the choice of who offers better governance couldn't be clearer.

The most notable part of Jeremy Corbyn's "leadership" has been his support for the outrageous and policies of the far left. He supports the unilateral disarmament of British nuclear weapons, while supporting the right of Iran to have its own unrestricted nuclear program. He's had an industrial policy to nationalize the mining of coal but not to burn coal, and supports self-determination for the people of Palestine but not for the p…