### 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.

### William Lane Craig and the Hartle-Hawking No Boundary Proposal

Classical standard hot Big Bang cosmology represents the universe as beginning from a singular dense point, with no prior description or explanation of classical spacetime. Quantum cosmology is different in that it replaces the initial singularity with a description in accord with some law the "quantum mechanical wave function of the universe", different approaches to quantum cosmology differ in their appeal either to describe the origin of the material content of the universe e.g., Tyron 1973, Linde 1983a, Krauss 2012 or the origin of spacetime itself e.g., Vilenkin 1982, Linde 1983b, Hartle-Hawking 1983, Vilenkin 1984.

These last few proposals by Vilenkin, Hartle-Hawking and others are solutions to the Wheeler-DeWitt equation and exist in a category of proposals called "quantum gravity cosmologies" which make cosmic applications of an approach to quantum gravity called "closed dynamic triangulation" or CDT (also known as Euclidean quantum gravity). I&#…

### How Should Thatcherites Remember the '80s?

Every now and again, when I talk to people about the '80s I'm told that it was a time of unhinged selfishness, that somehow or other we learned the price of everything but the value of nothing. I can just remember that infamous line from Billy Elliot; 'Merry Christmas Maggie Thatcher. We all celebrate today because its one day closer to your death'. If it reflected the general mood of the time, one might wonder how it is she won, not one but three elections.

In an era when a woman couldn't be Prime Minister and a working class radical would never lead the Conservative party, Thatcher was both and her launch into power was almost accidental owing in part to Manchester liberals and the Winter of Discontent. Yet I'm convinced her election victory in '79 was the only one that ever truly mattered. Simply consider the calamity of what preceded it, the 1970s was a decade of double-digit inflation, power cuts, mass strikes, price and income controls, and the three…

### Creation Of Universes from Nothing

The above paper "Creation of Universes from Nothing" was published in 1982, which was subsequently followed up in 1984 by a paper titled "Quantum Creation of Universes". I decided it would be a good idea to talk about these proposals, since last time I talked about the Hartle-Hawking model which was, as it turns out, inspired by the above work.
Alexander Vilenkin also explains in a non-technical way the essential idea in his book; Many World's in One – one of the best books I've ever read – it mostly covers cosmic inflationary theory but the 17th chapter covers how inflation may have begun. In fact Vilenkin is one of the main preponderant who helped develop inflation along with Steinhardt, Guth, Hawking, Starobinsky, Linde and others.
Although I won't talk about it here, Vilenkin also discovered a way of doing cosmology by using something called "topological defects" and he has been known for work he's done on cosmic strings, too.
In ex…