# A Equation of state w=1

1. Dec 21, 2017

### Demystifier

A free scalar field with Lagrangian density
$${\cal L}=\frac{1}{2}g^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi$$
has the energy momentum tensor with the equation of state $p=\rho$, i.e. $w=1$. The Lagrangian density above is a very natural Lagrangian, yet the equation of state $w=1$ seems not to be considered in cosmology. Why is it not considered?

Last edited: Dec 22, 2017
2. Dec 21, 2017

### bapowell

I believe $w=1$ is referred to as a "stiff fluid" in the literature. It's been considered, but I don't know how extensively or in what contexts.

3. Dec 21, 2017

### kimbyd

What observational puzzles would this solve? Such a fluid would dilute extremely rapidly, with density scaling as $a^{-6}$.

4. Dec 22, 2017

### Demystifier

5. Dec 22, 2017

### jerromyjon

Certainly not the matter/antimatter imbalance... I think that is the most important puzzle of way back when. His following link discusses elemental distribution, though.
Let me know if you find anything on the matter abundances, please!