Understanding the Zero Order Universe in Cosmology

[shirin]

In chapter 2 of Dodelson’s modern cosmology book, it reads:
“Implicit in this discussion will be the notion that the universe is smooth (none of the densities vary in space) and in equilibrium (the consequences of which will be explored in Section 2.3). In succeeding chapters, we will see that the deviations from equilibrium and smoothness are the source of much of the richness in the universe. Nonetheless, if only in order to understand the framework in which these deviations occur, a basic knowledge of the "zero order" universe is a must for any cosmologist. “
What does zero-order in this context mean? Zero order of what quantity? Does it mean a universe with a constant density everywhere?

 

[topsquark]

In chapter 2 of Dodelson’s modern cosmology book, it reads:
“Implicit in this discussion will be the notion that the universe is smooth (none of the densities vary in space) and in equilibrium (the consequences of which will be explored in Section 2.3). In succeeding chapters, we will see that the deviations from equilibrium and smoothness are the source of much of the richness in the universe. Nonetheless, if only in order to understand the framework in which these deviations occur, a basic knowledge of the "zero order" universe is a must for any cosmologist. “
What does zero-order in this context mean? Zero order of what quantity? Does it mean a universe with a constant density everywhere?

Zero order doesn't refer to a number, it's saying that the simple Universe he described is a "base case" that we can compare more complicated models to.

-Dan

 

[Bandersnatch]

It means the most coarse, simplest model. See here for more on the usage of such phrases: https://en.wikipedia.org/wiki/Order_of_approximation
(note that it's more of a mannerism than a well-defined term - zeroth order for one person can be first order for another)

In this context, it means that you assume the cosmological principle to hold perfectly everywhere in the universe. As you say - that the density of all components is the same everywhere. Something that is obviously not true even as you as much as look around you - there's a bunch of rock in one direction, and a whole lot of vacuum in another. There are stars here, and not much of anything there. Etc.
But starting this way lets you understand the underlying large-scale behaviour before you begin to include higher order approximations in the form of e.g. inhomogeneities nucleating filaments and galaxies.

Much like when modelling the motion of the Earth in the Solar System you could start by assuming, as your zeroth order approximation, that the Earth moves solely in the central gravitational field of the Sun and there are no other forces at play. Or maybe just that Kepler's laws hold perfectly. Which would lead you to a pretty good basic understanding of orbital motion. But then you'd want to start including perturbations from other planets and smaller bodies to improve your model, so that you can have precession, planetary migration, tides, and so on.