# What is the meaning of “background” in General Relativity?

I was reading a book on Topological defects of the very early universe as an example of the fundamental groups, and they say that "in an expanding homogeneous and isotropic universe, the background energy density is a function of time", I do not know what do they mean by "background", are they referring to the spacetime.

Could somebody please explain this to me? I am not into physics but I like general relativity.

Thanks

• There's no background, there's only background energy (aka. vacuum energy). – Hagen von Eitzen Feb 14 '14 at 16:27

So when they say "background energy density", it sounds like they are referring to the background $00$-component of the matter stress tensor.
To be slightly more explicit, you assume a metric of the form $$ds^2 = -dt^2+a^2(t)(\gamma_{ij}dx^i dx^j)$$ where $\gamma_{ij}$ is the metric for a maximally symmetric 3 dimensional space. The Einstein equations are $$R_{ab}-\frac12 R g_{ab} = 8\pi G T_{ab}.$$ The $00$-component of this equation is $$3 H^2 = 8\pi G \rho$$ where $H\equiv\dfrac{\dot{a}}{a}$ is the Hubble parameter, and $\rho\equiv T_{00}$ is the energy density. This $\rho$ is the background energy density they are referring to.