# Breaking of time diffeomorphisms in inflation

1. Aug 23, 2013

### Anne-Sylvie

Hello here,

I am currently working on the topic of inflation.

It seems that at the stage of inflation, the universe can be described as a de Sitter space. In such a space, all spacetime diffeomorphisms are preserved. (That is something I don't really understand but I keep reading that so I admit it for now.)

Now, I read that, in order to give the FLRW universe that we know today, the time diffeomorphisms are broken and therefore there is a Goldstone boson associated with this symmetry breaking. I also read somewhere else that it is not the inflaton field that is concerned by this broken symmetry but rather the fluctuation field $\delta \phi$ defined as $\phi(x,t) = \phi_0(t) + \delta \phi(x,t)$.

• What is the Goldstone boson ? It is not the inflaton field...
• Does it makes sense to say that only time diffs are broken, since space and time coordinates are not so evidently separated ? I know that the background field $\phi_0$ gives a clock but I'm still confused.
• Why is FLRW not invariant under time diffs ? Because of the evolution of $a(t)$ ?
• I thought that in order to apply Goldstone's theorem, the broken symmetry had to be continuous. When we speak about broken time diffs, is it a continuous symmetry ? (Maybe because it's only shift in time ?)

Sorry if it is not clear, as you can see I'm confused about this topic. Thank to anyone who can provide some answer, even partial.