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# Bassett, B. A. "Inflation dynamics and reheating." Reviews of modern physics 78.2 (2006):537.

## The Paper

Note: We will only be reading Sections I and II of this paper this week!

The .pdf file can be found here (Note you need to be logged in to use this link)

An external link to the paper is here.

The DOI is 10.1103/RevModPhys.78.537.

## Discussion

Wiki's explanation of “cosmic time” was rather terse. Is there a good way to understand how this relates to time in our frame? – $a^\dagger a$

A: As far as I understand, it is just a fancy word. It is time as a coordinate, and in a local Mincowski spacetime (any local system can be reduced to this), this “cosmic time” t is equivalent to time we use. The only concern is that the coordinate time may not be a physical quantity in some cases (it may not be a good “clock”). For example, during inflation, what drives and determines the inflation is inflaton field. In this context, the inflaton $\phi$ is the “clock,” and t is usually considered a rather auxiliary quantity. In any case, t is a coordinate time. – $\R$

Any hope for me to understand “tachyonic instability”? – $a^\dagger a$

A: I am not completely sure about all the implications it makes, but the basic idea is fairly simple (as far as I know). You can look at Fig. 3 in the paper. The field $\phi$ starts from up in the potential and the system (“universe”) rolls down the hill toward $\phi = 0$. At any given $\phi$, the minimum in potential is at $\chi =0$ at the beginning, and so the system oscillates around it. However, once $\phi = \phi_{c}$ is achieved, the potential bifurcates and $\chi = 0$ is no longer a stable equilibrium. The system becomes unstable and rolls down toward the new minima relatively fast. Since the effective mass term for $\chi$ gets negative sign (the curvature of the potential becomes negative in $\chi$ direction), it is called “tachyonic.” – $\R$

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