# A Decay of false vacuum in new inflation

1. Apr 2, 2017

### spaghetti3451

In new inflation, the time scale for the decay of the false vacuum is controlled by

$- m^{2} = \frac{\partial^{2}V}{\partial\phi^{2}}\bigg|_{\phi=0}.$

This is the negative mass-squared of the scalar field when it is at the top of the hill in the potential diagram. This is an adjustable parameter as far as new inflation is concerned, but $m$ has to be small compared to the Hubble constant or else the model does not lead to enough inflation. So, for parameters that are chosen to make the inflationary model work, the exponential decay of the false vacuum is slower than the exponential expansion.

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1. Why is the time scale for the decay of the false vacuum controlled by $- m^{2} = \frac{\partial^{2}V}{\partial\phi^{2}}\bigg|_{\phi=0}?$

2. Why does $m$ have to be small compared to the Hubble constant or else the model does not lead to enough inflation?

3. Why is the exponential decay of the false vacuum slower than the exponential expansion?

2. Apr 7, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.