Thanks for your help once again! I was able to solve it after reevaluating ##\frac{d^2 a}{dt^2}## and got ##\frac{\ddot a a-\dot a^2}{a^3}##.
And yeah it's 3P, messed up typing it in.
Homework Statement
Show that ##4\pi G(\dot \phi)^2=\epsilon a^2 H^2##
Homework Equations
Over dots mean derivative with respect to ##\eta##.
$$\frac{1}{a}\frac{d}{d\eta}=\frac{d}{dt}$$
$$H=\frac{\dot a}{a^2}$$
$$\epsilon=\frac{-\dot H}{aH^2}$$
$$(\frac{\dot...
Thank you both. Today with a clear head I figured it out.
$$H=\frac{\dot a}{a^2}$$
And so
$$\epsilon=\frac{2\dot a^2 -\ddot a a}{\dot a^2}$$
Which made things much easier.
That helps but I am still having trouble. With ##\epsilon=\frac{-\dot H}{a H^2}## I just end up going in circles. But if I work with ##\epsilon=\frac{d}{dt}\frac{1}{H}## I get the following:
$$\epsilon=\frac{d}{dt}\frac{1}{H}=\frac{\dot a^2 - \ddot a a}{\dot a^2}$$...
Homework Statement
The general goal of the problem is to derive some useful identities involving the slow-roll parameters during inflation.
For part a show that:
$$\frac {d} {d\eta} (\frac {1} {aH})= \epsilon - 1$$
Homework Equations
$$\epsilon \equiv \frac {d} {dt} (\frac {1} {H})= \frac...
Hello all!
I have a bachelors in computing but spent a couple of years studying physics at university and I finished last spring. I decided to take a break from school to study and hopefully do some research before heading back to graduate school.
My research interests are inflation and...