What is the Connection Between the Hubble Constant and Scalar Field Dynamics?

[nikhilb1997]

1. Homework Statement
If \phi is a usual field is it possible that
H\dot{\phi}=-\partial^2\phi/{\partial x^2}
Where H is the Hubble constant and the dot denotes time derivative
2. Homework Equations
H\dot{\phi}=-\partial^2\phi/{\partial x^2}
3. The Attempt at a Solution
I tried different ways but am not able to find the particular expression for Hubble constant used here.

 

[fzero]

On a curved spacetime, the Klein-Gordon equation for a massless scalar field is $\nabla^\mu \nabla_\mu \phi =0$. If the spacetime is of the FRW type, then there will be a term proportional to $H\dot{\phi}$. You seem to have missed the $\ddot{\phi}$ term in your expression, so you might want to go through the exercise of working this out from first principles.

 

[nikhilb1997]

On a curved spacetime, the Klein-Gordon equation for a massless scalar field is $\nabla^\mu \nabla_\mu \phi =0$. If the spacetime is of the FRW type, then there will be a term proportional to $H\dot{\phi}$. You seem to have missed the $\ddot{\phi}$ term in your expression, so you might want to go through the exercise of working this out from first principles.

Thanks a lot. I did miss that term because this was the part i was confused about but i guess that was important too.