Why include -xi*H in the equation of state?

[odd-socks]

I'm aware that the equation of state for a perfect fluid (when considering single fluid cosmology) is p=w*rho

However I've come across an equation of state of p=w*rho - xi*H, H being Hubble's parameter. However I cannot find an explanation of why you can put this in? Can anyone explain this to me please?

Thanks

 

[Chronos]

It is irrelevant. You wish to inject it into the cosmological constant?

 

[odd-socks]

its to look at equations for rhodot (d rho/dt) and Hdot (dH/dt) so solve as a dynamical system for rho and H