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

odd-socks
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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
 
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It is irrelevant. You wish to inject it into the cosmological constant?
 
its to look at equations for rhodot (d rho/dt) and Hdot (dH/dt) so solve as a dynamical system for rho and H
 

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