# Gravitational Radiation and Cosmological Constant

1. Jan 23, 2016

### Markus Hanke

How come that, in the context of discussing the search for gravitational waves, I never see the cosmological constant mentioned ? We know that $\Lambda \neq 0$, so this seems strange to me; in the presence of a non-vanishing constant, the background is not Ricci flat in the vacuum case, so this should have some impact on how the radiation propagates. In fact, in the linearised case, and in Lorentz gauge, the equation of motion for the perturbance $h_{\mu \nu}$ becomes

$$\displaystyle{\square \left ( h_{\mu \nu}-\frac{1}{2}\eta _{\mu \nu}h \right )=-2\Lambda \left (\eta_{\mu \nu}+h_{\mu \nu} \right )}$$

I guess over distances which can be considered small ( in the cosmological sense ) a case can be made to ignore the r.h.s.; but for very distant sources of gravitational radiation I don't think things are that simple.

Naively I would expect a Doppler-like effect ( a frequency shift ) for very distant sources, and I would also expect that the $\Lambda$ enters into how the radiation actually couples to the source in the first place. I am unfortunately not in a position to estimate the magnitude of the impact that has on the dynamics of the wave, so I am curious if anyone on here with more advanced knowledge can comment on that ? Is the cosmological constant taken into account in searches for gravitational waves ( e.g. at Advanced LIGO ) ? If not, why not ?

2. Jan 23, 2016

### haushofer

Good question. I guess it is because Lambda is incredibly small.

3. Jan 23, 2016

### Markus Hanke

Yes, you are right of course - but does that necessarily mean that it has a negligible impact on the dynamics of the wave ? I think that question deserves a closer look.

4. Jan 24, 2016

### George Jones

Staff Emeritus