Constraints on cosmological viscosity and self-interacting dark matter from gravitational wave observations

It has been shown that gravitational waves propagate through ideal fluids without experiencing any dispersion or dissipation. However, if the medium has a nonzero shear viscosity $\eta$, gravitational waves will be dissipated at a rate proportional to $G\eta$. We constrain dark matter and dark energy models with nonzero shear viscosity by calculating the dissipation of gravitational waves from GW150914 which propagate over a distance of 410 Mpc through the dissipative fluid and comparing the data with the theoretical prediction. This provides a proof-of-principle demonstration of the fact that future observations gravitational waves at LIGO have the potential of better constraining the viscosity of dark matter and dark energy.

Figure 1

The effect of viscosity on the GW strain time series: The red curve is the time series of strain of the observed GW data and the blue (dashed) curve is the theoretical strain when $Q=0$. When $Q=1$, green curve, the theoretical strain gets attenuated. All the time series are band-limited to the frequency range 30–350 Hz and the data is from the LIGO Hanford detector.

Figure 2

The constraints on $Q$ and $L$ at $1\sigma CL$ (inner, black contour) and $2\sigma CL$ (outer, red contour) for the data obtained from Hanford (upper panel) and Livingston (lower panel) observatories. The shaded region between the two vertical lines is the source distance with an uncertainty of 10% around the estimated central value of $L=410\mathrm{Mpc}$, the corresponding range of values of $Q$ can be easily seen.