Yes, but not significantly. Phenomenologically, they should be distinguishable as ripples of dm wouldn't travel at the speed of light and gw would.
If I'm not mistaken, they would be indistinguishable at our current level of tech because you'd have to do a sort of tomographic analysis by taking the same measurement at multiple points that are very distant from each other
Nanohertz GWs pass between us and a set of pulsar timing array (PTA) millisecond pulsars relatively nearby in the Milky Way. Where the source is a black hole binary, up to redshift the binary's orbital period induces a ~light-year diameter spherical volume of space between us and a pulsar to deform into an ellipsoid like an American football, and back again (it's a classical spin-2 wave in the Weyl tidal tensor field, so it's a bit more complicated than that, e.g. roughly you get the pointy ends developing along two sets of different axes, "plus" + and "cross" x, where for each you get wider along one axis and narrower on the other - visualization at [1]). The deformation of our ~light-year sphere is very small, on the order of a few metres, and very slow, as the evolution over spherical->ellipsoidal+->spherical->ellipsoidalx cycle takes months to years. Nevertheless a frequency speed up/slow down of the beam from a pulsar on the other side of an oscillating ~light-year volume shows up in interferometry.
There are a lot of binary sources across the sky whose orbits differ in duration and orientation (and likely ellipticity and mass-ratio) and distance from the Milky Way, so the idea is to spot one oscillating volume in between us and multiple pulsars, or one wave inducing ~identical oscillations (including their amplitude) in between us and several pulsars. Alternatively, one can see how well interferometry measurements of time-of-flight match the Hellings and Downs curve, which predicts timing residuals for a pulsar timing array in the presence of a a background from random binary sources all over the sky.
I'll be unusually speculative. I usually try to avoid that on HN. One could perhaps contrive a flow of dark matter which slightly delays a pulsar signal given enough time-of-flight, and with some effort could work out how that might mimic one gravitational wave source. It's much harder to do it for the sources all over the sky and at various orientations. Also, the dark matter density between us and the pulsar will have to avoid disturbing the orbits through the Milky Way of objects between us and the pulsars (e.g. gas clouds, stars), while remaining overdense enough to delay the beam path the requisite amount. I'd start with the idea of a wrought iron fence, where the bars are exactly aligned along our view of a pulsar, and then realize that the bars have to smear along their (cylindrical) radius. I'd need a smeared-bar/gap/differently-smeared-bar/gap cycle over the course of months to years, and I'd need that cycle to continue for decades. I'd also need to realign the long axis of the cylinders (harder to do than spherical regions) as Earth and the pulsar move with respect to each other; among other things I have to control the gravitational redshift of large background things (galactic star clusters and molecular clouds up to background galaxies with predictable light curves - supernovae, active galactic nuclei etc) at some angular separation from the pulsar. I'd end with realizing that nothing like this could be physical with cold dark matter for even one source, and because of the Hellings-Downs approach I'd have to do this for multiple pulsars.
On reflection it's easier to think about a density distribution of dark matter that is precisely -- conspiratorially even -- arranged to induce changes in the local proper motion of all the pulsars in the PTA. If the pulsars are drawn to an overdensity of dark matter behind them (from our point of view) and beside them periodically, one could mimic the effect of dim nanohertz sources. I think bright sources kill this idea though, because the requisite overdensity would affect orbits of objects near the pulsars. It's also easier to think of how these pockets of extra DM could smear out over experimental time than to keep them precisely overdense and precisely located with respect to the pulsars for many years.
[1] handy animated gif https://d18l82el6cdm1i.cloudfront.net/uploads/FP84etZqf6-pmo... where we see a ring of test particles at the margin of a slice through our spherical volume, the left is the + polarization the right is x. The change from circular to elliptical cross section is HUGELY exaggerated. The gravitational waves in question would not even change a pixel if we drew two oscillating-to-scale circles instead.
Thanks for the animated gif, that reminded me what a quadrupolar effect looks like, and yeah, it would be hard to believe that DM could do that just right across multiple correlated pulsars (but who knows, DM could be weird). Still suspicious of the statistics (as always) but this seems like a more reasonably sound observation, than LIGO/VIRGO even.
BTW don't shy away from being speculative. This was an effective explanation.
Take a child's mobile or a pair of differently-coloured tennis balls (say red and green) glued to the end of a paper tube and suspend that from the ceiling at about shoulder height. Set the thing spinning in the plane parallel to the ceiling. Step back a bit and choose one hand's index finger to point at one of the tennis balls and the other hand's to the other. Left index to red, right index to green. Extend and retract each arm to try to maintain a constant distance from each fingertip to the ball it's pointing at. Play with parallax so that you notice your arms crossing during part of the orbit (red ball on right at same distance to you as green ball on left) and uncrossing half an orbit later. You'll also notice the other phase where both fingers/arms point practically parallel but with one hand closer to you, then half an orbit later further from you.
Your fingers are basically indicating the masses in their circular orbit. For gravitational radiation from the orbiting binary tennis balls a ~cylinder of space where index fingers lie on the axis lengthens axially and contracts radially. (A really tiny amount). This is encoded in the Weyl tensor, which is the traceless part of the Riemann curvature tensor (for more on that, see Baez's stab at this, <https://math.ucr.edu/home/baez/gr/ricci.weyl.html>). In a linearization of the Einstein Field Equations, which is how most people are taught gravitational radiation, we get the h+ and hx polarizations; hx is maximal when your arms are crossed and half an orbit later, h+ maximizes when your arms are parallel. Most people also think about their mass-detector (fingertips) pointing at the nearest mass rather than always at one of the binary, and so miss the thinking behind "cross" and this edge-on vs a face-on view of the tennis ball binary.
Since it's currently estimated that >90% of the mass of the observable universe is 'dark' of some sort, it seems like gravity waves are indeed 'ripples' that also happen to affect normal matter.
I don't think this view is correct. Dark matter interacts through gravity, so of course it creates gravity waves. But that doesn't mean that gravity waves are ripples of dark matter.
