Shedding light on the dark universe with gravitational waves

SHADE is a project to develop the future techniques of gravitational wave cosmology. It uses the incredible new data from gravitational wave events and frontier galaxy surveys to tackle a long-standing, central problem in cosmology: the nature of dark energy.

The SHADE team are laying the foundations of a powerful technique called "Dark Sirens", which ensures maximum scientific return from joint analysis of gravitational and electromagnetic data. Gravitational wave astronomy is still in its fairly early days -- as of 2022 less than a hundred gravitational wave events have been detected. However, the techniques developed in the SHADE project will become hugely powerful as the number of detections rises to thousands over the next decade.

SHADE is funded by a Starting Grant from the European Research Council, commencing in February 2021 and running for five years in the first instance. The PI is Dr. Tessa Baker at the Institute of Cosmology and Gravitation, University of Portmsouth. The official entry of SHADE on the Cordis registry can be found here.

I wrote a public-friendly article about the science behind the SHADE project for EU Research magazine; you can find that here.


What are dark sirens?

Credit: Fermilab.

The GWs that have been detected to date by the LIGO-Virgo-KAGRA Collaboration are produced by three kinds of sources. These are:

  • Binary black holes (BBH) -- a black hole merging with another black hole.
  • Binary neutron stars (BNS) -- a neutron star (an ultra-dense stellar core formed behind after a star 'dies') merging with another neutron star.
  • Neutron star-black hole binaries (NSBHs) -- a black hole merging with a neutron star.

There are various differences between these three kinds of events, but let's note one thing: black holes have an event horizon, which means they can't emit light. Neutron stars, on the other hand, don't have an event horizon. That means that when a neutron star is involved in a merger event, we believe huge amounts of energetic radiation are released -- some of which could be detected by electromagnetic telescopes. If a merger event is detected in both GWs and electromagnetic signals, we call it a bright siren. In particular, bright sirens are especially exciting for cosmology because they enable us to probe both the distance and redshift to a single event, which is very rare in astronomy. The relationship between distance and redshift depends crucially on cosmology and the theory of gravity governing the universe. So, bright sirens provide us with an opportunity to test these things.

Prior to the first detections of GWs in 2015, there were generally optimistic expectations for the number of bright siren events we might see. However, so far this hasn't been borne out in reality, with only bright siren -- GW170817 -- being detected since 2015. (A subtlety here is that the GW detectors are not operational full-time, and were shut down for an extended period over the Covid-19 pandemic.) So what about all those nice tests of cosmology and gravity we wanted to do? Are they totally scuppered?

This is where dark sirens come in. Dark sirens are GWs without electromagnetic counterparts (so really, regular GW events). The name 'dark sirens' really refers to a set of techniques that allow us to still use these regular, non-counterpart events for cosmology. The crucial thing we need is a way to estimate their redshifts (remember this was easy in the bright siren case, see above). In the case of dark sirens, we access this information by using a galaxy catalogue, which gives positions and redshifts for millions of galaxies. Without an electromagnetic counterpart , we can't know which of the galaxies is the true host of the GW event. So instead, we marginalise over all of them. This is a fancy way of saying we effectively let each galaxy be the true host in turn, and look at the collective sum of all those results. Said another way, even though we don't know the true host galaxy, we can still estimate cosmological parameter statistically using all the possible host galaxies.


How do we put all of this into practice? There's several key ingredients:

  • Bayesian mathematics. A hierarchical Bayesian formalism alongs us to express how to compute the parameters we want (really, parameter posterior distributions) from the input data we have, and various modelling assumptions. You can find details of our Bayesian formalism in this paper, and an extension to modified gravity theores in this paper.
  • Software pipelines to evaluate this Bayesian hierarchical formalism. My team are developers of the code gwcosmo.
  • Gravitational wave data. Specifically, we use output posteriors of parameter estimation done by the LVK Collaboration, which estimates the distance, component masses and other parameters of detected GW events.
  • Galaxy catalogues, which supply positions and redshifts of the candiate host galaxies. A tricky part is that we need catalogues covering the whole sky, which aren't obtainable from a single ground-based telescope.
  • Galaxy catalogue completion algorithms. No telescope is perfect; all have limits on how far away they can detect faint objects. It's possible that a GW event happens in a galaxy our telescope didn't even see, for this reason. Hence, in the dark sirens analysis we must carefully model all the missing galaxies, which is a bit like trying to see the invisible. Here's a paper from my team on this subject.