Gravitational Waves and the Cosmological Conundrum

There is currently a crisis in cosmology. A decade or so ago, it seemed like astronomers had a good understanding of the expansion of the universe. By taking measurements of the cosmic microwave background, the radiation left over from the Big Bang, and by observing distant stars, they found that the universe was expanding at about 72 kilometres per second per megaparsec (km/s/Mpc). It had been known that the universe was expanding since Hubble had found that the light from distant galaxies was redshifted, that is, shifted towards the red end of the spectrum, and in his honour the rate of expansion is now known as the Hubble constant H₀. But in recent years, as the accuracy of the measurements has improved, astronomers have begun to see a disturbing trend in the data. The expansion rate, the Hubble constant, is different, depending on which part of the universe is being observed.

And the differences are significant. The most recent data on the cosmic microwave background from the early universe predicts that H₀ should be 67 km/s/Mpc, yet when astronomers analyse the light from distant supernovae they are measuring a H₀ of 74 km/s/Mpc. This gap has been widening for a few years now, and calls into question the very model on which our understanding of the universe is based, the Lambda cold dark matter model. From the brightness and mass of stars in nearby galaxies, to the age and size of the universe, H₀ is a cornerstone of modern cosmology. And cosmologists are beginning to wonder if they need some new physics to explain what they are seeing.

Science Check: The Hubble Constant

But what is H₀? When Edwin Hubble plotted the distances to nearby galaxies against their redshifts, he found a roughly linear relationship. Georges Lemaître had published similar findings a couple of years earlier, but Hubble’s higher profile at the time meant that it was he that initially garnered the credit for what has only recently become known as the Hubble-Lemaître Law. The law says that objects in an expanding universe move away from each other with a velocity proportionally related to their distance, and is expressed mathematically by $v=H_0 \times d$, where $v$ is how fast the galaxy is receding from us, $d$ is its distance from us, and $H_0$ is the Hubble constant. Thus, given a H₀ of 50 for example, galaxies at 1 Mpc would be moving away from us at 50 km/s, but galaxies twice as distant would be moving away twice as fast. And how far is a megaparsec? It's a distance equal to 3.26 million lightyears, which is a little bit further than the distance to the Andromeda galaxy.

Resolving the Hubble Tension

A new study by researchers at OzGrav, the ARC Centre of Excellence for Gravitational Wave Discovery, suggests that we may be able to settle the ‘Hubble tension’ in the very near future by observing gravitational waves. These are the ripples in space-time caused by massive objects like neutron stars and black holes that orbit in pairs, and were predicted by Einstein in 1916 but not observed until 2015 when the first black hole merger was detected. Gravitational wave observations can be used as an independent method to probe the history of the universe, and a new generation of more sensitive detectors should give scientists the ability to measure H₀ more accurately than ever before.

“Our work studied the prospect that, with third-generation gravitational wave detectors, we would be able to see every binary black hole merger in the universe”, says OzGrav PhD student and first author Zhiqiang You. Given such a wealth of data they showed that under certain conditions it would be possible to measure H₀ with unprecedented accuracy within just one year. Astronomers should also be able to see the distinguishing features of the Lambda cold dark matter model after only one week. This will all be welcome news to cosmologists.

To make these deductions, Zhiqiang You and his collaborators simulated a population of black hole binaries and mergers that represented the set of events that are expected to be detected by next generation detectors. Their analysis was done making use of a unique feature in the distribution of black holes; that, as suggested by current theories of black hole formation, there should not be any black holes with masses between 50 and 150 times the mass of our Sun. That means that any black holes they found in that mass range must have been receding from us due to the expansion of the universe to make it look as though they were that massive. As explained by Zhiqiang You, “if we know that black holes don’t occur in nature above 50 solar masses, and we see one that is 75 solar masses, then we know it has been redshifted. Thus the mass gap provides a way to measure redshift.”

They were then able to perform a statistical analysis to compute the parameters that described the population, and could work out how many events would be necessary to accurately measure H₀. They found that with an expected 100,000 black hole binary detections in the first year, errors in the measured value of H₀ would be less than about 0.5%. But the framework of their analysis goes further, and allows for inferences to be made about the masses of black holes, the rate of star formation, and the time over which black hole binaries merge. “Our results are exciting because we show that in coming years, when more sensitive detectors come online, we will be able to improve the measurement of the Hubble constant to better than one percent”, says Zhiqiang You.

One of the next generation gravitational wave detectors is the Einstein Telescope, which is scheduled to start looking at the sky sometime in the 2030s. While current detectors like LIGO and Virgo are L-shaped laser interferometers, with arms of 3 or 4-km in length, the Einstein Telescope will be a triangular laser interferometer with sides of 10-km. That means it will see a 10-fold increase in sensitivity, and be able to detection gravitational waves from the time before stars even existed. As said by Zhiqiang You, with just a hint of understatement, “this will resolve the outstanding debate (over the Hubble constant) and be an important step forward in understanding our universe”.