Cosmology Day July 2018

Lecture 6: Gravitational waves and cosmology

Dr Andrew Williamson


Dr Williamson received his PhD from Cardiff University working on gravitational waves and gamma-ray bursts as a member of the LIGO Scientific Collaboration, including a 4 month visit to the LIGO Livingston Observatory in Louisiana. He is currently a postdoctoral researcher at the Gravitation Astroparticle Physics Centre of the University of Amsterdam, and a member of the Virgo Collaboration.


Since the momentous first detection of gravitational waves in September 2015, gravitational waves have been detected from colliding pairs of black holes and neutron stars. Not only do gravitational waves give us an entirely new way to observe some of the extreme objects in the Universe, they also allow us to investigate the make-up, history and fate of the cosmos.

My notes from the lecture (if they don’t make sense then it is entirely my fault)

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams can be used to visualize relativistic effects such as why different observers perceive where and when events occur.


Spacetime is curved/warped in the presence of matter


An artist’s impression of gravitational waves generated by binary neutron stars. Credits: R. Hurt/Caltech-JPL

An animation of artist’s concept of gravitational wave propagation

Gravitational waves are a stretching and squashing of spacetime, and a loud gravitational wave may stretch and squash by one part in 1021.

As a gravitational wave passes an observer, that observer will find spacetime distorted by the effects of strain. Distances between objects increase and decrease rhythmically as the wave passes, at a frequency equal to that of the wave. This occurs despite such free objects never being subjected to an unbalanced force.


Spiral Dance of Black Holes Image credit: LIGO/T. Pyle

This illustration shows the merger of two black holes and the gravitational waves that ripple outward as the black holes spiral toward each other. The black holes—which represent those detected by LIGO on Dec. 26, 2015—were 14 and 8 times the mass of the sun, until they merged, forming a single black hole 21 times the mass of the sun. In reality, the area near the black holes would appear highly warped, and the gravitational waves would be difficult to see directly.

Gravitational wave interferometry

Interferometers are investigative tools used in many fields of science and engineering. They are called interferometers because they work by merging two or more sources of light to create an interference pattern, which can be measured and analysed; hence “Interfere-ometer”. The interference patterns generated by interferometers contain information about the object or phenomenon being studied. They are often used to make very small measurements that are not achievable any other way. This is why they are so powerful for detecting gravitational waves–LIGO’s interferometers are designed to measure a distance 1/10,000th the width of a proton!


Basic schematic of LIGO’s interferometers with an incoming gravitational wave depicted as arriving from directly above the detector. (Image: LIGO)

Constructive interference = gravitational wave

A gravitational-wave observatory (or gravitational-wave detector) is any device designed to measure gravitational waves, tiny distortions of spacetime that were first predicted by Einstein in 1916. Gravitational waves are perturbations in the theoretical curvature of spacetime caused by accelerated masses. The existence of gravitational radiation is a specific prediction of general relativity, but is a feature of all theories of gravity that obey special relativity. Since the 1960s, gravitational-wave detectors have been built and constantly improved. The present-day generation of resonant mass antennas and laser interferometers has reached the necessary sensitivity to detect gravitational waves from sources in the Milky Way. Gravitational-wave observatories are the primary tool of gravitational-wave astronomy.

A number of experiments have provided indirect evidence, notably the observation of binary pulsars, the orbits of which evolve precisely matching the predictions of energy loss through general relativistic gravitational-wave emission. The 1993 Nobel Prize in Physics was awarded for this work.

In February 2016, the Advanced LIGO team announced that they had detected gravitational waves from a black hole merger. The 2017 Nobel Prize in Physics was awarded for this work.

Operational and planned gravitational-wave detectors:

(1995) TAMA 300

(1995) GEO 600

(2002) LIGO

(2003) Mario Schenberg (Gravitational_Wave_Detector)

(2003) MiniGrail

(2005) Pulsar timing array (for Parkes radio-telescope)

(2006) CLIO

(2007) Virgo interferometer

(2015) Advanced LIGO

(2016) Advanced Virgo

(2018) KAGRA (LCGT)

(2023) IndIGO (LIGO-India)

(2025) TianQin

(2027) Deci-hertz Interferometer Gravitational wave Observatory (DECIGO)

(2034) Laser Interferometer Space Antenna (Lisa Pathfinder, a development mission was launched December 2015)

(2030s) Einstein Telescope


Design sensitivity curves for the Advanced LIGO, Advanced Virgo and LCGT second generation detectors. These curves are based on specific configurations of the detectors and are therefore subject to change.

GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence

On August 14, 2017 at 10∶30:43 UTC, the Advanced Virgo detector and the two Advanced LIGO detectors coherently observed a transient gravitational-wave signal produced by the coalescence of two stellar mass black holes, with a false-alarm rate of ≲1 in 27 000 years

GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral

On August 17, 2017 at 12∶41:04 UTC the Advanced LIGO and Advanced Virgo gravitational-wave detectors made their first observation of a binary neutron star inspiral. The signal, GW170817, was detected with a combined signal-to-noise ratio of 32.4 and a false-alarm-rate estimate of less than one per 8.0 x 104 years.

Observation of Gravitational Waves from a Binary Black Hole Merger

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal.

This was the first direct detection of gravitational waves and the first observation of a binary black hole merger.

Credit: Simulating extreme spacetime collaboration

A binary black hole (BBH) is a system consisting of two black holes in close orbit around each other. Like black holes themselves, binary black holes are often divided into stellar binary black holes, formed either as remnants of high-mass binary star systems or by dynamic processes and mutual capture, and binary supermassive black holes believed to be a result of galactic mergers.

The existence of stellar-mass binary black holes (and gravitational waves themselves) were finally confirmed when LIGO detected GW150914 (detected September 2015, announced February 2016), a distinctive gravitational wave signature of two merging stellar-mass black holes of around 30 solar masses each, occurring about 1.3 billion light years away. In its final moments of spiraling inward and merging, GW150914 released around 3 solar masses as gravitational energy, peaking at a rate of 3.6 x 1049 watts — more than the combined power of all light radiated by all the stars in the observable universe put together – during its last brief moments. Supermassive binary black hole candidates have been found but as yet, not categorically proven.

Immediately following the merger, the now single black hole will “ring” – oscillating in shape between a distorted, elongated spheroid and a flattened spheroid. This ringing is damped in the next stage, called the ringdown, by the emission of gravitational waves. The distortions from the spherical shape rapidly reduce until the final stable sphere is present, with a possible slight distortion due to remaining spin.

Computer simulation of the black hole binary system GW150914 as seen by a nearby observer, during its final inspiral, merge, and ringdown. The star field behind the black holes is being heavily distorted and appears to rotate and move, due to extreme gravitational lensing, as space-time itself is distorted and dragged around by the rotating black holes.

Accurate inspiral-merger-ringdown gravitational waveforms for non-spinning black-hole binaries including the effect of subdominant modes.



6(5.8) binary black hole mergers detected in the first two observation runs

Infers a rate of ~100 binary black hole mergers per cubic gigaparsecs per year with LIGO/VIRGO


One of the most interesting cosmic explosions for which we can expect to see both gravitational waves and high-energy neutrinos are called gamma-ray bursts (GRB). These bursts of very high energy photons come from particles, such as electrons and protons. The outflow of these particles is likely to originate from a black hole that is accreting matter. The black hole may be formed by either the merger of two neutron stars, or by the collapse of a particularly massive star. If part of the neutron star is ripped apart in the process, it can accrete onto the black hole and can supply the matter that will be accelerated to high velocities. The figure shows when and where, in these processes, one can expect the emission of gravitational waves and high-energy neutrinos. Credit: I. Bartos/Based on arXiv:1212.2289

A neutron star is the collapsed core of a giant star which before collapse had a total of between 10 and 29 solar masses.

Both gravitational and electromagnetic radiations have been detected in rapid succession for an explosive merging event for the first time. Data from the outburst fit well with a spectacular binary neutron-star death-spiral. The explosive episode was seen on August 17 in nearby NGC 4993, an elliptical galaxy only 130 million light years distant. Gravitational waves were seen first by the ground based LIGO and Virgo observatories, while seconds later the Earth-orbiting Fermi and INTEGRAL observatories detected gamma-rays, and hours after that Hubble and other observatories detected light throughout the electromagnetic spectrum. Pictured is an animated illustrative movie of the event’s likely progenitors. The video depicts hot neutron stars as they spiral in toward each other and emit gravitational radiation. As they merge, a powerful jet extends that drives the short-duration gamma-ray burst, followed by clouds of ejecta and, over time, an optical supernova-type episode called a kilonova. This first coincident detection confirms that LIGO events can be associated with short-duration gamma-ray bursts. Such powerful neutron star mergers are thought to have seeded the universe with many heavy nuclei including the iodine needed for life and the uranium and plutonium needed for nuclear fission power. You may already own a souvenir of one of these explosions — they are also thought to be the original creators of gold.

Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A

Illuminating Gravitational Waves: A Concordant Picture of Photons from a Neutron Star Merger

GRB 031203 was a gamma-ray burst (GRB) detected on December 3, 2003. A gamma-ray burst is a highly luminous flash associated with an explosion in a distant galaxy and producing gamma rays, the most energetic form of electromagnetic radiation, and often followed by a longer-lived “afterglow” emitted at longer wavelengths (X-ray, ultraviolet, optical, infrared, and radio). The amount of gamma-rays measured by Integral is about one thousand times less than what we would normally expect from a GRB. It was seen by X-rays and radio much later.

In gamma-ray astronomy, gamma-ray bursts (GRBs) are extremely energetic explosions that have been observed in distant galaxies. GRB 031203 was detected by INTEGRAL on December 3, 2003, at 22:01:28 UTC.

INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) is a currently operational space telescope for observing gamma rays. It was launched by the European Space Agency into Earth orbit in 2002, and is designed to detect some of the most energetic radiation that comes from space. It was the most sensitive gamma ray observatory in space before NASA’s Fermi was launched in 2008.

Illuminating Gravitational Waves: A Concordant Picture of Photons from a Neutron Star Merger


Snapshots from a hydrodynamic simulation of a cocoon generated by a choked jet with emission consistent with EM170817

Merging neutron stars offer an exquisite laboratory for simultaneously studying strong-field gravity and matter in extreme environments.

A cocoon shock breakout as the origin of the γ-ray emission in GW170817

The short Gamma-Ray Burst, GRB170817A, that followed the binary neutron star merger gravitational waves signal, GW170817, is not a usual sGRB. It is weaker by three orders of magnitude than the weakest sGRB seen before and its spectra, showing a hard early signal followed by a softer thermal spectrum, is unique.

Superluminal motion of a relativistic jet in the neutron star merger GW170817

Black holes: what was their role in shaping the universe? Violent deaths and their consequences

Kilonova Observations

On the astrophysical robustness of neutron star merger r-process This study explores the nucleosynthesis in the dynamic ejecta of compact binary mergers.

GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral Gravitational wave luminosity distance is encoded in the signal

If we have complementary redshift measurements we can infer the local expansion rate from gravitational wave events.

Gravitational lensing alone results in poor constraints.

Prospects for resolving the Hubble constant tension with standard sirens

The Hubble constant (H0) estimated from the local Cepheid-supernova (SN) distance ladder is in 3-σ tension with the value extrapolated from cosmic microwave background (CMB) data assuming the standard cosmological model.

A sample of ∼ 50 binary neutron star “standard sirens” (detectable within the next decade) will be able to adjudicate between the local and CMB estimates.

The paper demonstrated how existing and upcoming datasets can arbitrate the tension between estimates of H0 from the CMB and local distance ladder, throughout adopting the minimal cosmological model: a smooth expansion history and standard pre-recombination physics. It found that the inverse distance ladder formed from BOSS BAO measurements and the Pantheon SN sample yields an H0 posterior near-identical to Planck and inconsistent with the observed local distance ladder value. It quantified this tension using a model-testing framework based on the posterior predictive distribution, which relies only on the sampling distribution for one dataset given another. It then demonstrated how a typical sample of ∼50 BNS standard sirens, detectable by the LIGO and Virgo experiments within a decade, can independently arbitrate this tension.

A Hubble constant measurement from superluminal motion of the jet in GW170817

The Hubble constant (H0) measures the current expansion rate of the Universe, and plays a fundamental role in cosmology. Tremendous effort has been dedicated over the past decades to measure H0. Notably, Planck cosmic microwave background (CMB) and the local Cepheid-supernovae distance ladder measurements determine H0 with a precision of ∼ 1% and ∼ 2%. A 3-σ level of discrepancy exists between the two measurements, for reasons that have yet to be understood. Gravitational wave (GW) sources accompanied by electromagnetic (EM) counterparts offer a completely independent standard siren (the GW analogue of an astronomical standard candle) measurement of H0, as demonstrated following the discovery of the neutron star merger, GW170817. This measurement does not assume a cosmological model and is independent of a cosmic distance ladder. The first joint analysis of the GW signal from GW170817 and its EM localization led to a measurement of H0 = 74+16−8 km/s/Mpc (median and symmetric 68% credible interval). In this analysis, the degeneracy in the GW signal between the source distance and the weakly constrained viewing angle dominated the H0 measurement uncertainty. Recently, Mooley et al. (2018) obtained tight constraints on the viewing angle using high angular resolution imaging of the radio counterpart of GW170817. A significantly improved measurement H0 = 68.9+4.7−4.6 km/s/Mpc were obtained by using these new radio observations and combined with the previous GW and EM data. It is estimated that 15 more localized GW170817-like events (comparable signal-to-noise ratio, favourable orientation), having radio images and light curve data, will potentially bring resolution to the tension between the Planck and Cepheid-supernova measurements, as compared to 50–100 GW events without such data.

Masses in the Stellar Graveyard

LIGO-Virgo/Frank Elavsky/Northwestern LIGO and Virgo Announce Four New Gravitational-Wave Detections

BH and NS Mass Chart

The masses of stellar remnants are measured in many different ways. This graphic shows the masses for black holes detected through electromagnetic observations (purple); the black holes measured by gravitational-wave observations (blue); neutron stars measured with electromagnetic observations (yellow); and the masses of the neutron stars that merged in an event called GW170817, which were detected in gravitational waves (orange). The remnant of GW170817 is unclassified, and labelled as a question mark.


Beyond advanced LIGO and VIRGO

Cosmic explorer

Cosmic Explorer builds on the experience and success of current detectors, to create a next generation of instruments with an order of magnitude more sensitivity than Advanced LIGO. Several features define the Cosmic Explorer concept, and serve to differentiate it from other next-gen detectors.

The Laser Interferometer Space Antenna (LISA) is a European Space Agency mission designed to detect and accurately measure gravitational waves—tiny ripples in the fabric of space-time—from astronomical sources. LISA would be the first dedicated space-based gravitational wave detector. It aims to measure gravitational waves directly by using laser interferometry. The LISA concept has a constellation of three spacecraft, arranged in an equilateral triangle with sides 2.5 million km long, flying along an Earth-like heliocentric orbit. The distance between the satellites is precisely monitored to detect a passing gravitational wave.

Gravitational-wave sensitivity curves

Gravitational waves travel at the speed of light

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s