Does the mysterious dark matter experience gravity in the same way as ordinary matter? A team of scientists from MPA and the University of Geneva (Switzerland) has developed a new method to answer this question by measuring the time dilation in galaxy clusters. With future datasets, this method could detect violations of the equivalence principle at the level of a few percent.
In the 16th century, the Italian scientist Galileo Galilei is said to have dropped objects with different masses from the Leaning Tower of Pisa. With this experiment – possibly only imagined – he demonstrated that the acceleration of different bodies does not depend on their composition or mass. Since then, this seemingly counter-intuitive fact has become a fundamental pillar in our understanding of gravity, known as the weak equivalence principle. This principle states that any particle, regardless of its nature, experiences gravity in the same way.
Several experiments have confirmed with very high precision that the weak equivalence principle holds for all particles making up the ordinary matter around us. However, astrophysical and cosmological observations indicate that around 85 % of the matter in the Universe consists of unknown dark matter, which does not emit light and can only be probed through its gravitational impact on visible matter. If Galileo could have thrown a small amount of dark matter from the Pisa tower, would it have experienced the same acceleration as the other bodies? This remains a crucial open question, which could help shedding light on the nature of this mysterious component.
A team of researchers from MPA and the University of Geneva (Switzerland) – Sveva Castello, Enea Di Dio and Camille Bonvin – is determined to answer this question. Since dark matter has never been detected directly nor produced in a laboratory experiment, it is not possible to simply drop it from the Pisa tower. However, the team has designed a new method to perform an analogous experiment to Galileo’s in galaxy clusters. These are the largest gravitationally bound objects in the Universe and therefore provide the ideal environment to study the behaviour of dark matter under gravity. The new test consists in comparing the observed motion of the galaxies inside the clusters with the distortion of time generated by the clusters themselves.
Understanding the idea behind this test requires a small detour to the realm of Einstein’s theory of general relativity, providing our modern understanding of gravity. According to general relativity, the Universe can be described as a four-dimensional spacetime that gets distorted like a tablecloth in the presence of any object with a mass, such as galaxy clusters. This generates gravitational potential wells, which determine the motion of any particle under gravity. These distortions affect not only space but also time, so that a clock located at the bottom of a potential well ticks more slowly than one outside of it. This effect, known as time dilation or distortion of time, provides a direct measure of the depth of the gravitational potential well generated by a massive object.
If dark matter violates the weak equivalence principle, for example due to some unknown interactions, its motion under gravity will be different from the one predicted by general relativity. Since galaxies are mostly composed of dark matter, such a violation will impact their observed velocities inside a cluster. They will then move too fast or too slowly compared to the gravitational potential well of the cluster inferred from the distortion of time, clearly indicating an anomaly. Therefore, comparing galaxy velocities and the distortion of time in a galaxy cluster provides a powerful test of the weak equivalence principle.
Since we cannot send clocks across cosmological distances, how can we measure the distortion of time in galaxy clusters located billions of light-years away? This can be achieved by considering the impact of the distortion of time on light. Due to this effect, the wavelength of light emitted by galaxies in a cluster gets stretched and experiences a frequency shift, which is translated into a change of its observed colour. This leads to an observable gravitational redshift, which can be disentangled from other effects that change the colour of the light thanks to its symmetry properties when considering pairs of galaxies. This technique led to a first detection of this effect in 2011 by Radosław Wojtak, Steen H. Hansen and Jens Hjorth, who used a catalogue of around 100’000 galaxies in clusters by the Sloan Digital Sky Survey.
In this new study, the MPA-Geneva team predicted that existing measurements of the distortion of time can detect deviations from the weak equivalence principle at the level of 7-14 %. Ongoing galaxy surveys, such as the Euclid satellite and the Dark Energy Spectroscopic Instrument (DESI), will give access to larger samples of galaxy clusters and thus lead to an increased precision. In a realistic scenario, future datasets will be sensitive to violations of the equivalence principle at the level of a few percent.
As a next step, the team plans to apply the test to data. This will enable them to repeat Galileo’s experiment on astrophysical scales, providing crucial information on the properties of the mysterious dark matter in galaxy clusters. The discovery of a violation of the weak equivalence principle would have profound implications for cosmology, astrophysics and particle physics, and may also affect our fundamental understanding of gravity.
In the 16th century, the Italian scientist Galileo Galilei is said to have dropped objects with different masses from the Leaning Tower of Pisa. With this experiment – possibly only imagined – he demonstrated that the acceleration of different bodies does not depend on their composition or mass. Since then, this seemingly counter-intuitive fact has become a fundamental pillar in our understanding of gravity, known as the weak equivalence principle. This principle states that any particle, regardless of its nature, experiences gravity in the same way.
Several experiments have confirmed with very high precision that the weak equivalence principle holds for all particles making up the ordinary matter around us. However, astrophysical and cosmological observations indicate that around 85 % of the matter in the Universe consists of unknown dark matter, which does not emit light and can only be probed through its gravitational impact on visible matter. If Galileo could have thrown a small amount of dark matter from the Pisa tower, would it have experienced the same acceleration as the other bodies? This remains a crucial open question, which could help shedding light on the nature of this mysterious component.
A team of researchers from MPA and the University of Geneva (Switzerland) – Sveva Castello, Enea Di Dio and Camille Bonvin – is determined to answer this question. Since dark matter has never been detected directly nor produced in a laboratory experiment, it is not possible to simply drop it from the Pisa tower. However, the team has designed a new method to perform an analogous experiment to Galileo’s in galaxy clusters. These are the largest gravitationally bound objects in the Universe and therefore provide the ideal environment to study the behaviour of dark matter under gravity. The new test consists in comparing the observed motion of the galaxies inside the clusters with the distortion of time generated by the clusters themselves.
Understanding the idea behind this test requires a small detour to the realm of Einstein’s theory of general relativity, providing our modern understanding of gravity. According to general relativity, the Universe can be described as a four-dimensional spacetime that gets distorted like a tablecloth in the presence of any object with a mass, such as galaxy clusters. This generates gravitational potential wells, which determine the motion of any particle under gravity. These distortions affect not only space but also time, so that a clock located at the bottom of a potential well ticks more slowly than one outside of it. This effect, known as time dilation or distortion of time, provides a direct measure of the depth of the gravitational potential well generated by a massive object.
If dark matter violates the weak equivalence principle, for example due to some unknown interactions, its motion under gravity will be different from the one predicted by general relativity. Since galaxies are mostly composed of dark matter, such a violation will impact their observed velocities inside a cluster. They will then move too fast or too slowly compared to the gravitational potential well of the cluster inferred from the distortion of time, clearly indicating an anomaly. Therefore, comparing galaxy velocities and the distortion of time in a galaxy cluster provides a powerful test of the weak equivalence principle.
Since we cannot send clocks across cosmological distances, how can we measure the distortion of time in galaxy clusters located billions of light-years away? This can be achieved by considering the impact of the distortion of time on light. Due to this effect, the wavelength of light emitted by galaxies in a cluster gets stretched and experiences a frequency shift, which is translated into a change of its observed colour. This leads to an observable gravitational redshift, which can be disentangled from other effects that change the colour of the light thanks to its symmetry properties when considering pairs of galaxies. This technique led to a first detection of this effect in 2011 by Radosław Wojtak, Steen H. Hansen and Jens Hjorth, who used a catalogue of around 100’000 galaxies in clusters by the Sloan Digital Sky Survey.
In this new study, the MPA-Geneva team predicted that existing measurements of the distortion of time can detect deviations from the weak equivalence principle at the level of 7-14 %. Ongoing galaxy surveys, such as the Euclid satellite and the Dark Energy Spectroscopic Instrument (DESI), will give access to larger samples of galaxy clusters and thus lead to an increased precision. In a realistic scenario, future datasets will be sensitive to violations of the equivalence principle at the level of a few percent.
As a next step, the team plans to apply the test to data. This will enable them to repeat Galileo’s experiment on astrophysical scales, providing crucial information on the properties of the mysterious dark matter in galaxy clusters. The discovery of a violation of the weak equivalence principle would have profound implications for cosmology, astrophysics and particle physics, and may also affect our fundamental understanding of gravity.
Author:
Dr. Sveva Castello
Postdoc
Tel: 2007
Email: svevacas@mpa-garching.mpg.de
