June 7, 2023

SCIENCE GOALS

Euclid is an ESA mission to map the geometry of the universe by investigating the evolution of cosmic structures under two opposing effects:

  • Dark energy, a mysterious component driving the accelerating expansion of the universe. This expansion was predicted in 1927 by Georges Lemaître on the basis of a model built around the Friedmann-Lemaître equations between 1923 and 1925, and the theory of general relativity postulated by Albert Einstein in 1915. It was observed for the first time by Edwin Hubble in 1929, who subsequently devised an equation that defines his famous Hubble’s law, renamed the Hubble-Lemaître law at the congress of the International Astronomical Union (IAU) in 2018. The current standard cosmological model, based on observations much further back than Hubble’s, brought three astronomers, Saul Perlmutter, Brian P. Schmidt and Adam G. Reiss, a Nobel Prize in 2011 for their discovery that the universe has been expanding at an accelerating rate for several billion years under the effect of dark energy.

  • Gravity, which shapes how matter is distributed and thus binds stars and galaxies together within a filament structure called the cosmic web. Gravity itself originates in matter, but there is not enough visible matter to explain its effects, hence the theory that another kind of matter undetectable with current instruments must be present, which has been termed “dark matter”. The concept of dark matter was advanced for the first time by the astronomer Fritz Zwicky in 1933. By observing the cohesion of galaxies in the Coma Cluster—which takes its name from the Coma Berenices constellation—and calculating the cluster’s dynamic mass from Newton’s law, he found it was much greater than the cluster’s actual mass determined from the mass-luminosity law. Later, in 1973, the astronomer Vera Rubin came to the same conclusion using the rotation curves of numerous galaxies and measuring the rotational velocity of stars in the disk around their galactic centre via the Doppler-Fizeau effect. The velocities measured were far greater than those calculated with Newton’s law, thus suggesting a source of gravity much larger than that from visible matter, and validating the concept of dark matter. It is now estimated there is five times more dark matter than visible matter in the universe.

The standard cosmological model today allows us to estimate that the universe is made up of 69% dark energy, 26% dark matter and only 5% visible matter, known as baryonic matter (consisting of atoms). That means 95% of the universe has so far defied explanation. The existence and range of dark energy cannot be explained with our current understanding of fundamental physics, and dark energy remains hidden from all our instruments.

Constitution of the universe. Credit: Euclid consortium

The effects of gravity induced by visible and above all dark matter, and the effects of dark energy oppose each other and do not balance out. After a deceleration phase mainly due to gravitational effects induced by visible and dark matter over the first billions of years in its history, the universe is now therefore expanding at an accelerating rate driven by dark energy, which has quite clearly overcome the effects of gravity.

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History of the expansion of the universe. Credit: Euclid Redbook - Definition Study Report/ESA/SRE (2011)12, July 2011

Euclid’s observations will span the entire period up to ten billion years ago during which dark energy played a significant role in accelerating the universe’s expansion, covering objects up to a redshift z = 2. 

To track the evolution of large-scale structures in the universe, the redshift of galaxies and galaxy clusters will be measured to determine their spatial distribution over time. This will be determined precisely by spectrophotometry, sensing the redshift of characteristic emission lines like hydrogen’s. The mission plans to observe some 35 million sources.

The distribution of dark matter will be ascertained from images of galaxies warped in spacetime by an effect known as gravitational lensing. This means each source’s redshift will also need to be determined by photometric methods, complementing the images acquired by Euclid’s telescope with infrared photometry measurements on board the spacecraft and with the assistance of Earth-based telescopes in the visible spectrum. These telescopes will be located in the northern and southern hemispheres to cover the mission’s 14,700 square-degree field of investigation. The plan is to observe some 1.5 billion sources.

Today, we are therefore able to see the effects of dark energy and dark matter, but their precise nature remains a mystery. Euclid therefore intends to probe them using weak gravitational lensing (WL) and baryonic acoustic oscillations (BAO).

Weak gravitational lensing

A gravitational lens is formed by one or more very massive celestial bodies, typically a galaxy or galaxy cluster lying between the observer and a distant light source. Predicted by Einstein’s theory of general relativity, the gravitational field induced by such massive bodies deflects light in their vicinity, thus distorting images in the observer’s line of sight.

As formulated by Einstein in 1915, the deflection induced by the Sun is written α(rd) = 4GM/Rc2, where G is the gravitational constant, M the mass of the Sun, R the distance to the centre of the Sun, and c the speed of light. For a light ray passing in the near vicinity of the Sun, this value α = 1.745 arcseconds.

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Deflection of a light ray by the Sun. Credit: https://ichi.pro/fr/la-theorie-de-la-gravite-d-einstein-et-la-flexion-de...

This value was confirmed in brilliant fashion by astronomers during the total eclipse of the Sun of 29 May 1919, which occulted the bright Hyades star cluster, thus validating Einstein’s theory.

On a larger scale, the path of the image of a galaxy lying behind a cluster is also affected by the cluster’s gravitational effects. Where the observed light source, the lensing body and the observer are perfectly aligned, the image may take the form of an arc or an Einstein ring, in which case the effect is known as strong gravitational lensing.

Principle of strong gravitational lensing. Credit - ALMA (ESO NRAO NAOJ), L. Calçada (ESO), Y. Hezeh et al

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Einstein rings: Credit: Hubble Space Telescope (NASA/ESA)

If the observed source, lensing body and observer are not in alignment, the lensing effect will be weak and limited to distortions that may be more frequent but harder to see.

Illustrations of the lensing effect in a circular symmetry image. In the Abell 370 galaxy cluster, strong lensing arcs may be seen around the cluster. All background galaxies undergo a weak lensing effect. Credit: NASA, ESA, Hubble (Rogelio Bernal Andreo)

Euclid will use these to measure distortions in galaxy images induced by the gravitational effects of visible and dark matter in galaxy clusters to be able to deduce and map the dark matter that neither our eyes nor our instruments can see. The use of weak gravitational lensing requires extremely high-quality images, as distortions due to the optical system have to be suppressed or eliminated by calibration in order to measure the real distortion due to gravity. For more than a billion of them, gravitational distortion induced by dark matter will be measured with 50 times more precision than with Earth-based telescopes.

Left: reconstitution of dark matter for different redshift values by the Hubble Space Telescope (HST). Credit: ©ESA

Centre: image of the Abell 1689 cluster by HST. Credit: NASA, N. Benitez (JHU), T. Broadhurst (Racah Institute of Physics/The Hebrew University), H. Ford (JHU), M. Clampin (STScI),G. Hartig (STScI), G. Illingworth (UCO/Lick

Right: reconstitution for the same field of the distribution of dark matter for z = 0.189 (distance of approximately 60 Mpc corresponding to 2 billion years). Credit: NASA, ESA, D. Coe (NASA Jet Propulsion Laboratory/California Institute of Technology, and Space Telescope Science Institute), N. Benítez (Institute of Astrophysics of Andalucía, Spain), T. Broadhurst (University of the Basque Country, Spain), and H. Ford (Johns Hopkins University, USA)

Baryonic Acoustic Oscillations (BAO)

For a few hundred thousand years after the Big Bang, the universe was filled with a plasma of permanently interacting baryons—protons and neutrons—and photons. While gravity created accumulations of matter (baryons) where density was highest, the energy of these interactions created a pressure that opposed the effects of gravity. These opposing phenomena in turn created pressure oscillations in this plasma, in the form of spherical acoustic waves similar to sound waves. These baryonic acoustic oscillations (BAO) corresponded to the anisotropies we see in the cosmic microwave background (CMB). We can see this first image of the universe today because when its radiation was released from matter 380,000 years after the Big Bang (at approximately z = 1,100), photons were able to escape. At that instant, the baryons making up visible matter were caught in overdense regions, with filaments and walls separated by enormous voids, particularly on spherical wavefronts, around “shells”. And it is in these shells forming large-scale structures that stars, galaxies and clusters were born and evolved as the universe expanded.

Galaxy distribution showing a circular pattern along acoustic wavefronts. Credit: Zosia Rostomian, Lawrence Berkeley National Laboratory

When we analyse the distribution of a large number of galaxies in the local universe and plot a graph of the mean angular distance between galaxies as shown in the image above, we see a maximum probability around 500 million light-years (150 million parsec (pc), noted 150 Mpc, where one parsec equals roughly 30,000 billion kilometres). Two galaxies taken at random are more likely to be 150 Mpc apart than 100 or 200 Mpc, for example, and are most often in shells spanning 150 Mpc—500 million light-years—that today are the result of the universe’s expansion since decoupling occurred.

BAO peak showing distance between galaxies with highest likelihood of being found. The distance is roughly 500 million light-years or 150 Megaparsecs (Mpc). Credit: NASA Goddard Space Flight Center

To measure far-off distances in the universe, we generally use what are termed standard candles. These are sources of known brightness at a standard distance. Given that luminosity decreases with the square of distance, as photons propagate on a spherical surface, we simply cross-multiply—applying some astronomic corrections—to estimate the distance of a far-off source. The most commonly used standard candles are Cepheid variables and especially Type 1a supernovae. But Euclid will use BAOs, as they provide a standard ruler for measuring distances between galaxies. Combining this with redshift measurements by an infrared spectrometer, we will be abl

Standard distance of 150 Mpc corresponding to the BAO peak through the ages due to the expansion of the universe. Here, for example, 3.8 billion years ago (z = 0.8), this distance was 150 Mpc/(1+z), i.e. 83 Mpc. For the purposes of comparison, 5.5 Ga corresponds to z = 1 and at the time of decoupling that gave rise to the cosmic wave background (CMB) 13.7 billion years ago, z = 1,100. Credit: E M Huff, the SDSS-III team and the South Pole Telescope team; graphic by Zosia Rostomian.

BAOs therefore give us a standard ruler for measuring galaxy distances and clustering as a function of their redshift. To measure precisely, we need to ignore the peculiar velocity of galaxies for which the Doppler-Fizeau effect is added to that of expansion (redshift) and induces distortions in the distribution of galaxies in the direction parallel to the line of sight with respect to the perpendicular direction. These redshift space distortions (RSD) are directly related to a coherent collapsing effect of galaxies attracted to one another by gravitational interaction. This technique will allow us to piece together the history and evolution of large-scale structures in the universe in which galaxies and clusters come together under the action of gravity.

Euclid will attempt to piece together the history and evolution of large-scale structures in the universe over the last 10 billion years (z=2). Credit: DR

Map of the universe back to z = 0.15 (roughly 1.3 billion years ago) compiled from the Baryon Oscillation Spectroscopic Survey (BOSS) of the Sloan Digital Sky Survey (SDSS) showing the filament structure of the cosmic web. Credit: SDSS

Applied within the same cosmic volume, these techniques will provide not only a systematic cross-examination but also a measurement of large-scale structures for different physical fields—potential, density, velocities—required to test dark energy and gravity at cosmological scales.

With its wide-field capabilities and high-precision design, Euclid will enable us to:

  1. Seek to identify the properties of dark energy by precisely measuring acceleration and its variations at different epochs
  2. Test the validity of the theory of general relativity at the cosmic scale
  3. Seek to identify the nature and properties of dark matter by mapping it in three dimensions throughout the universe
  4. Refine our knowledge of the conditions that existed at the birth of our universe, which triggered the formation of the cosmic structures we see today

Ultimately, Euclid will help to answer many questions, and notably:

  • Is dark energy simply a cosmological constant like the one originally postulated by Einstein?
  • Is there a new type of field, like for example the magnetic and gravity fields we already know, that is evolving dynamically with the expansion of the universe?
  • Could dark energy be the manifestation of a breakdown in general relativity and a modification of the law of gravity?
  • What are the nature and properties of dark matter?
  • In what initial conditions did the large-scale structures of the universe form?
  • What future lies ahead for the universe over the next billions of years?

Euclid is geared to making new discoveries on an unprecedented scale, and could well serve as the main source informing detailed studies of ground facilities and future satellites.