#  Euclid – the Dark Universe detective

L. Linke on behalf of the Euclid Consortium  Universität Innsbruck, Institut
für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria

###### Abstract

Euclid is a recently launched medium-class mission by the European Space
Agency (ESA) designed to measure cosmological parameters, test the
cosmological standard model, and explore the nature of dark matter and dark
energy. To this end, Euclid conducts a survey of up to
$14\,000\,\mathrm{deg}^{2}$ of the extra-galactic sky and obtains optical and
near-infrared photometric measurements for more than a billion galaxies as
well as near-infrared slitless spectroscopy for more than 35 million galaxies.
These observations will be used to estimate galaxy clustering and cosmic
shear. It is expected that Euclid will achieve percent-level constraints on
the Dark Energy equation of state parameter. The survey will also be exploited
with a range of other cosmological probes and prove revolutionary for non-
cosmological science.

##  1 Introduction

The cosmological standard model, $\Lambda$CDM, is a remarkable success story,
able to describe a wide range of observations from the early Universe and the
cosmic microwave background (CMB) to today’s large-scale structure (LSS) with
just six parameters [1] [2] [3]. However, a range of issues have emerged with
this standard model. The first and most pressing is the nature of the dark
universe. As demonstrated by many independent observations, e.g., the CMB,
supernovae, or the LSS, the energy-matter budget of the Universe is dominated
by dark matter and dark energy, both of which cannot be described by the
standard particle physics and are fundamental puzzles to modern physics.

Another emerging issue is the difference in inferred parameter values from
probes of the early and late Universe. For example, measurements of the CMB
[1] predict, under the assumption of $\Lambda$CDM, a Hubble constant of
$H_{0}=67.5\pm 0.5\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}$, while direct
measurements via the distances and redshifts of cepheids and supernovae Type
Ia [4] suggest $H_{0}=73.04\pm
1.04\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}$ – a $5\sigma$ tension. A
similar, though less significant, tension is seen for the clustering parameter
$S_{8}$, for which measurements from the LSS at late times predict lower
values than inferred from the CMB [5].

To confirm or reject these tensions and to study the nature of dark matter and
dark energy, new observations are needed. Observations of the CMB are not
optimal for this quest, as the CMB is mainly sensitive to the properties of
the Universe at recombination when dark energy was negligible. Instead, the
cosmic expansion history and the growth of the LSS provide more information on
the influence of the dark universe. Accessing this information is the
principal goal of the recently started Euclid mission [6], which conducts
space-based surveys of the extragalactic sky and infers cosmological
information from two probes of the LSS.

The first probe is the three-dimensional clustering of galaxy positions. These
galaxies trace the (not directly observable) distribution of dark matter.
Overdensities in the matter distribution are linked directly to initial
density perturbations, the imprints of which we can also observe in the CMB.
Statistically, these overdensities in the galaxy distribution (and
equivalently of the matter field) can be described by the second-order
correlation function and its Fourier space analogue, the power spectrum. These
quantify the excess probability of finding two galaxies at a given separation
with respect to a uniform distribution. To see why this statistic incorporates
cosmological information, it is best to consider the most prominent feature: a
series of peaks in the power spectrum called baryon-acoustic oscillations
(BAOs) [7]. These peaks have the same physical origin as the oscillations of
the CMB temperature power spectrum, namely the interplay between pressure and
gravity for baryons before and during recombination. Therefore, the length
scale associated with the BAOs is related to the sound horizon, stretched by
the cosmic expansion. Thus, the BAO scale acts as a standard ruler and can be
used to determine the cosmic expansion history.

To measure the correlation functions of galaxy clustering, we require three-
dimensional positions. For these, spectroscopic redshifts are needed.
Furthermore, to quantify dark energy’s evolution, a wide redshift range
extending beyond $z=1$ is needed. At these redshifts, though, many galaxies
are mostly observable in the near-infrared (NIR). Thus, the extinction of
Earth’s atmosphere requires observations from space.

The second primary probe of the cosmic LSS is cosmic shear [8] [9]. This
effect describes the coherent distortion of the observed shapes of distant
galaxies due to weak gravitational lensing by foreground matter structures.
The lensing-induced shear in the galaxy images is a direct tracer of the
projected matter distribution and, therefore, complementary to the galaxy
clustering measurement, which depends on the bias between the galaxy and
matter distribution.

For cosmic shear, again, two-point correlation functions (and the related
power spectra) are the observable of choice. However, in contrast to galaxy
clustering, one considers two-dimensional correlations of the shapes of
galaxies at different projected positions on the sky. These correlations
depend on the total projected mass between the observer and galaxies, as well
as the distances between the observer, the lensing structure and the galaxies.
The dependencies lead to the sensitivity of cosmic shear to the matter
density, clustering, and cosmic expansion history. To optimally constrain the
latter, the source galaxies need to be divided into tomographic redshift bins,
and the correlations between different bins need to be considered. For this,
redshift estimates for each galaxy need to be available. However, provided the
bins are broader than associated errors, it is sufficient to use photometric
instead of spectroscopic redshift estimates. This allows for a much larger
source galaxy sample and extends the analysis to fainter, higher-redshift
galaxies for which spectroscopic observations might be unfeasible.

The key sources of noise for cosmic shear analyses are the intrinsic shapes of
galaxies. However, this noise is suppressed as more galaxies are considered,
as the correlation function estimation averages over the randomly orientated
shapes. Thus, for cosmic shear, it is vital to include as many galaxies as
possible in one’s sample.

Euclid was specifically designed to meet the requirements of both galaxy
clustering and cosmic shear. Thus, the start of this mission signals an
exciting period for these two probes of the LSS.

##  2 The Euclid mission

Euclid is a medium-class mission of the European Space Agency (ESA) and part
of its Cosmic Vision 2015-2025 programme. Historically, the mission arose from
two proposed surveys, SPACE [10], whose goals were galaxy clustering
measurements, and DUNE [11], which planned a cosmic shear analysis. These
surveys were proposed in 2007 and, due to their complementarity and similar
goals, combined. Formal acceptance of the combined mission occurred in 2011.
After a long design and development process to create the telescope and
instruments to tight specifications, Euclid finally launched on 1st July 2023.
Launch and journey to the Earth-Sun Lagrange point 2 occurred as planned, and
the first (unprocessed) test images were presented to the public less than a
month later. The first processed early-release observations were released on
7th November 2023, highlighting the wide field-of-view (FOV), crisp
resolution, and good detection of low-surface brightness objects. The
scientific survey started on 14th February 2024, and the first cosmological
results are expected in 2026.

As mentioned above, Euclid’s goal is to determine the evolution of dark
energy. Of particular interest is the equation-of-state $w$ of dark energy,
given by its pressure $p$ and density $\rho$ as $p=w\,\rho$. To cause the
accelerated expansion of the Universe, the $w$ of dark energy needs to be
smaller than $-1/3$. If $w$ is constant and equal to $-1$, dark energy behaves
exactly as expected for a cosmological constant $\Lambda$. However, $w$ can be
time-varying and thus a function of redshift $z$. Such a time-varying equation
of state can be parameterized as

$w(z)=w_{0}+w_{a}\frac{z}{1+z}\;,$ (1)

with free parameters $w_{0}$ and $w_{a}$. Euclid aims to determine these
parameters so precisely that the figure-of-merit (FOM), defined by

$\mathrm{FOM}=\frac{1}{\sqrt{\mathrm{det}\mathrm{Cov}(w_{0},w_{a})}}\;,$ (2)

reaches at least 400. Similarly, Euclid is supposed to constrain $\sigma_{8}$
to 1% and the sum of the neutrino masses $m_{\nu}$ to 0.03 eV. To reach these
high goals, galaxy clustering and cosmic shear need to be combined.

For this, Euclid uses a 1.2m primary mirror, which enables a large FOV of
$0.54\,\mathrm{deg}^{2}$ and two scientific instruments, the optical visible
imaging instrument VIS and the NIR spectrometer and photometer (NISP).

VIS [12], specifically designed to observe large parts of the sky with a high
resolution, consists of a large-format imager with a pixel size of
$0\hbox{$.\\!\\!^{\prime\prime}$}1$. The large FOV is covered by 36 CCDs
arranged in a square grid. VIS observes with a single bandpass
$I_{\scriptscriptstyle\rm E}$ in the range of 530–920 nm. This range was
chosen because it contains the maxima of the spectral energy distribution of
the targeted galaxies. Furthermore, galaxy shapes at these wavelengths are
mostly regular, thus enabling the precise shape measurements required for
cosmic shear analyses.

NISP [13] combines a multiband NIR photometer and a slitless grism
spectrometer. The photometer provides three passbands,
$Y_{\scriptscriptstyle\rm E}$ (949.6 nm–1212.3 nm), $J_{\scriptscriptstyle\rm
E}$(1167.6 nm–1567 nm) and $H_{\scriptscriptstyle\rm E}$(1521.5 nm–2021.4 nm).
Together, these can be used for photometric redshift estimates of galaxies
whose shapes have been measured from VIS images. The spectrometer contains
four grisms, which enable the simultaneous measurement of thousands of spectra
across the FOV. Most observations are carried out with the red grisms (1206
nm–1892 nm), of which there are three in NISP with different dispersion
directions. Two grims are used for science data acquisition in the EWS,
allowing the spectroscopic redshifts $z$ of galaxies to be determined to an
accuracy of $0.001(1+z)$. The NISP also carries a blue grism (926 nm–1366 nm),
which is used to characterize the observed galaxy population and is important
for non-cosmological science.

With these instruments, Euclid will measure the shapes of 1.5 billion galaxies
for cosmic shear analysis and the three-dimensional positions of 35 million
galaxies for galaxy clustering analysis. To do so, Euclid will undertake two
surveys [14]: the Euclid Wide Survey (EWS), shown in Fig. 1, and the Euclid
Deep Survey (EDS).

Figure 1: Area covered by the Euclid Wide Survey (EWS). Colours indicated in
which survey year the area is observed. Image Credit: ESA/Euclid/Euclid
Consortium. Work performed by ATG under contract for ESA

The EWS will map up to $14\,000\,\mathrm{deg}^{2}$ of the extragalactic sky.
This region encompasses almost all regions with low zodiacal background and
low Galactic extinction. In this region, VIS will observe extended sources
with an S/N $\geq 10$ up to a limiting magnitude of $I_{\scriptscriptstyle\rm
E}=24.5\mathrm{mag}$; while NISP reaches an S/N$\geq 5$ up to a limiting
magnitude of 24 mag in all three photometric bands. The EWS is divided into
$27\,500$ fields, each of which is observed once by the roughly 70.2-minute
reference observing sequence (ROS), which includes 6 VIS-exposures,
simultaneously to 4 grism, 4 $Y_{\scriptscriptstyle\rm E}$-, 4
$J_{\scriptscriptstyle\rm E}$\- and 4 $H_{\scriptscriptstyle\rm E}$-exposures,
as well as bias, dark, and flat images. The EWS will provide the bulk of
observing data for the cosmological analysis. However, to calibrate the
telescope and instruments, characterise the observed galaxies, and enhance the
galaxy shape measurements, it is accompanied by the EDS.

The EDS consists of three regions covering a total of $53\,\mathrm{deg}^{2}$.
These fields are observed multiple times (at least 40 repetitions of the ROS),
leading to limiting magnitudes fainter by two magnitudes than in the EWS. The
goal of the EDS is to reach a 99% complete and pure sample of $120\,000$
spectroscopically observed galaxies and accurate shapes of photometrically
observed galaxies. These samples allow for the characterization of the EWS
galaxy sample and calibration of the weak lensing shape measurement
algorithms. The EDS regions were explicitly chosen to overlap with past and
future observations, for example, the Herschel [15] and AKARI-NEP surveys
[16], the Chandra Deep Field South [17], Rubin deep-drilling fields [18], and
Spitzer [19], making them also a rich data set for non-cosmological science.

Additionally, Euclid observes the Euclid Auxiliary Fields (EAFs), which are
used to calibrate the photometric redshift estimation and quantify the colour
dependence of shape measurements. The EAFs are chosen to have been observed
already by ground- and space-based surveys and include, for example, the
COSMOS field [20].

##  3 From images to cosmology

The raw VIS and NISP images and spectroscopy measurements are processed in
computing facilities on the ground to catalogues of galaxies with shape
measures and redshift estimates, which are used to compute the correlation
functions and finally infer the cosmological parameters.

As a first step, the VIS and NISP images are processed by combining dithers,
considering flats and bias images, and extracting source catalogues. To
complement these catalogues, external data from ground-based surveys like the
Dark Energy Survey (DES) [21], the Ultraviolet Near Infrared Optical Northern
Survey (UNIONS), and the Legacy Survey of Space and Time (LSST) [18] are
calibrated and added to the Euclid data set. These external data are crucial
for estimating photometric redshift. Since VIS only observes in a single band,
it cannot determine galaxies’ redshifts. While NISP photometry provides colour
information in the NIR, optical photometry is required to reach the tight
constraints on the photometric redshift uncertainty.

Objects observed spectroscopically by NISP are assigned a spectroscopic
redshift estimate. For these, the object position in the photometric image is
mapped to its first-order dispersed image (the so-called spectrogram) in the
spectroscopic image. The one-dimensional spectrum of the object is then
extracted from the two-dimensional spectrogram. By template fitting to the
spectrum, one then obtains the redshift estimate [22].

For VIS-detected objects, shape measurements are carried out. These can be
difficult, in particular for faint and small galaxies, as the intrinsic
morphology of the galaxies is complex and unknown, instrument effects like the
PSF, pixelisation, and detector noise distort the shapes, and blending or
obscuration of galaxies further complicate the measurement.

An important part of Euclid’s shape measurements is the correct understanding
of the PSF. Euclid forward-models the PSF by using our knowledge of the
instrumental optics and including chromatic effects. However, this forward-
model is not static, but updated and refined throughout the mission. These
updates are based on empirical calibration against observed stars.

Once the shape and redshift estimates are added to the observed galaxy
catalogue, summary statistics like the second-order correlation functions and
power spectra are estimated. These are then compared to the cosmological model
using Bayesian inference and MCMC techniques. While this might seem like a
straightforward step, the high precision of Euclid’s measurements requires a
high accuracy of theoretical models used for the Euclid analysis. For example,
modelling approximations accurate enough for previous analysis might no longer
be appropriate for Euclid. Some higher-order corrections to the matter power
spectrum, such as magnification bias, can bias Euclid cosmological parameter
estimates by more than 1$\sigma$, if not taken into account [23].
Consequently, we need to account for these effects in the modelling.
Additionally, astrophysical effects, even if accounted for in previous
analyses, can play an even stronger role for Euclid. An example of these are
the correlations of intrinsic galaxy shapes, the so-called intrinsic
alignments [24]. These correlations contaminate the measured cosmic shear
signal and, if not taken into account, can severely bias cosmological
constraints [25]. While previous cosmic shear analyses mostly used the simple
phenomenological non-linear alignment model [26], this might not be accurate
enough at Euclid precision and other models might be required [27] [28].

Although these modelling concerns complicate the analysis, solving them will
be worthwhile. Figure 2 shows a forecast of Euclid constraints on a flat
cosmology with varying $w_{0}$ and $w_{a}$, both from weak lensing and galaxy
clustering alone and from their combination [29]. One sees that the different
probes are indeed complementary to each other. While lensing alone constrains
$\Omega_{\mathrm{m}}$ up to 3.4%, the full combination reaches 0.57%. The full
Euclid dataset will constrain $w_{0}$ and $w_{a}$ to the per cent level. Thus
Euclid will definitively answer whether dark energy behaves like a
cosmological constant or not.

Figure 2: Forecast for cosmological constraints from Euclid. Purple are
constraints using only galaxy clustering with spectroscopic redshift; yellow
using only cosmic shear. Orange are constraints when combining spectroscopic
clustering with cosmic shear and yellow from combining spectroscopic
clustering, cosmic shear, galaxy clustering with photometric redshifts and the
cross-correlations between clustering and shear. From Euclid Collaboration:
Blanchard et al. [29]

##  4 Additional cosmological probes

While the design choices for the Euclid mission were driven by galaxy
clustering and cosmic shear power spectra, their cosmological information can
be complemented by additional probes that benefit from the wide area, accurate
shape measurements, and high resolution of Euclid’s surveys.

Examples of these are higher-order statistics (HOS) of cosmic shear and galaxy
clustering. These encompass statistical properties of the matter structures
beyond the second-order correlation or the power spectra. HOS can be roughly
grouped into two categories: those that consider $n$th-order moments of the
density distribution (e.g. higher-order correlation functions [30]) and those
using topological information (e.g. peak statistics [31]). These HOS depend
differently an cosmological parameters than the standard power spectra. Thus,
combining HOS and second-order statistics can partially resolve degeneracies
and improve constraints on $\Omega_{\mathrm{m}}$ and $\sigma_{8}$ by factors
between 2 and 5 [32].

Another important cosmological probe is the abundance of galaxy clusters. This
abundance probes the clustering parameter $\sigma_{8}$, the matter density
$\Omega_{\mathrm{m}}$, as well as the cosmic structure growth rate, which in
turn is sensitive to $w_{0}$ and $w_{a}$. In the EWS, on the order of $10^{6}$
galaxy clusters of mass above $10^{14}M_{\odot}$ will be detected. Moreover,
Euclid will detect a large number of clusters at redshift beyond 1, which is
critical to constraining dark energy. Aside from the direct detection of
galaxy clusters, Euclid is also particularly useful when combined with
observation of the intra-cluster medium, e.g. from X-ray emission or the
Sunyaev–Zeldovich (SZ) effect. These observations provide well-characterized
cluster samples but lack estimates of the cluster masses. Here, weak lensing
measurements from Euclid will provide the necessary link between the observed
X-ray luminosity or SZ-signal and the dark matter distribution.

Due to the fine spatial resolution and depth, up to $2300$ strongly lensed
quasars are expected in the EDS. They provide an additional cosmological probe
via time-delay measurements. Multiple images of the same source arrive at the
observer at different times due to the lights’ deflection and gravitational
time delay. The differences between the images depend on cosmological
distances and, therefore, the Hubble constant. Using the combination of strong
and weak lensing, Euclid’s observations will also provide detailed mass models
of galaxy clusters. These allow for constraining cosmological parameters and
testing $\Lambda$CDM against alternative dark matter models.

Additional cosmological information can be accessed by correlating cosmic
shear and the spatial galaxy distribution with maps of the gravitational
lensing of the CMB. This CMB lensing is caused (partially) by the same LSS as
the cosmic shear, but due to the large distance to the last scattering
surface, the lensing signal depends differently on the cosmic expansion
history and the structure growth rate. Similarly to HOS, CMB-LSS cross-
correlations thus reduce parameter degeneracies. Combining Euclid with data
from the upcoming Simons Observatory can reduce the uncertainty on some
parameters of generalised cosmological models by factors up to ten [33].

Euclid will observe $2\times 10^{6}$ quasars in the EWS, of which ten
thousands fulfil the conditions for a tight relation between their rest-frame
UV and rest-frame X-ray emission, i.e., unobscured UV and X-ray energies, no
radio emission, and negligible host galaxy contribution [34]. These quasars
can be calibrated to become standard candles and direct probes of the cosmic
expansion history. By combining spectroscopic redshift estimates from NISP
with X-ray data, $\Omega_{\mathrm{m}}$ and $w_{0}$ can be estimated
independent of the primary cosmological probes.

Finally, Euclid can also probe the cosmic expansion history with cosmic
chronometers. These consist of massive, passively-evolving galaxies, which are
a physically homogenous population and, at each redshift, are the oldest
objects. Their formation history is well understood, so it is possible to
determine their differential age as a function of redshift. This gives us an
estimate of the relation between cosmic time and redshift and, thus, the
cosmic expansion history. Forecasts for Euclid expect to constrain $H_{0}$
with cosmic chronometers independently of other probes with a 4% precision
[35].

##  5 Non-cosmological science

Euclid data will also prove a treasure trove for a wide range of non-
cosmological research.

For example, Euclid will prove crucial for understanding the formation,
evolution, and structure of galaxies. Due to its fine resolution, Euclid will
obtain resolved images of a considerable fraction of observed galaxies over a
large redshift range. These unveil the morphologies of galaxies throughout
cosmic time, giving clues to galaxy evolution models. Euclid will help in
characterizing physical properties like the star-formation rate (SFR) of
galaxies throughout time by observing up to 67 million H$\alpha$-emitting
galaxies up to $z=1.8$ in the EWS [36]. As the H$\alpha$ \- emission intensity
is strongly correlated to the SFR, these observations constrain the SFR-to-
stellar mass relation. Moreover, due to its ability to detect low-surface
brightness objects, Euclid will observe many faint features of nearby
galaxies, such as stellar streams or tidal remnants, as well as dwarf galaxies
[37]. These objects are crucial for understanding galaxy formation at the low-
mass end. Finally, Euclid can also reveal the relation between galaxy
properties and the dark matter halos they reside in. For this, the weak
lensing measurements can be used to trace the dark matter distribution, which
is then compared to the position of galaxies with varying physical properties.
These correlations are crucial tests of galaxy evolution models.

##  6 Conclusion

Euclid is a crucial experiment for exploring the dark universe, particularly
the time evolution of dark energy, by tracing the cosmic large-scale
structure. It is designed, built, and calibrated to deliver some of the most
precise galaxy clustering and cosmic shear results ever obtained.

After its successful launch on 1st July 2023, travel to L2, and science
performance verification, the scientific survey started on 14th February 2024,
with an expected mission length of 6 years. At the time of writing, the first
data are pouring in, and the first science results are prepared to be
published. The first cosmological results will be published in 2026, together
with a full release of all data observed in the first survey year.

Several additional probes of cosmology complement the primary cosmological
probes. This is useful for achieving the best cosmological results as well as
for checking and verifying consistency. Euclid’s surveys will also provide an
excellent dataset for non-cosmological research, including galaxy evolution
and stellar physics.

## Acknowledgments

LL acknowledges support from the Austrian Research Promotion Agency (FFG) and
the Federal Ministry of the Republic of Austria for Climate Action,
Environment, Mobility, Innovation and Technology (BMK) via grant 900565. The
Euclid Consortium acknowledges the European Space Agency and a number of
agencies and institutes that have supported the development of Euclid, in
particular the Agenzia Spaziale Italiana, the Belgian Science Policy, the
Canadian Euclid Consortium, the French Centre National d’Etudes Spatiales, the
Deutsches Zentrum für Luft- und Raumfahrt, the Danish Space Research
Institute, the Fundação para a Ciência e a Tecnologia, the Hungarian Academy
of Sciences, the Ministerio de Ciencia, Innovación y Universidades, the
National Aeronautics and Space Administration, the National Astronomical
Observatory of Japan, the Netherlandse Onderzoekschool Voor Astronomie, the
Norwegian Space Agency, the Research Council of Finland, the Romanian Space
Agency, the State Secretariat for Education, Research and Innovation (SERI) at
the Swiss Space Office (SSO), and the United Kingdom Space Agency. A complete
and detailed list is available on the Euclid web site (http://www.euclid-
ec.org).

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