The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015–2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14 000 deg² of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.

The global network of gravitational-wave observatories now includes five detectors, namely LIGO Hanford, LIGO Livingston, Virgo, KAGRA, and GEO 600. These detectors collected data during their third observing run, O3, composed of three phases: O3a starting in 2019 April and lasting six months, O3b starting in 2019 November and lasting five months, and O3GK starting in 2020 April and lasting two weeks. In this paper we describe these data and various other science products that can be freely accessed through the Gravitational Wave Open Science Center at https://gwosc.org. The main data set, consisting of the gravitational-wave strain time series that contains the astrophysical signals, is released together with supporting data useful for their analysis and documentation, tutorials, as well as analysis software packages.

We construct an updated and extended compilation of growth-rate data based on recent redshift-space distortion measurements. The data set consists of 34 data points and includes corrections for model dependence. In order to minimize overlap and maximize the independence of the data points, we also construct a subsample of this compilation (a “gold” growth data set) which consists of 18 data points. We test the consistency of this data set with the best-fit $\mathrm{Planck}15/\mathrm{\Lambda }\mathrm{CDM}$ parameters in the context of General Relativity using the evolution equation for the growth factor $\delta (a)$ with a $w\mathrm{CDM}$ background. We find tension at the $\sim 3\sigma$ level between the best-fit parameters $w$ (the dark energy equation of state), ${\mathrm{\Omega }}_{0m}$ (the matter density parameter), and ${\sigma }_8$ (the matter power spectrum normalization on scales $8h^{-1}\mathrm{Mpc}$) and the corresponding $\mathrm{Planck}15/\mathrm{\Lambda }\mathrm{CDM}$ parameters ($w=-1$, ${\mathrm{\Omega }}_{0m}=0.315$, and ${\sigma }_8=0.831$). We show that the tension disappears if we allow for evolution of the effective Newton constant, parametrized as $G_{\mathrm{eff}}(a)/G_{\mathrm{N}}=1+g_a(1-a{)}^n-g_a(1-a{)}^{2n}$ with $n\ge 2$ where $g_a$ and $n$ are parameters of the model, $a$ is the scale factor, and $z=1/a-1$ is the redshift. This parametrization satisfies three important criteria: a) positive energy of the graviton ($G_{\mathrm{eff}}>0$), b) consistency with big bang nucleosynthesis constraints ($G_{\mathrm{eff}}(a\ll 1)/G_{\mathrm{N}}=1$), and c) consistency with Solar System tests ($G_{\mathrm{eff}}(a=1)/G_{\mathrm{N}}=1$ and $G_{\mathrm{eff}}^{\prime }(a=1)/G_{\mathrm{N}}=0$). We show that the best-fit form of $G_{\mathrm{eff}}(z)$ obtained from the growth data corresponds to weakening gravity at recent redshifts (decreasing function of $z$), and we demonstrate that this behavior is not consistent with any scalar-tensor Lagrangian with a real scalar field. Finally, we use MGCAMB to find the best-fit $G_{\mathrm{eff}}(z)$ obtained from the Planck cosmic microwave background power spectrum on large angular scales and show that it is a mildly increasing function of $z$, in $3\sigma$ tension with the corresponding decreasing best-fit $G_{\mathrm{eff}}(z)$ obtained from the growth data.

We have performed a comparative analysis of three recent and reliable SnIa datasets available in the literature: the Full Gold (FG) dataset (157 data points $0<z<1.75$), a Truncated Gold (TG) dataset (140 data points $0<z<1$) and the most recent Supernova Legacy Survey (SNLS) dataset (115 data points $0<z<1$). We have analyzed and compared the likelihood of cosmological constant and dynamical dark energy parametrizations allowing for crossing of the phantom divide line (PDL). We find that, even though the constraints obtained using the three datasets are consistent with each other at the 95% confidence level, the latest (SNLS) dataset shows distinct trends which are not shared by the Gold datasets. We find that the best fit dynamical $w(z)$ obtained from the SNLS dataset does not cross the PDL $w=-1$ and remains above and close to the $w=-1$ line for the whole redshift range $0<z<1$ showing no evidence for phantom behavior. The $\Lambda +\mathrm{\text{Cold}}\mathrm{\text{Dark}}\mathrm{\text{Matter}}$ (LCDM) parameter values ($w_0=-1$, $w_1=0$) almost coincide with the best fit parameters of the dynamical $w(z)$ parametrizations. In contrast, the best fit dynamical $w(z)$ obtained from the Gold datasets (FG and TG) clearly crosses the PDL and departs significantly from the PDL $w=-1$ line while the LCDM parameter values are about $2\sigma$ away from the best fit $w(z)$. In addition, the $({\Omega }_{0m},{\Omega }_{\Lambda })$ parameters in a LCDM parametrization without a flat prior, fit by the SNLS dataset, favor the minimal flat LCDM concordance model. The corresponding fit with the Gold datasets mildly favors a closed universe and the flat LCDM parameter values are $1\sigma –2\sigma$ away from the best fit $({\Omega }_{0m},{\Omega }_{\Lambda })$.

We investigate the cosmological predictions of several $f(T)$ models, with up to two parameters, at both the background and the perturbation levels. Using current cosmological observations (geometric supernovae type Ia, cosmic microwave background and baryonic acoustic oscillation and dynamical growth data) we impose constraints on the distortion parameter, which quantifies the deviation of these models from the concordance $$\Lambda${}$ cosmology at the background level. In addition we constrain the growth index $$\gamma${}$ predicted in the context of these models using the latest perturbation growth data in the context of three parametrizations for $$\gamma${}$. The evolution of the best fit effective Newton constant, which incorporates the $f(T)$-gravity effects, is also obtained along with the corresponding $1$\sigma${}$ error regions. We show that all the viable parameter sectors of the $f(T)$ gravity models considered practically reduce these models to $$\Lambda${}\mathrm{CDM}$. Thus, the degrees of freedom that open up to $$\Lambda${}\mathrm{CDM}$ in the context of $f(T)$ gravity models are not utilized by the cosmological data leading to an overall disfavor of these models.