The Einstein Telescope (ET), a proposed European ground-based gravitational-wave detector of third-generation, is an evolution of second-generation detectors such as Advanced LIGO, Advanced Virgo, and KAGRA which could be operating in the mid 2030s. ET will explore the universe with gravitational waves up to cosmological distances. We discuss its main scientific objectives and its potential for discoveries in astrophysics, cosmology and fundamental physics.

The astronomical event GW170817, detected in gravitational and electromagnetic waves, is used to determine the expansion rate of the Universe, which is consistent with and independent of existing measurements. The gravitational-wave signature of merging black holes or neutron stars yields the distance to the merger. If a counterpart is observed and its recession velocity arising from the Hubble flow is known, then a calibration of the Hubble constant that is entirely independent of the usual 'distance ladder' is possible. The gravitational-wave event of 17 August 2017 (GW170817) corresponded to the merger of two neutron stars, and an associated 'kilonova' was seen. Daniel Holz and the LIGO–Virgo collaboration, along with a group of astronomers involved with the search for the counterpart, have determined that the Hubble constant calculated this way is about 70 kilometres per second per megaparsec. This is consistent with other determinations, but independent of them. On 17 August 2017, the Advanced LIGO1 and Virgo2 detectors observed the gravitational-wave event GW170817—a strong signal from the merger of a binary neutron-star system3. Less than two seconds after the merger, a γ-ray burst (GRB 170817A) was detected within a region of the sky consistent with the LIGO–Virgo-derived location of the gravitational-wave source4,5,6. This sky region was subsequently observed by optical astronomy facilities7, resulting in the identification8,9,10,11,12,13 of an optical transient signal within about ten arcseconds of the galaxy NGC 4993. This detection of GW170817 in both gravitational waves and electromagnetic waves represents the first ‘multi-messenger’ astronomical observation. Such observations enable GW170817 to be used as a ‘standard siren’14,15,16,17,18 (meaning that the absolute distance to the source can be determined directly from the gravitational-wave measurements) to measure the Hubble constant. This quantity represents the local expansion rate of the Universe, sets the overall scale of the Universe and is of fundamental importance to cosmology. Here we report a measurement of the Hubble constant that combines the distance to the source inferred purely from the gravitational-wave signal with the recession velocity inferred from measurements of the redshift using the electromagnetic data. In contrast to previous measurements, ours does not require the use of a cosmic ‘distance ladder’19: the gravitational-wave analysis can be used to estimate the luminosity distance out to cosmological scales directly, without the use of intermediate astronomical distance measurements. We determine the Hubble constant to be about 70 kilometres per second per megaparsec. This value is consistent with existing measurements20,21, while being completely independent of them. Additional standard siren measurements from future gravitational-wave sources will enable the Hubble constant to be constrained to high precision.

We present cosmological results from a combined analysis of galaxy clustering and weak gravitational lensing, using $1321{\mathrm{deg}}^2$ of griz imaging data from the first year of the Dark Energy Survey (DES Y1). We combine three two-point functions: (i) the cosmic shear correlation function of 26 million source galaxies in four redshift bins, (ii) the galaxy angular autocorrelation function of 650,000 luminous red galaxies in five redshift bins, and (iii) the galaxy-shear cross-correlation of luminous red galaxy positions and source galaxy shears. To demonstrate the robustness of these results, we use independent pairs of galaxy shape, photometric-redshift estimation and validation, and likelihood analysis pipelines. To prevent confirmation bias, the bulk of the analysis was carried out while “blind” to the true results; we describe an extensive suite of systematics checks performed and passed during this blinded phase. The data are modeled in flat $\mathrm{\Lambda }\mathrm{CDM}$ and $w\mathrm{CDM}$ cosmologies, marginalizing over 20 nuisance parameters, varying 6 (for $\mathrm{\Lambda }\mathrm{CDM}$) or 7 (for $w\mathrm{CDM}$) cosmological parameters including the neutrino mass density and including the $457\times 457$ element analytic covariance matrix. We find consistent cosmological results from these three two-point functions and from their combination obtain $S_8\equiv {\sigma }_8({\mathrm{\Omega }}_m/0.3{)}^{0.5}=0.773_{-0.020}^{+0.026}$ and ${\mathrm{\Omega }}_m=0.267_{-0.017}^{+0.030}$ for $\mathrm{\Lambda }\mathrm{CDM}$; for $w\mathrm{CDM}$, we find $S_8=0.782_{-0.024}^{+0.036}$, ${\mathrm{\Omega }}_m=0.284_{-0.030}^{+0.033}$, and $w=-0.82_{-0.20}^{+0.21}$ at 68% C.L. The precision of these DES Y1 constraints rivals that from the Planck cosmic microwave background measurements, allowing a comparison of structure in the very early and late Universe on equal terms. Although the DES Y1 best-fit values for $S_8$ and ${\mathrm{\Omega }}_m$ are lower than the central values from Planck for both $\mathrm{\Lambda }\mathrm{CDM}$ and $w\mathrm{CDM}$, the Bayes factor indicates that the DES Y1 and Planck data sets are consistent with each other in the context of $\mathrm{\Lambda }\mathrm{CDM}$. Combining DES Y1 with Planck, baryonic acoustic oscillation measurements from SDSS, 6dF, and BOSS and type Ia supernovae from the Joint Lightcurve Analysis data set, we derive very tight constraints on cosmological parameters: $S_8=0.802\pm 0.012$ and ${\mathrm{\Omega }}_m=0.298\pm 0.007$ in $\mathrm{\Lambda }\mathrm{CDM}$ and $w=-1.00_{-0.04}^{+0.05}$ in $w\mathrm{CDM}$. Upcoming Dark Energy Survey analyses will provide more stringent tests of the $\mathrm{\Lambda }\mathrm{CDM}$ model and extensions such as a time-varying equation of state of dark energy or modified gravity.

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

This overview paper describes the legacy prospect and discovery potential of the Dark Energy Survey (DES) beyond cosmological studies, illustrating it with examples from the DES early data. DES is using a wide-field camera (DECam) on the 4 m Blanco Telescope in Chile to image 5000 sq deg of the sky in five filters (grizY). By its completion, the survey is expected to have generated a catalogue of 300 million galaxies with photometric redshifts and 100 million stars. In addition, a time-domain survey search over 27 sq deg is expected to yield a sample of thousands of Type Ia supernovae and other transients. The main goals of DES are to characterize dark energy and dark matter, and to test alternative models of gravity; these goals will be pursued by studying large-scale structure, cluster counts, weak gravitational lensing and Type Ia supernovae. However, DES also provides a rich data set which allows us to study many other aspects of astrophysics. In this paper, we focus on additional science with DES, emphasizing areas where the survey makes a difference with respect to other current surveys. The paper illustrates, using early data (from ‘Science Verification’, and from the first, second and third seasons of observations), what DES can tell us about the Solar system, the Milky Way, galaxy evolution, quasars and other topics. In addition, we show that if the cosmological model is assumed to be Λ+cold dark matter, then important astrophysics can be deduced from the primary DES probes. Highlights from DES early data include the discovery of 34 trans-Neptunian objects, 17 dwarf satellites of the Milky Way, one published z > 6 quasar (and more confirmed) and two published superluminous supernovae (and more confirmed).

The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on ‘Black holes, Gravitational waves and Fundamental Physics’.