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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.

Euclid is a European Space Agency medium-class mission selected for launch in 2019 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.

We explore the simple inter-relationships between mass, star formation rate, and environment in the SDSS, zCOSMOS, and other deep surveys. We take a purely empirical approach in identifying those features of galaxy evolution that are demanded by the data and then explore the analytic consequences of these. We show that the differential effects of mass and environment are completely separable to z [?] 1, leading to the idea of two distinct processes of "mass quenching" and "environment quenching." The effect of environment quenching, at fixed over-density, evidently does not change with epoch to z [?] 1 in zCOSMOS, suggesting that the environment quenching occurs as large-scale structure develops in the universe, probably through the cessation of star formation in 30%-70% of satellite galaxies. In contrast, mass quenching appears to be a more dynamic process, governed by a quenching rate. We show that the observed constancy of the Schechter M* and as for star-forming galaxies demands that the quenching of galaxies around and above M* must follow a rate that is statistically proportional to their star formation rates (or closely mimic such a dependence). We then postulate that this simple mass-quenching law in fact holds over a much broader range of stellar mass (2 dex) and cosmic time. We show that the combination of these two quenching processes, plus some additional quenching due to merging naturally produces (1) a quasi-static single Schechter mass function for star-forming galaxies with an exponential cutoff at a value M* that is set uniquely by the constant of proportionality between the star formation and mass quenching rates and (2) a double Schechter function for passive galaxies with two components. The dominant component (at high masses) is produced by mass quenching and has exactly the same M* as the star-forming galaxies but a faint end slope that differs by Das [?] 1. The other component is produced by environment effects and has the same M* and as as the star-forming galaxies but an amplitude that is strongly dependent on environment. Subsequent merging of quenched galaxies will modify these predictions somewhat in the denser environments, mildly increasing M* and making as slightly more negative. All of these detailed quantitative inter-relationships between the Schechter parameters of the star-forming and passive galaxies, across a broad range of environments, are indeed seen to high accuracy in the SDSS, lending strong support to our simple empirically based model. We find that the amount of post-quenching "dry merging" that could have occurred is quite constrained. Our model gives a prediction for the mass function of the population of transitory objects that are in the process of being quenched. Our simple empirical laws for the cessation of star formation in galaxies also naturally produce the "anti-hierarchical" run of mean age with mass for passive galaxies, as well as the qualitative variation of formation timescale indicated by the relative a-element abundances.

New statistical properties of dark matter halos in Lagrangian space are presented. Tracing back the dark matter particles constituting bound halos resolved in a series of N-body simulations, we measure quantitatively the correlations of the proto-halo's inertia tensors with the local tidal tensors and investigate how the correlation strength depends on the proto-halo's sphericity, local density, and filtering scale. It is shown that the majority of the proto-halos exhibit strong correlations between the two tensors provided that the tidal field is smoothed on the proto-halo's mass scale. The correlation strength is found to increase as the proto-halo's sphericity increases, as the proto-halo's mass increases, and as the local density becomes close to the critical value, d ec . It is also found that those peculiar proto-halos which exhibit exceptionally weak correlations between the two tensors tend to acquire higher specific angular momentum in Eulerian space, which is consistent with the linear tidal torque theory. In the light of our results, it is intriguing to speculate a hypothesis that the low surface brightness galaxies observed at present epoch correspond to the peculiar proto-halos with extreme low sphericity whose inertia tensors are weakly correlated with the local tidal tensors.

Galaxies on the largest scales of the universe are observed to be embedded in the filamentary cosmic web, which is shaped by the nonlinear tidal field. As an efficient tool to quantitatively describe the statistics of this cosmic web, we present the anisotropic two-point correlation functions of the nonlinear traceless tidal field in the principal-axis frame, which are measured using numerical data from an N-body simulation. We show that both the nonlinear density and traceless tidal fields are more strongly correlated along the directions perpendicular to the eigenvectors associated with the largest eigenvalues of the local tidal field. The correlation length scale of the traceless tidal field is found to be [?]20 h -1Mpc, which is much larger than that of the density field [?]5 h -1Mpc. We also provide analytic fitting formulae for the anisotropic correlation functions of the traceless tidal field, which turn out to be in excellent agreement with the numerical results. We expect that our numerical results and analytical formula are useful to disentangle cosmological information from the filamentary network of the large-scale structures.

We present a new method to directly map the neutral-hydrogen distribution during the reionization epoch and constrain the emission properties of the highest redshift quasars (QSOs). As a tracer of H I, we propose to use the Lya radiation produced by quasar ionization fronts (I-fronts) that expand in the partially ionized intergalactic medium (IGM) before reionization is complete. These Lya photons are mainly generated by H I collisional excitations. Combining two radiative transfer models (one for the QSO ionizing radiation and one for the Lya photons), we estimate the expected Lya spectral shape and surface brightness (SBLya) for a large number of configurations where we varied both the properties of the ionizing QSO and of the surrounding medium. We find that the expected signal is observable as a single (broad) emission line with a characteristic width of 100-200 km s[?]1. The expected SBLya produced at redshift z [?] 6.5 within a fully neutral region (at mean density) by a typical QSO I-front lies in the range 10[?]21 to 10[?]20 ergs s[?]1 cm[?]2 arcsec[?]2 and decreases proportionally to (1 + z)2 for a given QSO age. QSOs with harder spectra may produce a significantly brighter emission at early phases. The signal may cover up to a few hundred square arcminutes on the sky and should be already detectable with current facilities by means of moderate- to high-resolution spectroscopy. The detection of this Lya emission can shed new light on the reionization history, the age and the emission properties of the highest redshift QSOs.

Brightness temperature fluctuations in the redshifted 21 cm background from the cosmic dark ages are generated by irregularities in the gas density distribution and can thus be used to determine the statistical properties of density fluctuations in the early universe. Here we derive the most general expansion of brightness temperature fluctuations up to second order in terms of all the possible sources of spatial fluctuations. We then focus on the three-point statistics and compute the angular bispectrum of brightness temperature fluctuations generated prior to the epoch of hydrogen reionization. For simplicity, we neglect redshift-space distortions. We find that low-frequency radio experiments with arcminute angular resolution can easily detect non-Gaussianity produced by nonlinear gravity, with high signal-to-noise ratio. The bispectrum thus provides a unique test of the gravitational instability scenario for structure formation and can be used to measure the cosmological parameters. Detecting the signature of primordial non-Gaussianity produced during or right after an inflationary period is more challenging but still possible. An ideal experiment limited by cosmic variance only and with an angular resolution of a few arcseconds has the potential to detect primordial non-Gaussianity with a nonlinearity parameter of fNL ~ 1. Additional sources of error such as weak lensing and an imperfect foreground subtraction could severely hamper the detection of primordial non-Gaussianity, which will benefit from the use of optimal estimators combined with tomographic techniques.

The incidence of strong Mg II systems in gamma-ray burst (GRB) spectra is a few times higher than in quasar (QSO) spectra. We investigate several possible explanations for this effect, including dust obscuration bias, clustering of the absorbers, different beam sizes of the sources, multiband magnification bias of GRBs, and association of the absorbers with the GRB event or the circumburst environment. We find that (1) the incidence rate of Mg II systems in QSO spectra could be underestimated by a factor of 1.3-2 due to dust obscuration; (2) the equivalent width distribution of the Mg II absorbers along GRBs is consistent with that observed along QSOs, thus suggesting that the absorbers are more extended than the beam sizes of the sources; (3) on average, GRB afterglows showing more than one Mg II system are a factor of 1.7 brighter than the others, suggesting a lensing origin of the observed discrepancy; (4) gravitational lensing (in different forms, from galaxy lensing to microlensing) can bias high the counts of Mg II systems along GRBs if the luminosity functions of the prompt gamma-ray emission and of the optical afterglows have a mean faint-end slope approaching -5/3 to -2; and (5) some of the absorbers can be associated with the circumburst environment or produced by supernova remnants unrelated to the GRB event itself but lying in the same star-forming region. With the possible exception of magnification bias, it is unlikely that one of these effects on its own can fully account for the observed counts. However, the combined action of some of them can substantially reduce the statistical significance of the discrepancy.

We report the results of a survey for fluorescent Lya emission carried out in the field surrounding the z = 3.1 quasar QSO 0420-388 using the Focal Reducer/Low Dispersion Spectrograph 2 (FORS2) instrument on the Very Large Telescope (VLT). We first review the properties expected for fluorescent Lya emitters, compared with those of other nonfluorescent Lya emitters. Our observational search detected 13 Lya sources sparsely sampling a volume of ~14,000 comoving Mpc3 around the quasar. The properties of these in terms of (1) the line equivalent width, (2) the line profile, and (3) the value of the surface brightness related to the distance from the quasar all suggest that several of these may be plausibly fluorescent. Moreover, their number is in good agreement with the expectation from theoretical models. One of the best candidates for fluorescence is sufficiently far behind QSO 0420-388 that it would imply that the quasar has been active for (at least) ~60 Myr. Further studies on such objects will give information about protogalactic clouds and on the radiative history (and beaming) of the high-redshift quasars.

We combine a high-resolution hydro simulation of the LCDM cosmology with two radiative transfer schemes (for continuum and line radiation) to predict the properties, spectra, and spatial distribution of fluorescent Lya emission at z ~ 3. We focus on line radiation produced by recombinations in the dense intergalactic medium ionized by UV photons. In particular, we consider both a uniform background and the case in which gas clouds are illuminated by a nearby quasar. We find that the emission from optically thick regions is substantially less than predicted from the widely used static, plane-parallel model. The effects induced by a realistic velocity field and by the complex geometric structure of the emitting regions are discussed in detail. We make predictions for the expected brightness and size distributions of the fluorescent sources. Our results account for recent null detections and can be used to plan new observational campaigns both in the field (to measure the intensity of the diffuse UV background) and in the proximity of bright quasars (to understand the origin of high column density absorbers).

We present a new measure of the angular two-point correlation function of Lyman break galaxies (LBGs) at z ~ 3, obtained from the variance of galaxy counts in two-dimensional cells. By avoiding binning of the angular separations, this method is significantly less affected by shot noise than traditional measures and allows for a more accurate determination of the correlation function. We used a sample of about 1000 galaxies with [?] 25.5 extracted from the survey by Steidel and collaborators and found the following results. At scales in the range 30'' [?] th [?] 100'', the angular correlation function w(th) can be accurately described as a power law with slope b = 0.50img1.gif (1 s random)-0.10 (systematic), shallower than the measure presented by Giavalisco and collaborators. However, the spatial correlation length, derived by Limber deprojection, is in very good agreement with the previous measures, confirming the strong spatial clustering of these sources. We discuss in detail the effects of both random and systematic errors, in particular of the so-called integral constraint bias, to which we set a lower limit using numerical simulations. This suggests that the current samples do not yet provide a "fair representation" of the large-scale distribution of LBGs at z ~ 3. An intriguing result of our analysis is that at angular separations smaller than th [?] 30'' the correlation function seems to depart from the power law fitted at larger scales and become smaller. This feature is detected at the ~90% confidence level and, if real, can provide information on the number density and spatial distribution of LBGs within their host halos as well as the size and the mass of the halos.

Recent evidence appears to link gamma-ray bursts (GRBs) to star-forming regions in galaxies at cosmological distances. If short-lived massive stars are the progenitors of GRBs, the rate of events per unit cosmological volume should be an unbiased tracer (i.e., unaffected by dust obscuration and surface brightness limits) of the cosmic history of star formation. Here we use realistic estimates for the evolution of the stellar birthrate in galaxies to model the number counts, redshift distribution, and time-delay factors of GRBs. We present luminosity function fits to the BATSE log N- log Prelation for different redshift distributions of the bursts. Our results imply about 1-2 GRBs for every one million Type II supernovae, and a characteristic "isotropic-equivalent" burst luminosity in the range 3-20 × 1051ergs s-1(for H0= 65 km s-1Mpc-1). We compute the rate of multiple imaging of background GRBs due to foreground mass condensations in a ?-dominated cold dark matter cosmology, assuming that dark halos approximate singular isothermal spheres on galaxy scales and Navarro-Frenk-White profiles on group/cluster scales, and are distributed in mass according to the Press-Schechter model. We show that the expected sensitivity increase of Swiftrelative to BATSE could result in a few strongly lensed individual bursts detected down to a photon flux of 0.1 cm-2s-1in a 3 yr survey. Because of the partial sky coverage, however, it is unlikely that the Swiftsatellite will observe recurrent events (lensed pairs).

Ongoing searches for supernovae (SNe) at cosmological distances have recently started to provide large numbers of events with measured redshifts and apparent brightnesses. Compared to quasars or galaxies, Type Ia SNe represent a population of sources with well-known intrinsic properties and could be used to detect gravitational lensing even in the absence of multiple or highly distorted images. We investigate the lensing effect of background SNe due to mass condensations in three popular cold dark matter cosmologies (LCDM, OCDM, and SCDM) and compute lensing frequencies, rates of SN explosions, and distributions of arrival-time differences and image separations. If dark halos approximate singular isothermal spheres on galaxy scales and Navarro-Frenk-White profiles on group/cluster scales, and are distributed in mass according to the Press-Schechter theory, then about one of every 12 SNe at z ~ 1 will be magnified by Dm [?] 0.1 mag (SCDM). The detection rate of SNe Ia with magnification Dm [?] 0.3 is estimated to be of the order of a few events yr-1 deg-2 at maximum B light and IAB [?] 25, 100 times smaller than the total rate expected at these magnitude levels. In the field, events magnified by more than 0.75 mag are 7 times less frequent; about one-fifth of them give rise to observable multiple images. While the time delay between the images is shorter than 3 days in ~25% of the cases (shorter than 30 days in 50%) (SCDM), a serious bias against the detection of small-separation events in ground-based surveys is caused by the luminosity of the foreground lensing galaxy. Because of the flat K-correction and wide luminosity function, Type II SNe dominate the number counts at IAB > 25 and have the largest fraction of lensed objects. The optimal survey sensitivity for Type Ia SNe magnified by Dm [?] 0.75 mag is IAB [?] 23. Magnification bias increases their incidence by a factor of 50 in samples with IAB [?] 22, dropping to a factor of 3.5 at 24 mag. At faint magnitudes, the enhancement is larger for SNe II.

We present a stochastic approach to the spatial clustering of dark matter haloes in Lagrangian space. Our formalism is based on a local formulation of the ‘excursion set’ approach by Bond et al., which automatically accounts for the ‘cloud‐in‐cloud’ problem in the identification of bound systems. Our method allows us to calculate correlation functions of haloes in Lagrangian space using either a multidimensional Fokker–Planck equation with suitable boundary conditions, or an array of Langevin equations with spatially correlated random forces. We compare the results of our method with theoretical predictions for the halo autocorrelation function considered in the literature, and find good agreement with the results recently obtained within a treatment of halo clustering in terms of ‘counting fields’ by Catelan et al. Finally, the possible effect of spatial correlations on numerical simulations of halo merger trees is discussed.

Accepted 1998 January 26. Received 1998 January 26; in original form 1997 August 13This paper presents a stochastic approach to the clustering evolution of dark matter haloes in the Universe. Haloes, identified by a Press–Schechter‐type algorithm in Lagrangian space, are described in terms of ‘counting fields’, acting as non‐linear operators on the underlying Gaussian density fluctuations. By ensemble‐averaging these counting fields, the standard Press–Schechter mass function as well as analytic expressions for the halo correlation function and corresponding bias factors of linear theory are obtained, extending the recent results by Mo & White. The non‐linear evolution of our halo population is then followed by solving the continuity equation, under the sole hypothesis that haloes move by the action of gravity. This leads to an exact and general formula for the bias fieldof dark matter haloes, defined as the local ratio between their number density contrast and the mass density fluctuation. Besides being a function of position and ‘observation’ redshift, this random field depends upon the mass and formation epoch of the objects and is both non‐linear and non‐local. The latter features are expected to leave a detectable imprint on the spatial clustering of galaxies, as described, for instance, by statistics like the bispectrum and the skewness. Our algorithm may have several interesting applications, among which is the possibility of generating mock halo catalogues from low‐resolution N‐body simulations.