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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.

In this thesis we discuss how late time anisotropies in the cosmic microwave background (CMB), such as the integrated Sachs-Wolfe effect (ISW), can be detected and used to constrain cosmology, and in particular to investigate the nature of dark energy and modified gravity theories. We present the state-of-the-art measurement of this phenomenon together with some of its applications. We also discuss how cosmic reionisation can be studied with a similar technique. The ISW is interesting because in the standard model it can only be produced if the Universe undergoes a transition to a curvature or dark energy phase. A direct measurement of this effect is challenging, because the signal is combined with the primary CMB anisotropies, whose amplitude is bigger. However, since the ISW signal has been originated at late times, we can extract it by correlating the total CMB anisotropies with a tracer of the large scale structure, such as a galaxy catalogue. We first describe the ISW measurement as obtained by cross-correlating the CMB maps from WMAP with a catalogue of quasars from the Sloan Digital Sky Survey (SDSS); we obtain a positive correlation at the 2σ level. The analysis is then extended to a collection of six different catalogues, which bring the total significance of the measurement up to ~ 4.5σ and is the current state-of-the-art in the field.

Bayesian model comparison penalizes models with more free parameters that are allowed to vary over a wide range, and thus offers the most robust method to decide whether some given data require new parameters. In this paper, we ask a simple question: do current cosmological data require extensions of the simplest single-field inflation models? Specifically, we calculate the Bayesian evidence of a totally anti-correlated isocurvature perturbation and a running spectral index of the scalar curvature perturbation. These parameters are motivated by recent claims that the observed temperature anisotropy of the cosmic microwave background on large angular scales is too low to be compatible with the simplest inflation models. Both a subdominant, anti-correlated cold dark matter isocurvature component and a negative running index succeed in lowering the large-scale temperature power spectrum. We show that the introduction of isocurvature perturbations is disfavored, whereas that of the running spectral index is only moderately favored, even when the BICEP2 data are included in the analysis without any foreground subtraction.

We apply a new method to measure primordial non-Gaussianity, using the cross-correlation between galaxy surveys and the CMB lensing signal to measure galaxy bias on very large scales, where local-type primordial non-Gaussianity predicts a \\(k^2\\) divergence. We use the CMB lensing map recently published by the Planck collaboration, and measure its external correlations with a suite of six galaxy catalogues spanning a broad redshift range. We then consistently combine correlation functions to extend the recent analysis by Giannantonio et al. (2013), where the density-density and the density-CMB temperature correlations were used. Due to the intrinsic noise of the Planck lensing map, which affects the largest scales most severely, we find that the constraints on the galaxy bias are similar to the constraints from density-CMB temperature correlations. Including lensing constraints only improves the previous statistical measurement errors marginally, and we obtain \\( f_{\\mathrm{NL}} = 12 \\pm 21 \\) (1\\(\\sigma\\)) from the combined data set. However, the lensing measurements serve as an excellent test of systematic errors: we now have three methods to measure the large-scale, scale-dependent bias from a galaxy survey: auto-correlation, and cross-correlation with both CMB temperature and lensing. As the publicly available Planck lensing maps have had their largest-scale modes at multipoles \\(l<10\\) removed, which are the most sensitive to the scale-dependent bias, we consider mock CMB lensing data covering all multipoles. We find that, while the effect of \\(f_{\\mathrm{NL}}\\) indeed increases significantly on the largest scales, so do the contributions of both cosmic variance and the intrinsic lensing noise, so that the improvement is small.

We derive constraints on feedback by active galactic nuclei (AGN) by setting limits on their thermal Sunyaev-Zel'dovich (SZ) imprint on the cosmic microwave background (CMB). The amplitude of any SZ signature is small and degenerate with the poorly known sub-mm spectral energy distribution of the AGN host galaxy and other unresolved dusty sources along the line of sight. Here we break this degeneracy by combining microwave and sub-mm data from Planck with all-sky far-infrared maps from the AKARI satellite. We first test our measurement pipeline using the Sloan Digital Sky Survey (SDSS) redMaPPer catalogue of galaxy clusters, finding a highly significant detection ($>$$20\\sigma\\() of the SZ effect together with correlated dust emission. We then constrain the SZ signal associated with spectroscopically confirmed quasi-stellar objects (QSOs) from SDSS data release 7 (DR7) and the Baryon Oscillation Spectroscopic Survey (BOSS) DR12. We obtain a low-significance (\\)1.6\\sigma\\() hint of an SZ signal, pointing towards a mean thermal energy of \\)\\simeq 5 \\times 10^{60}\\( erg, lower than reported in some previous studies. A comparison of our results with high-resolution hydrodynamical simulations including AGN feedback suggests QSO host masses of \\)M_{200c} \\sim 4 \\times 10^{12}~h^{-1}M_\\odot$, but with a large uncertainty. Our analysis provides no conclusive evidence for an SZ signal specifically associated with AGN feedback.

We study the potential of the kinematic SZ effect as a probe for cosmology, focusing on the pairwise method. The main challenge is disentangling the cosmologically interesting mean pairwise velocity from the cluster optical depth and the associated uncertainties on the baryonic physics in clusters. Furthermore, the pairwise kSZ signal might be affected by internal cluster motions or correlations between velocity and optical depth. We investigate these effects using the Magneticum cosmological hydrodynamical simulations, one of the largest simulations of this kind performed to date. We produce tSZ and kSZ maps with an area of \\(\\simeq 1600~\\mathrm{deg}^2\\), and the corresponding cluster catalogues with \\(M_{500c} \\gtrsim 3 \\times 10^{13}~h^{-1}M_\\odot\\) and \\(z \\lesssim 2\\). From these data sets we calibrate a scaling relation between the average Compton-\\(y\\) parameter and optical depth. We show that this relation can be used to recover an accurate estimate of the mean pairwise velocity from the kSZ effect, and that this effect can be used as an important probe of cosmology. We discuss the impact of theoretical and observational systematic effects, and find that further work on feedback models is required to interpret future high-precision measurements of the kSZ effect.

Segmenting the boundary between tumor and healthy tissue during surgical cancer resection poses a significant challenge. In recent years, Hyperspectral Imaging (HSI) combined with Machine Learning (ML) has emerged as a promising solution. However, due to the extensive information contained within the spectral domain, most ML approaches primarily classify individual HSI (super-)pixels, or tiles, without taking into account their spatial context. In this paper, we propose an improved methodology that leverages the spatial context of tiles for more robust and smoother segmentation. To address the irregular shapes of tiles, we utilize Graph Neural Networks (GNNs) to propagate context information across neighboring regions. The features for each tile within the graph are extracted using a Convolutional Neural Network (CNN), which is trained simultaneously with the subsequent GNN. Moreover, we incorporate local image quality metrics into the loss function to enhance the training procedure's robustness against low-quality regions in the training images. We demonstrate the superiority of our proposed method using a clinical ex vivo dataset consisting of 51 HSI images from 30 patients. Despite the limited dataset, the GNN-based model significantly outperforms context-agnostic approaches, accurately distinguishing between healthy and tumor tissues, even in images from previously unseen patients. Furthermore, we show that our carefully designed loss function, accounting for local image quality, results in additional improvements. Our findings demonstrate that context-aware GNN algorithms can robustly find tumor demarcations on HSI images, ultimately contributing to better surgery success and patient outcome.

We study structure formation in the presence of primordial non-Gaussianity of the local type with parameters f_NL and g_NL. We show that the distribution of dark-matter halos is naturally described by a multivariate bias scheme where the halo overdensity depends not only on the underlying matter density fluctuation delta, but also on the Gaussian part of the primordial gravitational potential phi. This corresponds to a non-local bias scheme in terms of delta only. We derive the coefficients of the bias expansion as a function of the halo mass by applying the peak-background split to common parametrizations for the halo mass function in the non-Gaussian scenario. We then compute the halo power spectrum and halo-matter cross spectrum in the framework of Eulerian perturbation theory up to third order. Comparing our results against N-body simulations, we find that our model accurately describes the numerical data for wavenumbers k < 0.1-0.3 h/Mpc depending on redshift and halo mass. In our multivariate approach, perturbations in the halo counts trace phi on large scales and this explains why the halo and matter power spectra show different asymptotic trends for k -> 0. This strongly scale-dependent bias originates from terms at leading order in our expansion. This is different from what happens using the standard univariate local bias where the scale-dependent terms come from badly behaved higher-order corrections. On the other hand, our biasing scheme reduces to the usual local bias on smaller scales where |phi| is typically much smaller than the density perturbations. We finally discuss the halo bispectrum in the context of multivariate biasing and show that, due to its strong scale and shape dependence, it is a powerful tool for the detection of primordial non-Gaussianity from future galaxy surveys.

We present posterior likelihoods and Bayesian model selection analysis for generalized cosmological models where the primordial perturbations include correlated adiabatic and cold dark matter isocurvature components. We perform nested sampling with flat and, for the first time, curved spatial geometries of the Universe, using data from the cosmic microwave background (CMB) anisotropies, the Union supernovae (SN) sample and a combined measurement of the integrated Sachs-Wolfe (ISW) effect. The CMB alone favors a 3% (positively correlated) isocurvature contribution in both the flat and curved cases. The non-adiabatic contribution to the observed CMB temperature variance is 0 < alpha_T < 7% at 98% CL in the curved case. In the flat case, combining the CMB with SN data artificially biases the result towards the pure adiabatic LCDM concordance model, whereas in the curved case the favored level of non-adiabaticity stays at 3% level with all combinations of data. However, the ratio of Bayes factors, or Delta ln(evidence), is more than 5 points in favor of the flat adiabatic LCDM model, which suggests that the inclusion of the 5 extra parameters of the curved isocurvature model is not supported by the current data. The results are very sensitive to the second and third acoustic peak regions in the CMB temperature angular power: therefore a careful calibration of these data will be required before drawing decisive conclusions on the nature of primordial perturbations. Finally, we point out that the odds for the flat non-adiabatic model are 1:3 compared to the curved adiabatic model. This may suggest that it is not much less motivated to extend the concordance model with 4 isocurvature degrees of freedom than it is to study the spatially curved adiabatic model.

We study the matter bispectrum of large-scale structure by comparing the predictions of different perturbative and phenomenological models with the full three-dimensional bispectrum from \\(N\\)-body simulations estimated using modal methods. We show that among the perturbative approaches, effective field theory succeeds in extending the range of validity furthest on intermediate scales, at the cost of free additional parameters. By studying the halo model, we show that although it is satisfactory in the deeply non-linear regime, it predicts a deficit of power on intermediate scales, worsening at redshifts \\(z>0\\). By comparison with the \\(N\\)-body bispectrum on those scales, we show that there is a significant squeezed component underestimated in the halo model. On the basis of these results, we propose a new three-shape model, based on the tree-level, squeezed and constant bispectrum shapes we identified in the halo model; after calibration this fits the simulations on all scales and redshifts of interest. We extend this model further to primordial non-Gaussianity of the local and equilateral types by showing that the same shapes can be used to describe the additional non-Gaussian component in the matter bispectrum. This method provides a HALOFIT-like prototype of the bispectrum that could be used to describe and test parameter dependencies and should be relevant for the bispectrum of weak gravitational lensing and wider applications.