In order to investigate the origin of the ongoing tension between the amplitude of matter fluctuations measured by weak lensing experiments at low redshifts and the value inferred from the cosmic microwave background anisotropies, we reconstruct the evolution of this amplitude from z ∼ 2 using existing large-scale structure data. To do so, we decouple the linear growth of density inhomogeneities from the background expansion, and constrain its redshift dependence making use of a combination of 6 different data sets, including cosmic shear, galaxy clustering and CMB lensing. We analyze these data under a consistent harmonic-space angular power spectrum-based pipeline. We show that current data constrain the amplitude of fluctuations mostly in the range 0.2 < z < 0.7, where it is lower than predicted by Planck. This difference is mostly driven by current cosmic shear data, although the growth histories reconstructed from different data combinations are consistent with each other, and we find no evidence of systematic deviations in any particular experiment. In

The aim of this paper is to show the existence and attainability of Karush–Kuhn–Tucker optimality conditions for weakly efficient Pareto points for vector equilibrium problems with the addition of constraints in the novel context of Hadamard manifolds, as opposed to the classical examples of Banach, normed or Hausdorff spaces. More specifically, classical necessary and sufficient conditions for weakly efficient Pareto points to the constrained vector optimization problem are presented. The results described in this article generalize results obtained by Gong (2008) and Wei and Gong (2010) and Feng and Qiu (2014) from Hausdorff topological vector spaces, real normed spaces, and real Banach spaces to Hadamard manifolds, respectively. This is done using a notion of Riemannian symmetric spaces of a noncompact type as special Hadarmard manifolds.

The Cosmic Infrared Background (CIB) traces the emission of star-forming galaxies throughout all cosmic epochs. Breaking down the contribution from galaxies at different redshifts to the observed CIB maps would allow us to probe the history of star formation. In this paper, we cross-correlate maps of the CIB with galaxy samples covering the range z ≲ 2 to measure the bias-weighted star-formation rate (SFR) density 〈bρSFR〉 as a function of time in a model independent way. This quantity is complementary to direct measurements of the SFR density ρSFR, giving a higher weight to more massive haloes, and thus provides additional information to constrain the physical properties of star formation. Using cross-correlations of the CIB with galaxies from the DESI Legacy Survey and the extended Baryon Oscillation Spectroscopic Survey, we obtain high signal-to-noise ratio measurements of 〈bρSFR〉, which we then use to place constraints on halo-based models of the star-formation history. We fit halo-based SFR models to our data and compare the recovered ρSFR with direct measurements of this quantity. We find a qualitatively good agreement between both independent datasets, although the details depend on the specific halo model assumed. This constitutes a useful robustness test for the physical interpretation of the CIB, and reinforces the role of CIB maps as valuable astrophysical probes of the large-scale structure. We report our measurements of 〈bρSFR〉 as well as a thorough account of their statistical uncertainties, which can be used to constrain star-formation models in combination with other data.

We constrain the expansion history of the Universe and the cosmological matter density fraction in a model-independent way by exclusively making use of the relationship between background and perturbations under a minimal set of assumptions. We do so by employing a Gaussian process to model the expansion history of the Universe from present time to the recombination era. The expansion history and the cosmological matter density are then constrained using recent measurements from cosmic chronometers, Type-Ia supernovae, baryon acoustic oscillations, and redshift-space distortion data. Our results show that the evolution in the reconstructed expansion history is compatible with the Planck 2018 prediction at all redshifts. The current data considered in this study can constrain a Gaussian process on H(z) to an average $9.4 \%$ precision across redshift. We find Ωm = 0.224 ± 0.066, lower but statistically compatible with the Planck 2018 cosmology. Finally, the combination of future DESI measurements with the CMB measurement considered in this work holds the promise of $8 \%$ average constraints on a model-independent expansion history as well as a five-fold tighter Ωm constraint using the methodology developed in this work.

Understanding the physics of star formation is one of the key problems facing modern astrophysics. The Cosmic Infrared Background (CIB), sourced by the emission from all dusty star-forming galaxies since the epoch of reionisation, is a complementary probe to study the star formation history, as well as an important extragalactic foreground for studies of the Cosmic Microwave Background (CMB). In this paper, we make high signal-to-noise measurements of the cross-correlation between maps of the CIB from the Planck experiment, and cosmic shear measurements from the Dark Energy Survey and Kilo-Degree Survey. Cosmic shear, is a direct tracer of the matter distribution, and thus we can use its cross-correlation with the CIB to directly test our understanding of the link between the star formation rate (SFR) density and the matter density. We use our measurements to place constraints on a halo-based model of the SFR that parametrises the efficiency with which gas is transformed into stars as a function of halo mass and redshift. These constraints are enhanced by using model-independent measurements of the bias-weighted SFR density extracted from the tomographic cross-correlation of galaxies and the CIB. We are able to place constraints on the peak efficiency at low redshifts, $\eta =0.445^{+0.055}_{-0.11}$, and on the halo mass at which this peak efficiency is achieved today log10(M1/M⊙) = 12.17 ± 0.25. Our constraints are in excellent agreement with direct measurements of the SFR density, as well as other CIB-based studies.