Null tests of the standard model using the linear model formalism

We test both the FLRW geometry and $\Lambda$CDM cosmology in a model independent way by reconstructing the Hubble function $H(z)$, the comoving distance $D(z)$ and the growth of structure $f\sigma_8(z)$ using the most recent data available. We use the linear model formalism in order to optimally reconstruct the latter cosmological functions, together with their derivatives and integrals. We then evaluate four of the null tests available in literature: $Om_{1}$ by Sahni et al., $Om_{2}$ by Zunckel \& Clarkson, $Ok$ by Clarkson et al., and $ns$ by Nesseris \& Sapone. For all the four tests we find agreement, within the errors, with the standard cosmological model.Comment: 8 pages, 7 figures and 1 tabl

Intrinsic uncertainty on the nature of dark energy

We argue that there is an intrinsic noise on measurements of the equation of state parameter $w=p/\rho$ from large-scale structure around us. The presence of the large-scale structure leads to an ambiguity in the definition of the background universe and thus there is a maximal precision with which we can determine the equation of state of dark energy. To study the uncertainty due to local structure, we model density perturbations stemming from a standard inflationary power spectrum by means of the exact Lema\^{i}tre-Tolman-Bondi solution of Einstein's equation, and show that the usual distribution of matter inhomogeneities in a $\Lambda$CDM cosmology causes a variation of $w$ -- as inferred from distance measures -- of several percent. As we observe only one universe, or equivalently because of the cosmic variance, this uncertainty is systematic in nature.Comment: 12 pages, 3 figures. Version as accepted for publication in Physics of the Dark Universe (Open Access

Constraining the halo mass function with observations

The abundances of dark matter halos in the universe are described by the halo mass function (HMF). It enters most cosmological analyses and parametrizes how the linear growth of primordial perturbations is connected to these abundances. Interestingly, this connection can be made approximately cosmology independent. This made it possible to map in detail its near-universal behavior through large-scale simulations. However, such simulations may suffer from systematic effects, especially if baryonic physics is included. In this paper we ask how well observations can constrain directly the HMF. The observables we consider are galaxy cluster number counts, galaxy cluster power spectrum and lensing of type Ia supernovae. Our results show that DES is capable of putting the first meaningful constraints on the HMF, while both Euclid and J-PAS can give stronger constraints, comparable to the ones from state-of-the-art simulations. We also find that an independent measurement of cluster masses is even more important for measuring the HMF than for constraining the cosmological parameters, and can vastly improve the determination of the halo mass function. Measuring the HMF could thus be used to cross-check simulations and their implementation of baryon physics. It could even, if deviations cannot be accounted for, hint at new physics.Comment: v2: small improvements to the text; matches accepted version. 13 pages, 8 figure