We assume that dark matter is comprised of axion-like particles (ALPs) generated by the realignment mechanism in the post-inflationary scenario. This leads to isocurvature fluctuations with an amplitude of order one for scales comparable to the horizon at the time when the ALP field starts oscillating. The power spectrum of these fluctuations is flat for small wave numbers, extending to scales relevant for cosmological observables. Denoting the relative isocurvature amplitude at k * = 0.05 Mpc −1 by f iso , Planck observations of the cosmic microwave background (CMB) yield f iso < 0.31 at the 2σ-level. This excludes the hypothesis of post-inflationary ALP dark matter with masses m a < 10 −20 -10 −16 eV, where the range is due to details of the ALP mass-temperature dependence. Future CMB stage IV and 21-cm intensity mapping experiments may improve these limits by 1-2 orders of magnitude in m a .

We study the spherical collapse model in the presence of external gravitational tidal shear fields for different dark energy scenarios and investigate the impact on the mass function and cluster number counts. While previous studies of the influence of shear and rotation on δ c have been performed with heuristically motivated models, we try to avoid this model dependence and sample the external tidal shear values directly from the statistics of the underlying linearly evolved density field based on first order Lagrangian perturbation theory. Within this selfconsistent approach, in the sense that we restrict our treatment to scales where linear theory is still applicable, only fluctuations larger than the scale of the considered objects are included into the sampling process which naturally introduces a mass dependence of δ c . We find that shear effects are predominant for smaller objects and at lower redshifts, i. e. the effect on δ c is at or below the percent level for the ΛCDM model. For dark energy models we also find small but noticeable differences, similar to ΛCDM. The virial overdensity ∆ V is nearly unaffected by the external shear. The now mass dependent δ c is used to evaluate the mass function for different dark energy scenarios and afterwards to predict cluster number counts, which indicate that ignoring the shear contribution can lead to biases of the order of 1σ in the estimation of cosmological parameters like Ω m , σ 8 or w.

Fast radio bursts (FRBs) are very short and bright transients visible over extragalactic distances. The radio pulse undergoes dispersion caused by free electrons along the line of sight, most of which are associated with the large-scale structure (LSS). The total dispersion measure therefore increases with the line of sight and provides a distance estimate to the source. We present the first measurement of the Hubble constant using the dispersion measure – redshift relation of FRBs with identified host counterpart and corresponding redshift information. A sample of nine currently available FRBs yields a constraint of $H_0 = 62.3 \pm 9.1 \, \rm {km} \, \rm {s}^{-1}\, \rm {Mpc}^{-1}$, accounting for uncertainty stemming from the LSS, host halo and Milky Way contributions to the observed dispersion measure. We discuss possible biases arising from highly dispersed signals, and break the degeneracy between the expansion rate and the mean free electron abundance with a prior on the physical baryon density. The main current limitation is statistical, and we estimate that a few hundred events with corresponding redshifts are sufficient for a per cent measurement of H0. This is a number well within reach of ongoing FRB searches. We perform a forecast using a realistic mock sample to demonstrate that a high-precision measurement of the expansion rate is possible without relying on other cosmological probes. FRBs can therefore arbitrate the current tension between early and late time measurements of H0 in the near future.

Future observations of the large-scale structure have the potential to investigate cosmological models with a high degree of complexity, including the properties of gravity on large scales, the presence of a complicated dark energy component, and the addition of neutrinos changing structures on small scales. Here we study Horndeski theories of gravity, the most general minimally coupled scalar-tensor theories of second order. While the cosmological background evolution can be described by an effective equation of state, the perturbations are characterised by four free functions of time. We consider a specific parametrisation of these functions tracing the dark energy component. The likelihood of the full parameter set resulting from combining cosmic microwave background primary anisotropies including their gravitational lensing signal, tomographic angular galaxy clustering and weak cosmic shear, together with all possible non-vanishing cross-correlations is evaluated; both with the Fisher-formalism as well as without the assumption of a specific functional form of the posterior through Monte-Carlo Markov-chains (MCMCs). Our results show that even complex cosmological models can be constrained and could exclude variations of the effective Newtonian gravitational coupling larger than 10% over the age of the Universe. In particular, we confirm strong correlations between parameter groups. Furthermore, we find that the expected contours from MCMC are significantly larger than those from the Fisher analysis even with the vast amount of signal provided by stage IV experiments, illustrating the importance of a proper treatment of non-Gaussian likelihoods and the high level of precision needed for unlocking the sensitivity on gravitational parameters.

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