Do current observational data confirm the assumptions of the cosmological principle, or is there statistical evidence for deviations from spatial homogeneity on large scales? To address these questions, we developed a flexible framework based on spherically symmetric, but radially inhomogeneous Lemaître-Tolman-Bondi (LTB) models with synchronous Big Bang. We expanded the (local) matter density profile in terms of flexible interpolation schemes and orthonormal polynomials. A Monte Carlo technique in combination with recent observational data was used to systematically vary the shape of these profiles. In the first part of this article, we reconsider giant LTB voids without dark energy to investigate whether extremely fine-tuned mass profiles can reconcile these models with current data. While the local Hubble rate and supernovae can easily be fitted without dark energy, however, model-independent constraints from the Planck 2013 data require an unrealistically low local Hubble rate, which is strongly inconsistent with the observed value; this result agrees well with previous studies. In the second part, we explain why it seems natural to extend our framework by a non-zero cosmological constant, which then allows us to perform general tests of the cosmological principle. Moreover, these extended models facilitate explorating whether fluctuations in the local matter density profile might potentially alleviate the tension between local and global measurements of the Hubble rate, as derived from Cepheid-calibrated type Ia supernovae and CMB experiments, respectively. We show that current data provide no evidence for deviations from spatial homogeneity on large scales. More accurate constraints are required to ultimately confirm the validity of the cosmological principle, however.

Abstract. In this work we review the theory of the spherical collapse model and critically analyse the aspects of the numerical implementation of its fundamental equations. By extending a recent work by [1], we show how different aspects, such as the initial integration time, the definition of constant infinity and the criterion for the extrapolation method (how close the inverse of the overdensity has to be to zero at the collapse time) can lead to an erroneous estimation (a few per mill error which translates to a few percent in the mass function) of the key quantity in the spherical collapse model: the linear critical overdensity δ c , which plays a crucial role for the mass function of halos. We provide a better recipe to adopt in designing a code suitable to a generic smooth dark energy model and we compare our numerical results with analytic predictions for the EdS and the ΛCDM models. We further discuss the evolution of δ c for selected classes of dark energy models as a general test of the robustness of our implementation. We finally outline which modifications need to be taken into account to extend the code to more general classes of models, such as clustering dark energy models and non-minimally coupled models.Keywords: Large scale structure of the universe -dark energy theory -cosmological perturbation theory ArXiv ePrint: 1708.02477 1 Both authors contributed equally to this work.

In this paper we study long range modifications of gravity in the consistent framework of bigravity, which introduces a second massive spin-2 field and allows to continuously interpolate between the regime of General Relativity (mediated by a massless spin-2 field) and massive gravity (mediated by a massive spin-2 field). In particular we derive for the first time the equations for light deflection in this framework and study the effect on the lensing potential of galaxy clusters. By comparison of kinematic and lensing mass reconstructions, stringent bounds can be set on the parameter space of the new spin-2 fields. Furthermore, we investigate galactic rotation curves and the effect on the observable dark matter abundance within this

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.

We present a method of estimating the lensing potential from massive galaxy clusters for given observational X-ray data. The concepts developed and applied in this work can be easily combined with other techniques to infer the lensing potential, e.g. weak gravitational lensing or galaxy kinematics, to obtain an overall best-fit model for the lensing potential. After elaborating on the physical details and assumptions the method is based on, we explain how the numerical algorithm itself is implemented with a Richardson-Lucy algorithm as a central part. Our reconstruction method is tested on simulated galaxy clusters with a spherically symmetric NFW density profile filled with gas in hydrostatic equilibrium. We describe in detail how these simulated observational data sets are created and how they need to be fed into our algorithm. We tested the robustness of the algorithm against small parameter changes and estimate the quality of the reconstructed lensing potentials. As it turns out, we achieve a very high degree of accuracy in reconstructing the lensing potential. The statistical errors remain below 2.0%, whereas the systematical error does not exceed 1.0%.

Continental collision zones are usually associated with large‐scale strike‐slip shear zones. In most cases, these shear zones are complex and consist of multiple strands, varying in width, length, and total displacement. Here we present 2‐D numerical models to simulate the formation of such shear zones at different depth levels within the crust, under either brittle (frictional/plastic) or ductile conditions. Localization of shear zones is initiated by a material contrast (heterogeneity) of the material parameters. We systematically test the rate of strain weakening in brittle and in ductile regimes to understand its influence on the development of shear zone networks. Our simulations suggest that the development of antithetic faults in a brittle shear zone system is closely linked to a decrease in the angle of friction during deformation. In general, variation of the strain weakening also has a significant influence on ductile shear zones. Numerical results show that the geometry and thickness of the localized high strain zone are especially affected by weakening mechanisms during deformation. Furthermore, the interconnection and interaction of the shear strands lead to a more complex kinematic pattern, which lead to a local change in the maximum principal stress axis. These interaction of shear strands may explain the occurrence of shear‐related structures (e.g., folds) or differing characteristics of shear zones, such as the thickness of shear zones or the orientation of the faults to the stress field, which are consistent with field observations.

Spherical collapse has turned out to be a successful semi-analytic model to study structure formation in different DE models and theories of gravity, but nevertheless, the process of virialization is commonly studied on the basis of the virial theorem of classical mechanics. In the present paper, a fully generally-relativistic virial theorem based on the Tolman-Oppenheimer-Volkoff (TOV) solution for homogeneous, perfect-fluid spheres is constructed for the Einstein-de Sitter and ΛCDM cosmologies. We investigate the accuracy of classical virialization studies on cosmological scales and consider virialization from a more fundamental point of view. Throughout, we remain within general relativity and the class of FLRW models. The virialization equation is set up and solved numerically for the virial radius, yvir, from which the virial overdensity ∆V is directly obtained. Leading order corrections in the post-Newtonian framework are derived and quantified. In addition, problems in the application of this formalism to dynamical DE models are pointed out and discussed explicitly. We show that, in the weak field limit, the relative contribution of the leading order terms of the post-Newtonian expansion are of the order of 10 −3 % and the solution of Wang & Steinhardt (1998) (see [1]) is precisely reproduced. Apart from the small corrections, the method could provide insight into the process of virialization from a more fundamental point of view.PACS numbers: 95.30. Sf, 95.35.+d, 95.36.+x, 04.20.Jb

We study the evolution of linear perturbations in a Lemaître-Tolman-Bondi (LTB) void model with realistic cosmological initial conditions. Linear perturbation theory in LTB models is substantially more complicated than in standard Friedmann universes as the inhomogeneous background causes gauge-invariant perturbations couple at first order. As shown by Clarkson et al. (2009) ([21]), the evolution is constrained by a system of linear partial differential equations which need to be integrated numerically. We present a new numerical scheme using finite element methods to solve this equation system and generate scalar initial conditions based on Gaussian random fields with an underlying power spectrum for the Bardeen potential. After spherical harmonic decomposition, the initial fluctuations are propagated in time and estimates of angular power spectra of each gauge invariant variable are computed as functions of redshift. This allows to analyse the coupling strength in a statistical way. We find significant couplings up to 25% for large and deep voids of Gpc scale as required to fit the distance redshift relations of SNe.