Clustering and redshift-space distortions in interacting dark energy cosmologies

We investigate the spatial properties of the large scale structure (LSS) of the Universe in the framework of coupled dark energy (cDE) cosmologies. Using the public halo catalogues from the CoDECS simulations -- the largest set of N-body experiments to date for such cosmological scenarios -- we estimate the clustering and bias functions of cold dark matter (CDM) haloes, both in real- and redshift-space. Moreover, we investigate the effects of the dark energy (DE) coupling on the geometric and dynamic redshift-space distortions, quantifying the difference with respect to the concordance LambdaCDM model. At z~0, the spatial properties of CDM haloes in cDE models appear very similar to the LambdaCDM case, even if the cDE models are normalized at last scattering in order to be consistent with the latest Cosmic Microwave Background (CMB) data. At higher redshifts, we find that the DE coupling produces a significant scale-dependent suppression of the halo clustering and bias function. This effect, that strongly depends on the coupling strength, is not degenerate with sigma8 at scales r<5-10 Mpc/h. Moreover, we find that the coupled DE strongly affects both the linear distortion parameter, beta, and the pairwise peculiar velocity dispersion, sigma12. Although the models considered in this work are found to be all in agreement with presently available observational data, the next generation of galaxy surveys will be able to put strong constraints on the level of coupling between DE and CDM exploiting the shape of redshift-space clustering anisotropies.Comment: 11 pages, 7 figures. Minor changes, references added. MNRAS publishe

Popularity versus Similarity in Growing Networks

Popularity is attractive -- this is the formula underlying preferential attachment, a popular explanation for the emergence of scaling in growing networks. If new connections are made preferentially to more popular nodes, then the resulting distribution of the number of connections that nodes have follows power laws observed in many real networks. Preferential attachment has been directly validated for some real networks, including the Internet. Preferential attachment can also be a consequence of different underlying processes based on node fitness, ranking, optimization, random walks, or duplication. Here we show that popularity is just one dimension of attractiveness. Another dimension is similarity. We develop a framework where new connections, instead of preferring popular nodes, optimize certain trade-offs between popularity and similarity. The framework admits a geometric interpretation, in which popularity preference emerges from local optimization. As opposed to preferential attachment, the optimization framework accurately describes large-scale evolution of technological (Internet), social (web of trust), and biological (E.coli metabolic) networks, predicting the probability of new links in them with a remarkable precision. The developed framework can thus be used for predicting new links in evolving networks, and provides a different perspective on preferential attachment as an emergent phenomenon

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic R\"ossler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.Comment: 12 pages, 13 figure

Scattering of gravitational radiation. Intensity fluctuations

Aims. The effect of gravitational microlensing on the intensity of gravitational radiation as it propagates through an inhomogeneous medium is considered. Lensing by both stars and a power law spectrum of density perturbations is examined. Methods. The long wavelengths characteristic of gravitational radiation mandate a statistical, physical-optics approach to treat the effect of the lensing. Results. A model for the mass power spectrum of a starfield, including the effects of clustering and allowing for a distribution of stellar masses, is constructed and used to determine both the amplitude of fluctuations in the gravitational wave strain and its associated temporal fluctuation spectrum. For a uniformly distributed starfield the intensity variance scales linearly with stellar density, σ, but is enhanced by a factor ≳σr^2_F when clustering is important, where r_F is the Fresnel scale. The effect of lensing by a power law mass spectrum, applicable to lensing by small scale fluctuations in gas and dark matter, is also considered. For power law mass density spectra with indices steeper than −2 the wave amplitude exhibits rms fluctuations 1.3^(1/4)(D_(eff)/1 Gpc)^(1/2)%, where is the variance in the mass surface density measured in M^2_⊙ pc^(−4) and D_(eff) is the effective distance to the lensing medium. For shallower spectra the amplitude of the fluctuations depends additionally on the inner length scale and power law index of the density fluctuations. The intensity fluctuations are dominated by temporal fluctuations on long timescales. For lensing material moving at a speed v across the line of sight the fluctuation timescale exceeds v^(−1)(D_(eff)λ)^(1/2). Lensing by small scale structure induces at most ≈15% rms variations if the line of sight to a gravitational wave source intersects a region with densities ~100 M_⊙ pc^(−2), which are typically encountered in the vicinity of galaxy clusters