In $Lambda$CDM cosmology, structure formation is halted shortly after dark energy dominates the mass/energy budget of the Universe. A manifestation of this effect is that in such a cosmology the turnaround radius has an upper bound. Recently, a new,
local, test for the existence of dark energy in the form of a cosmological constant was proposed based on this turnaround bound. Before designing an experiment that, through high-precision determination of masses and turnaround radii, will challenge $Lambda$CDM cosmology, we have to answer two important questions: first, when turnaround-scale structures are predicted to be close enough to their maximum size, so that a possible violation of the bound may be observable. Second, which is the best mass scale to target for possible violations of the bound. Using the Press-Schechter formalism, we find that turnaround structures have in practice already stopped forming, and consequently, the turnaround radius of structures must be very close to the maximum value today. We also find that the mass scale of $sim 10^{13} M_odot$ characterizes turnaround structures that start to form in a statistically important number density today. This mass scale also separates turnaround structures with different cosmological evolution: smaller structures are no longer readjusting their mass distribution inside the turnaround scale, they asymptotically approach their ultimate abundance from higher values, and they are common enough to have, at some epoch, experienced major mergers with structures of comparable mass; larger structures exhibit the opposite behavior. We call this mass scale the transitional mass scale and we argue that it is the optimal for the purpose outlined above. As a corollary result, we explain the different accretion behavior of small and larger structures observed in already conducted numerical simulations.
For a general dark-energy equation of state, we estimate the maximum possible radius of massive structures that are not destabilized by the acceleration of the cosmological expansion. A comparison with known stable structures constrains the equation
of state. The robustness of the constraint can be enhanced through the accumulation of additional astrophysical data and a better understanding of the dynamics of bound cosmic structures.
Whether a correlation exists between the radio and gamma-ray flux densities of blazars is a long-standing question, and one that is difficult to answer confidently because of various observational biases which may either dilute or apparently enhance
any intrinsic correlation between radio and gamma-ray luminosities. We introduce a novel method of data randomization to evaluate quantitatively the effect of these biases and to assess the intrinsic significance of an apparent correlation between radio and gamma-ray flux densities of blazars. The novelty of the method lies in a combination of data randomization in luminosity space (to ensure that the randomized data are intrinsically, and not just apparently, uncorrelated) and significance assessment in flux space (to explicitly avoid Malmquist bias and automatically account for the limited dynamical range in both frequencies). The method is applicable even to small samples that are not selected with strict statistical criteria. For larger samples we describe a variation of the method in which the sample is split in redshift bins, and the randomization is applied in each bin individually; this variation is designed to yield the equivalent to luminosity-function sampling of the underlying population in the limit of very large, statistically complete samples. We show that for a smaller number of redshift bins, the method yields a worse significance, and in this way it is conservative in that it does not assign a stronger, artificially enhanced significance. We demonstrate how our test performs as a function of number of sources, strength of correlation, and number of redshift bins used, and we show that while our test is robust against common-distance biases and associated false positives for uncorrelated data, it retains the power of other methods in rejecting the null hypothesis of no correlation for correlated data.
