We introduce to astrophysics the threshold clustering function S2 first derived by Torquato et al. (1988), which effectively samples the flux probability distribution (PDF) of the Ly-alpha forest at different spatial scales. These statistics are tested on mock Ly-alpha forest spectra based on various toy models for He II reionization, with homogeneous models with various temperature-density relations as well as models with temperature inhomogeneities. These mock samples have systematics and noise added to simulate the latest Sloan Digital Sky Survey Data Release 7 (SDSS DR7) data. We find that the flux PDF from SDSS DR7 can be used to constrain the temperature-density relation gamma (where T \propto (1 + Delta)^{gamma -1}) of the intergalactic medium (IGM) at z=2.5 to a precision of Delta(gamma) = 0.2 at ~4-sigma confidence. The flux PDF is degenerate to temperature inhomogeneities in the IGM arising from He II reionization, but we find S2 can detect these inhomogeneities at ~5-sigma, with the assumption that the flux continuum of the Ly-alpha forest can be determined to 9% accuracy, approximately the error from current fitting methods. If the flux continuum can be determined to 3% accuracy, then S2 is capable of constraining the characteristic scale of temperature inhomogeneities, with ~4-sigma differentiation between toy models with hot bubble radii of 50 Mpc/h and 100 Mpc/h.
Dynamics of anisotropic f(R) cosmology
We construct general anisotropic cosmological scenarios governed by an f(R) gravitational sector. Focusing then on Kantowski-Sachs geometries in the case of $R^n$-gravity we perform a detailed phase-space analysis. We find that at late times the universe can result to a state of accelerating expansion, and additionally, for a particular n-range (2<n<3) it exhibits phantom behavior. Furthermore, isotropization has been achieved independently of the initial anisotropy degree. Moreover, contracting solutions have also a large probability to be the late-time states of the universe. Finally, we can also obtain the realization of the cosmological bounce and turnaround, as well as of cyclic cosmology. These features indicate that anisotropic geometries in modified gravitational frameworks present radically different cosmological behaviors comparing to the simple isotropic scenarios.
The dynamics of generalized Palatini Theories of Gravity
It is known that in f(R) theories of gravity with an independent connection which can be both non-metric and non symmetric, this connection can always be algebraically eliminated in favour of the metric and the matter fields, so long as it is not coupled to the matter explicitly. We show here that this is a special characteristic of f(R) actions, and it is not true for actions that include other curvature invariants. This contradicts some recent claims in the literature. We clarify the reasons of this contradiction.
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