Quantum Gravity effects near the null black hole singularity

The structure of the Cauchy Horizon singularity of a black hole formed in a generic collapse is studied by means of a renormalization group equation for quantum gravity. It is shown that during the early evolution of the Cauchy Horizon the increase of the mass function is damped when quantum fluctuations of the metric are taken into account.Comment: 15 Pages, one figure. Minor changes in the presentation, to appear on Phys.Rev.

Cosmological Perturbations in Renormalization Group Derived Cosmologies

A linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid Universe with dynamically evolving Newton constant $G$ and cosmological constant $\Lambda$ is presented. A gauge-invariant formalism is developed by means of the covariant approach, and the acoustic propagation equations governing the evolution of the comoving fractional spatial gradients of the matter density, $G$, and $\Lambda$ are thus obtained. Explicit solutions are discussed in cosmologies where both $G$ and $\Lambda$ vary according to renormalization group equations in the vicinity of a fixed point.Comment: 22 pages, revtex, subeqn.sty, to appear on IJMP

An effective action for asymptotically safe gravity

Asymptotically safe theories of gravitation have received great attention in recent times. In this framework an effective action embodying the basic features of the renormalized flow around the non-gaussian fixed point is derived and its implications for the early universe are discussed. In particular, a "landscape" of a countably infinite number of cosmological inflationary solutions characterized by an unstable de Sitter phase lasting for a large enough number of e-folds is found.Comment: 5 pages, to appear as a Rapid Communication in Physical Review

A Class of Renormalization Group Invariant Scalar Field Cosmologies

We present a class of scalar field cosmologies with a dynamically evolving Newton parameter $G$ and cosmological term $\Lambda$. In particular, we discuss a class of solutions which are consistent with a renormalization group scaling for $G$ and $\Lambda$ near a fixed point. Moreover, we propose a modified action for gravity which includes the effective running of $G$ and $\Lambda$ near the fixed point. A proper understanding of the associated variational problem is obtained upon considering the four-dimensional gradient of the Newton parameter.Comment: 10 pages, RevTex4, no figures, to appear on GR

Seismology of Procyon A: determination of mode frequencies, amplitudes, lifetimes, and granulation noise

The F5 IV-V star Procyon A (aCMi) was observed in January 2001 by means of the high resolution spectrograph SARG operating with the TNG 3.5m Italian telescope (Telescopio Nazionale Galileo) at Canary Islands, exploiting the iodine cell technique. The time-series of about 950 spectra carried out during 6 observation nights and a preliminary data analysis were presented in Claudi et al. 2005. These measurements showed a significant excess of power between 0.5 and 1.5 mHz, with ~ 1 m/s peak amplitude. Here we present a more detailed analysis of the time-series, based on both radial velocity and line equivalent width analyses. From the power spectrum we found a typical p-mode frequency comb-like structure, identified with a good margin of certainty 11 frequencies in the interval 0.5-1400 mHz of modes with l=0,1,2 and 7< n < 22, and determined large and small frequency separations, Dn = 55.90 \pm 0.08 muHz and dnu_02=7.1 \pm 1.3 muHz, respectively. The mean amplitude per mode (l=0,1) at peak power results to be 0.45 \pm 0.07 m/s, twice larger than the solar one, and the mode lifetime 2 \pm 0.4 d, that indicates a non-coherent, stochastic source of mode excitation. Line equivalent width measurements do not show a significant excess of power in the examined spectral region but allowed us to infer an upper limit to the granulation noise.Comment: 10 pages, 15 figures, 4 tables. Accepted for publication in A&

The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity

We discuss various basic conceptual issues related to coarse graining flows in quantum gravity. In particular the requirement of background independence is shown to lead to renormalization group (RG) flows which are significantly different from their analogs on a rigid background spacetime. The importance of these findings for the asymptotic safety approach to Quantum Einstein Gravity (QEG) is demonstrated in a simplified setting where only the conformal factor is quantized. We identify background independence as a (the ?) key prerequisite for the existence of a non-Gaussian RG fixed point and the renormalizability of QEG.Comment: 2 figures. Talk given by M.R. at the WE-Heraeus-Seminar "Quantum Gravity: Challenges and Perspectives", Bad Honnef, April 14-16, 2008; to appear in General Relativity and Gravitatio

Networks of equities in financial markets

We review the recent approach of correlation based networks of financial equities. We investigate portfolio of stocks at different time horizons, financial indices and volatility time series and we show that meaningful economic information can be extracted from noise dressed correlation matrices. We show that the method can be used to falsify widespread market models by directly comparing the topological properties of networks of real and artificial markets.Comment: 9 pages, 8 figures. Accepted for publication in EPJ