The gravitational wave contribution to CMB anisotropies and the amplitude of mass fluctuations from COBE results

A stochastic background of primordial gravitational waves may substantially contribute, via the Sachs--Wolfe effect, to the large--scale Cosmic Microwave Background (CMB) anisotropies recently detected by COBE. This implies a {\it bias} in any resulting determination of the primordial amplitude of density fluctuations. We consider the constraints imposed on $n<1$ (``tilted") power--law fluctuation spectra, taking into account the contribution from both scalar and tensor waves, as predicted by power--law inflation. The gravitational--wave contribution to CMB anisotropies generally reduces the required {\it rms} level of mass fluctuation, thereby increasing the linear {\it bias parameter}, even in models where the spectral index is close to the Harrison--Zel'dovich value $n=1$. This ``gravitational--wave bias" helps to reconcile the predictions of CDM models with observations on pairwise galaxy velocity dispersion on small scales.Comment: 11 pages. Two figures available upon reques

The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models

We analyze the temperature three--point correlation function and the skewness of the Cosmic Microwave Background (CMB), providing general relations in terms of multipole coefficients. We then focus on applications to large angular scale anisotropies, such as those measured by the {\em COBE} DMR, calculating the contribution to these quantities from primordial, inflation generated, scalar perturbations, via the Sachs--Wolfe effect. Using the techniques of stochastic inflation we are able to provide a {\it universal} expression for the ensemble averaged three--point function and for the corresponding skewness, which accounts for all primordial second--order effects. These general expressions would moreover apply to any situation where the bispectrum of the primordial gravitational potential has a {\em hierarchical} form. Our results are then specialized to a number of relevant models: power--law inflation driven by an exponential potential, chaotic inflation with a quartic and quadratic potential and a particular case of hybrid inflation. In all these cases non--Gaussian effects are small: as an example, the {\em mean} skewness is much smaller than the cosmic {\em rms} skewness implied by a Gaussian temperature fluctuation field.Comment: 18 pages; LaTeX; 4 PostScript figures included at the end of the file; SISSA REF.193/93/A and DFPD 93/A/8

On Relativistic Perturbations of Second and Higher Order

We present the results of a study of the gauge dependence of spacetime perturbations. In particular, we consider gauge invariance in general, we give a generating formula for gauge transformations to an arbitrary order n, and explicit transformation rules at second order.Comment: 6 pages, latex, with special style included, Proceedings of the 12th Italian Conference on General Relativity and Gravitational Physic

Recent results from the Pierre Auger Observatory

The main results from the Auger Observatory are described. A steepening of the spectrum is observed at the highest energies, supporting the expectation that above $4\times 10^{19}$ eV the cosmic ray energies are significantly degraded by interactions with the CMB photons (the GZK effect). This is further supported by the correlations observed above $6\times 10^{19}$ eV with the distribution of nearby active galaxies, which also show the potential of Auger to start the era of charged particle astronomy. The lack of observation of photons or neutrinos strongly disfavors top-down models, and these searches may approach in the long term the sensitivity required to test the fluxes expected from the secondaries of the very same GZK process. Bounds on the anisotropies at EeV energies contradict hints from previous experiments that suggested a large excess from regions near the Galactic centre or the presence of a dipolar type modulation of the cosmic ray flux.Comment: 6 p., 8 figs., proceedings of the XXIII International Conference on Neutrino Physics and Astrophysics (Neutrino 08

Relativistic second-order perturbations of the Einstein-de Sitter Universe

We consider the evolution of relativistic perturbations in the Einstein-de Sitter cosmological model, including second-order effects. The perturbations are considered in two different settings: the widely used synchronous gauge and the Poisson (generalized longitudinal) one. Since, in general, perturbations are gauge dependent, we start by considering gauge transformations at second order. Next, we give the evolution of perturbations in the synchronous gauge, taking into account both scalar and tensor modes in the initial conditions. Using the second-order gauge transformation previously defined, we are then able to transform these perturbations to the Poisson gauge. The most important feature of second-order perturbation theory is mode-mixing, which here also means, for instance, that primordial density perturbations act as a source for gravitational waves, while primordial gravitational waves give rise to second-order density fluctuations. Possible applications of our formalism range from the study of the evolution of perturbations in the mildly non-linear regime to the analysis of secondary anisotropies of the Cosmic Microwave Background.Comment: Revised version with minor changes, accepted in The Physical Review D; LaTeX file using RevTeX macros, 28 page