S. Mollerach

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 s anisotropies, such as those measured by the 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 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 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 mean skewness is much smaller than the cosmic rms skewness implied by a Gaussian temperature fluctuation field.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.

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.

Lensing of ultra-high energy cosmic rays in turbulent magnetic fields

We consider the propagation of ultra high energy cosmic rays through turbulent magnetic fields and study the transition between the regimes of single and multiple images of point-like sources. The transition occurs at energies around Ec Z 41 EeV(Brms/5 μG)(L/2 kpc)3/2(50 pc/Lc)1/2, where L is the distance traversed by the CRs with electric charge Ze in the turbulent magnetic field of root mean square strength Brms and coherence length Lc. We find that above 2Ec only sources located in a fraction of a few % of the sky can reach large amplifications of its principal image or start developing multiple images. New images appear in pairs with huge magnifications, and they remain amplified over a significant range of energies. At decreasing energies the fraction of the sky in which sources can develop multiple images increases, reaching about 50% for E > Ec/2. The magnification peaks become however increasingly narrower and for E < Ec/3 their integrated effect becomes less noticeable. If a uniform magnetic field component is also present it would further narrow down the peaks, shrinking the energy range in which they can be relevant. Below E Ec/10 some kind of scintillation regime is reached, where many demagnified images of a source are present but with overall total magnification of order unity. We also search for lensing signatures in the AGASA data studying two-dimensional correlations in angle and energy and find some interesting hints.

On the ultrahigh energy cosmic ray horizon

We compute the ultrahigh energy cosmic ray horizon, i.e. the distance up to which cosmic ray sources may significantly contribute to the fluxes above a certain threshold on the observed energies. We obtain results both for proton and heavy nuclei sources.

Large-scale magnetic fields from density perturbations

We derive the minimal seed magnetic field which unavoidably arises in the radiation and matter eras, prior to recombination, by the rotational velocity of ions and electrons, gravitationally induced by the nonlinear evolution of primordial density perturbations. The resulting magnetic field power spectrum is fully determined by the amplitude and spectral index of density perturbations. The rms amplitude of the seed field at recombination is B{approx_equal}10{sup -23}({lambda}/Mpc){sup -2} G, on comoving scales {lambda} > or approx.1 Mpc.

CMB polarization from secondary vector and tensor modes

We consider a novel contribution to the polarization of the cosmic microwave background induced by vector and tensor modes generated by the nonlinear evolution of primordial scalar perturbations. Our calculation is based on relativistic second-order perturbation theory and allows us to estimate the effects of these secondary modes on the polarization angular power spectra. We show that a nonvanishing B-mode polarization unavoidably arises from pure scalar initial perturbations, thus limiting our ability to detect the signature of primordial gravitational waves generated during inflation. This secondary effect dominates over that of primordial tensors for an inflationary tensor-to-scalar ratio

Cosmic microwave background anisotropies from second order gravitational perturbations

rl{10}^{\ensuremath{-}6}.

PeV neutrinos from the propagation of ultra-high energy cosmic rays

The magnitude of the effect is smaller than the contamination produced by the conversion of polarization of type E into type B, by weak gravitational lensing. However, the lensing signal can be cleaned, making the secondary modes discussed here the actual background limiting the detection of small amplitude primordial gravitational waves.

The East-West method: an exposure-independent method to search for large scale anisotropies of cosmic rays

This paper presents a complete analysis of the effects of second order gravitational perturbations on cosmic microwave background anisotropies, taking explicitly into account scalar, vector and tensor modes. We also consider the second order perturbations of the metric itself obtaining them, for a universe dominated by a collisionless fluid, in the Poisson gauge, by transforming the known results in the synchronous gauge. We discuss the resulting second order anisotropies in the Poisson gauge, and analyze the possible relevance of the different terms. We expect that, in the simplest scenarios for structure formation, the main effect comes from the gravitational lensing by scalar perturbations that is known to give a few percent contribution to the anisotropies at small angular scales.

Astrophysical magnetic field reconstruction and spectroscopy with ultra high energy cosmic rays

We discuss the possibility that the PeV neutrinos recently observed by IceCube are produced by the interactions of extragalactic cosmic rays during their propagation through the radiation backgrounds. We show that the fluxes resulting from the decays of neutrons produced in the interactions of cosmic ray protons with the CMB background are suppressed (E 2 d��/dE < 10 −10 GeV/cm 2 s sr), with those resulting from the decays of pions produced in the interactions with the UV/optical/IR backgrounds being the dominant ones at PeV energies. The anti-neutrino fluxes produced by the decay of neutrons resulting from the photodisintegration of heavy nuclei with CMB photons are also shown to be quite suppressed (E 2 � d��/dE < 10 −11 GeV/cm 2 s sr), while those produced by photo-pion processes with UV/optical/IR backgrounds may be larger, although they are not expected to be above those achievable in the pure proton case. Scenarios with mixed composition and low cutoff rigidities can lead to PeV neutrino fluxes enhanced with respect to those in the pure Fe scenarios. We also discuss the possible impact of the Glashow resonance for the detection of these scenarios, showing that it plays a moderate role.