Disformal invariance of continuous media with linear equation of state

We show that the effective theory describing single component continuous media with a linear and constant equation of state of the form $p=w\rho$ is invariant under a 1-parameter family of continuous disformal transformations. In the special case of $w=1/3$ (ultrarelativistic gas), such a family reduces to conformal transformations. As examples, perfect fluids, homogeneous and isotropic solids are discussed.Comment: latex, 7 page

High-Resolution Simulations of Cosmic Microwave Background non-Gaussian Maps in Spherical Coordinates

We describe a new numerical algorithm to obtain high-resolution simulated maps of the Cosmic Microwave Background (CMB), for a broad class of non-Gaussian models. The kind of non-Gaussianity we account for is based on the simple idea that the primordial gravitational potential is obtained by a non-linear but local mapping from an underlying Gaussian random field, as resulting from a variety of inflationary models. Our technique, which is based on a direct realization of the potential in spherical coordinates and fully accounts for the radiation transfer function, allows to simulate non-Gaussian CMB maps down to the Planck resolution ($\ell_{\rm max} \sim 3,000$), with reasonable memory storage and computational time.Comment: 9 pages, 5 figures. Submitted to ApJ. A version with higher quality figures is available at http://www.pd.infn.it/~liguori/content.htm

Living with ghosts in Horava-Lifshitz gravity

We consider the branch of the projectable Horava-Lifshitz model which exhibits ghost instabilities in the low energy limit. It turns out that, due to the Lorentz violating structure of the model and to the presence of a finite strong coupling scale, the vacuum decay rate into photons is tiny in a wide range of phenomenologically acceptable parameters. The strong coupling scale, understood as a cutoff on ghosts' spatial momenta, can be raised up to $\Lambda \sim 10$ TeV. At lower momenta, the projectable Horava-Lifshitz gravity is equivalent to General Relativity supplemented by a fluid with a small positive sound speed squared ($10^{-42}\lesssim$) $c^2_s \lesssim 10^{-20}$, that could be a promising candidate for the Dark Matter. Despite these advantages, the unavoidable presence of the strong coupling obscures the implementation of the original Horava's proposal on quantum gravity. Apart from the Horava-Lifshitz model, conclusions of the present work hold also for the mimetic matter scenario, where the analogue of the projectability condition is achieved by a non-invertible conformal transformation of the metric.Comment: 33 pages, 1 figure. The proof of an equivalence between the IR limit of the projectable Horava-Lifshitz gravity and the mimetic matter scenario is given in Appendix A. Version accepted for publication in JHE

Tests for primordial non-Gaussianity

We investigate the relative sensitivities of several tests for deviations from Gaussianity in the primordial distribution of density perturbations. We consider models for non-Gaussianity that mimic that which comes from inflation as well as that which comes from topological defects. The tests we consider involve the cosmic microwave background (CMB), large-scale structure (LSS), high-redshift galaxies, and the abundances and properties of clusters. We find that the CMB is superior at finding non-Gaussianity in the primordial gravitational potential (as inflation would produce), while observations of high-redshift galaxies are much better suited to find non-Gaussianity that resembles that expected from topological defects. We derive a simple expression that relates the abundance of high-redshift objects in non-Gaussian models to the primordial skewness.Comment: 6 pages, 2 figures, MNRAS in press (minor changes to match the accepted version

Paramagnetic‐Resonance Absorption of Ions with Spin 5/2: Mn++ in Calcite

The theory of the paramagnetic‐resonance absorption of ions with S = S=52 in crystalline fields of trigonal symmetry is presented. The case of manganous ions in calcite (CaCO3) is taken as an example. It is shown that the splitting of the fine‐structure satellites into doublets first reported by Hurd, Sachs, and Hershberger [Phys. Rev. 93, 373 (1954)] can be accounted for by assuming that the manganous ions can occupy the two nonequivalent Ca++ sites at random. The maximum splitting was measured at X band and K band and found to be 19.3±0.5 gauss. The value computed from the theory, assuming an ionic model, is 23.8 gauss. In addition, five pairs of weak lines were found, each pair occurring midway between adjacent hyperfine groups. The origin of these lines is uncertain. The applicability of the present theory to Al2O3:Fe, a zero‐field maser material, and to the photosensitive Fe+++ center in CdS is pointed out.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71145/2/JCPSA6-33-2-601-1.pd

A numerical study of the effects of primordial non-Gaussianities on weak lensing statistics

While usually cosmological initial conditions are assumed to be Gaussian, inflationary theories can predict a certain amount of primordial non-Gaussianity which can have an impact on the statistical properties of the lensing observables. In order to evaluate this effect, we build a large set of realistic maps of different lensing quantities starting from light-cones extracted from large dark-matter only N-body simulations with initial conditions corresponding to different levels of primordial local non-Gaussianity strength $f_{\rm NL}$. Considering various statistical quantities (PDF, power spectrum, shear in aperture, skewness and bispectrum) we find that the effect produced by the presence of primordial non-Gaussianity is relatively small, being of the order of few per cent for values of $|f_{\rm NL}|$ compatible with the present CMB constraints and reaching at most 10-15 per cent for the most extreme cases with $|f_{\rm NL}|=1000$. We also discuss the degeneracy of this effect with the uncertainties due to the power spectrum normalization $\sigma_8$ and matter density parameter $\Omega_{\rm m}$, finding that an error in the determination of $\sigma_8$ ($\Omega_{\rm m}$) of about 3 (10) per cent gives differences comparable with non-Gaussian models having $f_{\rm NL}=\pm 1000$. These results suggest that the possible presence of an amount of primordial non-Gaussianity corresponding to $|f_{\rm NL}|=100$ is not hampering a robust determination of the main cosmological parameters in present and future weak lensing surveys, while a positive detection of deviations from the Gaussian hypothesis is possible only breaking the degeneracy with other cosmological parameters and using data from deep surveys covering a large fraction of the sky.Comment: accepted by MNRA

A Comment on the Path Integral Approach to Cosmological Perturbation Theory

It is pointed out that the exact renormalization group approach to cosmological perturbation theory, proposed in Matarrese and Pietroni, JCAP 0706 (2007) 026, arXiv:astro-ph/0703563 and arXiv:astro-ph/0702653, constitutes a misnomer. Rather, having instructively cast this classical problem into path integral form, the evolution equation then derived comes about as a special case of considering how the generating functional responds to variations of the primordial power spectrum.Comment: 2 pages, v2: refs added, published in JCA

General Relativistic Dynamics of Irrotational Dust: Cosmological Implications

The non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is analyzed within General Relativity. Relativistic and Newtonian solutions are compared, stressing the different role of boundary conditions in the two theories. Cosmological implications of relativistic effects, already present at second order in perturbation theory, are studied and the dynamical role of the magnetic part of the Weyl tensor is elucidated.Comment: 12 pages , DFPD 93/A/6

The mass density field in simulated non-Gaussian scenarios

In this work we study the properties of the mass density field in the non-Gaussian world models simulated by Grossi et al. 2007. In particular we focus on the one-point density probability distribution function of the mass density field in non-Gausian models with quadratic non-linearities quantified by the usual parameter f_NL. We find that the imprints of primordial non-Gaussianity are well preserved in the negative tail of the probability function during the evolution of the density perturbation. The effect is already noticeable at redshifts as large as 4 and can be detected out to the present epoch. At z=0 we find that the fraction of the volume occupied by regions with underdensity delta < -0.9, typical of voids, is about 1.3 per cent in the Gaussian case and increases to ~2.2 per cent if f_NL=-1000 while decreases to ~0.5 per cent if f_NL=+1000. This result suggests that void-based statistics may provide a powerful method to detect non-Gaussianity even at low redshifts which is complementary to the measurements of the higher-order moments of the probability distribution function like the skewness or the kurtosis for which deviations from the Gaussian case are detected at the 25-50 per cent level.Comment: revised version, 9 Pages, 8 figures, MNRAS in pres

On the Physical Significance of Infra-red Corrections to Inflationary Observables

Inflationary observables, like the power spectrum, computed at one- and higher-order loop level seem to be plagued by large infra-red corrections. In this short note, we point out that these large infra-red corrections appear only in quantities which are not directly observable. This is in agreement with general expectations concerning infra-red effects.Comment: 11 pages; LateX file; 5 figures. Some coefficients in Eq.(A6) corrected; References adde