Gravitational Wave Background from a Cosmological Population of Core-Collapse Supernovae

We analyse the stochastic background of gravitational radiation emitted by a cosmological population of core-collapse supernovae. The supernova rate as a function of redshift is deduced from an observation-based determination of the star formation rate density evolution. We then restrict our analysis to the range of progenitor masses leading to black hole collapse. In this case, the main features of the gravitational-wave emission spectra have been shown to be, to some extent, independent of the initial conditions and of the equation of state of the collapsing star, and to depend only on the black hole mass and angular momentum. We calculate the overall signal produced by the ensemble of black-hole collapses throughout the Universe, assuming a flat cosmology with vanishing cosmological constant. Within a wide range of parameter values, we find that the spectral strain amplitude has a maximum at a few hundred Hz with an amplitude between $10^{-28}$ and $10^{-27} Hz^{-1/2}$; the corresponding closure density, $\Omega_{GW}$, has a maximum amplitude ranging between $10^{-11}$ and $10^{-10}$ in the frequency interval $\sim 1.5-2.5$ kHz. Contrary to previous claims, our observation-based determination leads to a duty cycle of order 0.01, making our stochastic backgound a non-continuous one. Although the amplitude of our background is comparable to the sensitivity that can be reached by a pair of advanced LIGO detectors, the characteristic shot-noise structure of the predicted signal might be in principle exploited to design specific detection strategies.Comment: 12 pages, LaTeX (uses mn.sty), 13 figures, 2 tables, accepted for publication in MNRA

Statistics of cosmological fields

AbstractThe general problem of the statistics of the primordial curvature perturbation field in cosmology is reviewed. The search for non-Gaussian signatures in cosmological perturbations, originated from inflation in the early Universe is discussed both from the theoretical point of view and in connection with constraints coming from recent observations and future prospects for observing/constraining them

Cosmic Microwave Background Anisotropies up to Second Order

These lecture notes present the computation of the full system of Boltzmann equations describing the evolution of the photon, baryon and cold dark matter fluids up to second order in perturbation theory, as recently studied in (Bartolo, Matarrese & Riotto 2006, 2007). These equations allow to follow the time evolution of the cosmic microwave background anisotropies at all angular scales from the early epoch, when the cosmological perturbations were generated, to the present, through the recombination era. The inclusion of second-order contributions is mandatory when one is interested in studying possible deviations from Gaussianity of cosmological perturbations, either of primordial (e.g. inflationary) origin or due to their subsequent evolution. Most of the emphasis in these lectures notes will be given to the derivation of the relevant equations for the study of cosmic microwave background anisotropies and to their analytical solutions.Comment: 53 pages, LaTeX file. Lectures given by S.M. at Les Houches Summer School - Session 86: Particle Physics and Cosmology: The Fabric of Spacetime, Les Houches, France, 31 Jul - 25 Aug 2006. To appear in the Proceedings. Second version with minor misprints correcte

Post-Newtonian cosmological dynamics of plane-parallel perturbations and back-reaction

We study the general relativistic non-linear dynamics of self-gravitating irrotational dust in a cosmological setting, adopting the comoving and synchronous gauge, where all the equations can be written in terms of the metric tensor of spatial hyper-surfaces orthogonal to the fluid flow. Performing an expansion in inverse powers of the speed of light, we obtain the post-Newtonian equations, which yield the lowest-order relativistic effects arising during the non-linear evolution. We then specialize our analysis to globally plane-parallel configurations, i.e. to the case where the initial perturbation field depends on a single coordinate. The leading order of our expansion, corresponding to the "Newtonian background", is the Zel'dovich approximation, which, for plane-parallel perturbations in the Newtonian limit, represents an exact solution. This allows us to find the exact analytical form for the post-Newtonian metric, thereby providing the post-Newtonian extension of the Zel'dovich solution: this accounts for some relativistic effects, such as the non-Gaussianity of primordial perturbations. An application of our solution in the context of the back-reaction proposal is eventually given, providing a post-Newtonian estimation of kinematical back-reaction, mean spatial curvature and average scale-factor.Comment: revised to match the version accepted for publication in JCA

Extended Quintessence: imprints on the cosmic microwave background spectra

We describe the observable features of the recently proposed Extended Quintessence scenarios on the Cosmic Microwave Background (CMB) anisotropy spectra. In this class of models a scalar field $\phi$, assumed to provide most of the cosmic energy density today, is non-minimally coupled to the Ricci curvature scalar $R$. We implement the linear theory of cosmological perturbations in scalar tensor gravitational theories to compute CMB temperature and polarization spectra. All the interesting spectral features are affected: on sub-degree angular scales, the acoustic peaks change both in amplitude and position; on larger scales the low redshift dynamics enhances the Integrated Sachs Wolfe effect. These results show how the future CMB experiments could give information on the vacuum energy as well as on the structure of the gravitational Lagrangian term.Comment: 4 pages including 1 figure, to be published in the proceedings of the COSMO99 meeting, held in Trieste, September 199

ΔN\Delta N Formalism and Conserved Currents in Cosmology

The $\Delta N$ formalism, based on the counting of the number of e-folds during inflation in different local patches of the Universe, has been introduced several years ago as a simple and physically intuitive approach to calculate (non-linear) curvature perturbations from inflation on large sales, without resorting to the full machinery of (higher-order) perturbation theory. Later on, it was claimed the equivalence with the results found by introducing a conserved fully non-linear current $\zeta_\mu$, thereby allowing to directly connect perturbations during inflation to late-Universe observables. We discus some issues arising from the choice of the initial hyper-surface in the $\Delta N$ formalism. By using a novel exact expression for $\zeta_\mu$, valid for any barotropic fluid, we find that it is not in general related to the standard uniform density curvature perturbation $\zeta$; such a result conflicts with the claimed equivalence with $\Delta N$ formalism. Moreover, a similar analysis is done for the proposed non-perturbative generalization ${\cal R}_\mu$ of the comoving curvature perturbation ${\cal R}$.Comment: 19 pages, 1 figures. Final version accepted for publication in JCAP. Title slightly changed to avoid confusion with existing literature. Expanded content with the same conclusion

Stochastic background of gravitational waves generated by a cosmological population of young, rapidly rotating neutron stars

We estimate the spectral properties of the stochastic background of gravitational radiation emitted by a cosmological population of hot, young, rapidly rotating neutron stars. Their formation rate as a function of redshift is deduced from an observation-based determination of the star formation history in the Universe, and the gravitational energy is assumed to be radiated during the spin-down phase associated to the newly discovered r-mode instability. We calculate the overall signal produced by the ensemble of such neutron stars, assuming various cosmological backgrounds. We find that the spectral strain amplitude has a maximum $\approx (2-4)\times 10^{-26} {Hz}^{-1/2}$, at frequencies $\approx (30-60)$ Hz, while the corresponding closure density, $h^2 \Omega_{GW}$, has a maximum amplitude plateau of $\approx (2.2-3.3) \times 10^{-8}$ in the frequency range $(500-1700)$ Hz. We compare our results with a preliminary analysis done by Owen et al. (1998), and discuss the detectability of this background.Comment: 8 pages, 9 figures, accepted for publication in MNRA

Perturbative Unitarity of Inflationary Models with Features

We consider the pertubative consistency of inflationary models with features with effective field theory methods. By estimating the size of one-loop contributions to the three-point function, we find the energy scale where their contribution is of the same order of the tree-level amplitude. It is well-known that beyond that scale, perturbative unitarity is lost and the theory is no more under theoretical control. Requiring that all the relevant energy scales of the problem are below this cutoff, we derive a strong upper bound on the sharpness of the feature, or equivalently on its characteristic time scale, which is independent on the amplitude of the feature itself. We point out that the sharp features which seem to provide better fits to the CMB power spectrum are already outside this bound, questioning the consistency of the models that predict them

The Effective Field Theory of Inflation Models with Sharp Features

We describe models of single-field inflation with small and sharp step features in the potential (and sound speed) of the inflaton field, in the context of the Effective Field Theory of Inflation. This approach allows us to study the effects of features in the power-spectrum and in the bispectrum of curvature perturbations, from a model-independent point of view, by parametrizing the features directly with modified "slow-roll" parameters. We can obtain a self-consistent power-spectrum, together with enhanced non-Gaussianity, which grows with a quantity $\beta$ that parametrizes the sharpness of the step. With this treatment it is straightforward to generalize and include features in other coefficients of the effective action of the inflaton field fluctuations. Our conclusion in this case is that, excluding extrinsic curvature terms, the only interesting effects at the level of the bispectrum could arise from features in the first slow-roll parameter $\epsilon$ or in the speed of sound $c_s$. Finally, we derive an upper bound on the parameter $\beta$ from the consistency of the perturbative expansion of the action for inflaton perturbations. This constraint can be used for an estimation of the signal-to-noise ratio, to show that the observable which is most sensitive to features is the power-spectrum. This conclusion would change if we consider the contemporary presence of a feature and a speed of sound $c_s < 1$, as, in such a case, contributions from an oscillating folded configuration can potentially make the bispectrum the leading observable for feature models.Comment: 31 pages, 11 figures; references added, accepted version for publication in JCA