An exact Jacobi map in the geodesic light-cone gauge

The remarkable properties of the recently proposed geodesic light-cone (GLC) gauge allow to explicitly solve the geodetic-deviation equation, and thus to derive an exact expression for the Jacobi map J^A_B(s,o) connecting a generic source s to a geodesic observer o in a generic space time. In this gauge J^A_B factorizes into the product of a local quantity at s times one at o, implying similarly factorized expressions for the area and luminosity distance. In any other coordinate system J^A_B is simply given by expressing the GLC quantities in terms of the corresponding ones in the new coordinates. This is explicitly done, at first and second order, respectively, for the synchronous and Poisson gauge-fixing of a perturbed, spatially-flat cosmological background, and the consistency of the two outcomes is checked. Our results slightly amend previous calculations of the luminosity-redshift relation and suggest a possible non-perturbative way for computing the effects of inhomogeneities on observations based on light-like signals.Comment: 26 pages, no figures. Inconsequential modification of an equation, comments and references added. Version accepted for publication in JCA

A new approach to the propagation of light-like signals in perturbed cosmological backgrounds

We present a new method to compute the deflection of light rays in a perturbed FLRW geometry. We exploit the properties of the Geodesic Light Cone (GLC) gauge where null rays propagate at constant angular coordinates irrespectively of the given (inhomogeneous and/or anisotropic) geometry. The gravitational deflection of null geodesics can then be obtained, in any other gauge, simply by expressing the angular coordinates of the given gauge in terms of the GLC angular coordinates. We apply this method to the standard Poisson gauge, including scalar perturbations, and give the full result for the deflection effect in terms of the direction of observation and observed redshift up to second order, and up to third order for the leading lensing terms. We also compare our results with those presently available in the literature and, in particular, we provide a new non trivial check of a previous result on the luminosity-redshft relation up to second order in cosmological perturbation theory.Comment: 37 pages, no figures. Typos corrected, comments and references added. Version accepted for publication in JCA

Adiabatic regularization of the graviton stress-energy tensor in de Sitter space-time

We study the renormalized energy-momentum tensor of gravitons in a de Sitter space-time. After canonically quantizing only the physical degrees of freedom, we adopt the standard adiabatic subtraction used for massless minimally coupled scalar fields as a regularization procedure and find that the energy density of gravitons in the E(3) invariant vacuum is proportional to H^4, where H is the Hubble parameter, but with a positive sign. According to this result the scalar expansion rate, which is gauge invariant in de Sitter space-time, is increased by the fluctuations. This implies that gravitons may then add to conformally coupled matter in driving the Starobinsky model of inflation.Comment: 5 pages, revtex, final version accepted for publication in PR

Stochastic growth of quantum fluctuations during slow-roll inflation

We compute the growth of the mean square of quantum fluctuations of test fields with small effective mass during a slowly changing, nearly de Sitter stage which took place in different inflationary models. We consider a minimally coupled scalar with a small mass, a modulus with an effective mass $\propto H^2$ (with $H$ as the Hubble parameter) and a massless non-minimally coupled scalar in the test field approximation and compare the growth of their relative mean square with the one of gauge-invariant inflaton fluctuations. We find that in most of the single field inflationary models the mean square gauge invariant inflaton fluctuation grows {\em faster} than any test field with a non-negative effective mass. Hybrid inflationary models can be an exception: the mean square of a test field can dominate over the gauge invariant inflaton fluctuation one on suitably choosing parameters. We also compute the stochastic growth of quantum fluctuation of a second field, relaxing the assumption of its zero homogeneous value, in a generic inflationary model; as a main result, we obtain that the equation of motion of a gauge invariant variable associated, order by order, with a generic quantum scalar fluctuation during inflation can be obtained only if we use the number of e-folds as the time variable in the corresponding Langevin and Fokker-Planck equations for the stochastic approach. We employ this approach to derive some bounds in the case of a model with two massive fields.Comment: 9 pages, 4 figures. Added references, minor changes, matches the version to be published in Phys. Rev.

Isotropic Observers and the Inflationary Backreaction Problem

In an inflationary regime driven by a free massive inflaton we derive within a genuinely gauge invariant approach the backreaction effects due to long wavelength scalar fluctuations on the effective Hubble factor and equation of state with respect to a class of observers which sees an inhomogeneous and isotropic Universe. We find that, for such so-called isotropic observers, contrary to what happens for the observables defined by free-falling observers, there is an effect to leading order in the slow-roll parameter in the direction of slowing down the measured rate of expansion and of having an effective equation of state less de Sitter like. From a general point of view the isotropic observers result has to be considered complementary to other cases (observers) in helping to characterize the physical properties of the models under investigation.Comment: 16 pages, latex. Comments added, errors and typos corrected, main results unchanged. Version accepted for publication in Class. Quantum Gra

Primordial black holes formation in a early matter dominated era from the pre-big bang scenario

We discuss the production of primordial black holes in an early matter dominated era, which typically takes place in string inspired early universe cosmological models. In particular, we consider a pre-big bang scenario (extending previous results regarding formation in the radiation dominated era) where the enhancement of curvature perturbations is induced by a variation of the sound-speed parameter c_s during the string phase of high-curvature inflation. After imposing all relevant observational constraints, we find that the considered class of models is compatible with the production of a large amount of primordial black holes, in the mass range relevant to dark matter, only for a small range of the parameters space. On the other hand, we find that a huge production of light primordial black holes may occur both in such matter dominated era and in the radiation dominated one.Comment: 7 pages, 3 figure

Do stochastic inhomogeneities affect dark-energy precision measurements?

The effect of a stochastic background of cosmological perturbations on the luminosity-redshift relation is computed to second order through a recently proposed covariant and gauge-invariant light-cone averaging procedure. The resulting expressions are free from both ultraviolet and infrared divergences, implying that such perturbations cannot mimic a sizable fraction of dark energy. Different averages are estimated and depend on the particular function of the luminosity distance being averaged. The energy flux, being minimally affected by perturbations at large z, is proposed as the best choice for precision estimates of dark-energy parameters. Nonetheless, its irreducible (stochastic) variance induces statistical errors on \Omega_{\Lambda}(z) typically lying in the few-percent range.Comment: 5 pages, 3 figures. Comments and references added. Typos corrected. Version accepted for publication in Phys. Rev. Let

Primordial Black Holes from Pre-Big Bang inflation

We discuss the possibility of producing a significant fraction of dark matter in the form of primordial black holes in the context of the pre-big bang inflationary scenario. We take into account, to this purpose, the enhancement of curvature perturbations possibly induced by a variation of the sound-speed parameter $c_s$ during the string phase of high-curvature inflation. After imposing all relevant observational constraints, we find that the considered class of models is compatible with the production of a large amount of primordial black holes in the mass range relevant to dark matter, provided the sound-speed parameter is confined in a rather narrow range of values, $0.003 < c_s < 0.01$.Comment: 26 pages, two figures. Many new references and a few comments added. Version accepted for publication in JCA

Second Order Gauge-Invariant Perturbations during Inflation

The evolution of gauge invariant second-order scalar perturbations in a general single field inflationary scenario are presented. Different second order gauge invariant expressions for the curvature are considered. We evaluate perturbatively one of these second order curvature fluctuations and a second order gauge invariant scalar field fluctuation during the slow-roll stage of a massive chaotic inflationary scenario, taking into account the deviation from a pure de Sitter evolution and considering only the contribution of super-Hubble perturbations in mode-mode coupling. The spectra resulting from their contribution to the second order quantum correlation function are nearly scale-invariant, with additional logarithmic corrections to the first order spectrum. For all scales of interest the amplitude of these spectra depend on the total number of e-folds. We find, on comparing first and second order perturbation results, an upper limit to the total number of e-folds beyond which the two orders are comparable.Comment: 17 pages, 6 figures. Final version to appear in Phys. Rev.

Primordial black holes from pre-big bang inflation

We discuss the possibility of producing a significant fraction of dark matter in the form of primordial black holes in the context of the pre-big bang inflationary scenario. We take into account, to this purpose, the enhancement of curvature perturbations possibly induced by a variation of the sound-speed parameter cs during the string phase of high-curvature inflation. After imposing all relevant observational constraints, we find that the considered class of models is compatible with the production of a large amount of primordial black holes in the mass range relevant to dark matter, provided the sound-speed parameter is confined in a rather narrow range of values, 0.003 cs 0.01