arXiv subjects
Publications and source records attributed to G. Marozzi.
In this article, we compare different formulations of the number count prescription using the convenient formalism of the Geodesic-Light-Cone gauge. We then find a simple, exact, and very general expression of such a prescription which is suitable for generalised applications.
We study the energy-momentum tensor and helicity of gauge fields coupled through $g ϕF \tilde{F}/4$ to a pseudo-scalar field $ϕ$ driving inflation. Under the assumption of a constant time derivative of the background inflaton, we compute analitically divergent and finite terms of the energy density and helicity of gauge fields for any value of the coupling $g$. We introduce a suitable adiabatic expansion for mode functions of physical states of the gauge fields which correctly reproduces ultraviolet divergences in average quantities and identify corresponding counterterms. Our calculations shed light on the accuracy and the range of validity of approximated analytic estimates of the energy density and helicity terms previously existed in the literature in the strongly coupled regime only, i.e. for $g \dot ϕ/(2H) \gg 1$. We discuss the implications of our analytic calculations for the backreaction of quantum fluctuations onto the inflaton evolution.
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, $0.003 < c_s < 0.01$.
High-precision constraints on primordial non-Gaussianity (PNG) will significantly improve our understanding of the physics of the early universe. Among all the subtleties in using large scale structure observables to constrain PNG, accounting for relativistic corrections to the clustering statistics is particularly important for the upcoming galaxy surveys covering progressively larger fraction of the sky. We focus on relativistic projection effects due to the fact that we observe the galaxies through the light that reaches the telescope on perturbed geodesics. These projection effects can give rise to an effective $f_{\rm NL}$ that can be misinterpreted as the primordial non-Gaussianity signal and hence is a systematic to be carefully computed and accounted for in modelling of the bispectrum. We develop the technique to properly account for relativistic effects in terms of purely observable quantities, namely angles and redshifts. We give some examples by applying this approach to a subset of the contributions to the tree-level bispectrum of the observed galaxy number counts calculated within perturbation theory and estimate the corresponding non-Gaussianity parameter, $f_{\rm NL}$, for the local, equilateral and orthogonal shapes. For the local shape, we also compute the local non-Gaussianity resulting from terms obtained using the consistency relation for observed number counts. Our goal here is not to give a precise estimate of $f_{\rm NL}$ for each shape but rather we aim to provide a scheme to compute the non-Gaussian contamination due to relativistic projection effects. For the terms considered in this work, we obtain contamination of $f_{\rm NL}^{\rm loc} \sim {\mathcal O}(1)$.
Including the metric fluctuations of a realistic cosmological geometry we reconsider an earlier suggestion that measuring the relative time-of-flight of ultra-relativistic particles can provide interesting constraints on fundamental cosmological and/or particle parameters. Using convenient properties of the geodetic light-cone coordinates we first compute, to leading order in the Lorentz factor and for a generic (inhomogeneous, anisotropic) space-time, the relative arrival times of two ultra-relativistic particles as a function of their masses and energies as well as of the details of the large-scale geometry. Remarkably, the result can be written as an integral over the unperturbed line-of-sight of a simple function of the local, inhomogeneous redshift. We then evaluate the irreducible scatter of the expected data-points due to first-order metric perturbations, and discuss, for an ideal source of ultra-relativistic particles, the resulting attainable precision on the determination of different physical parameters.
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.
We consider the backreaction of the long wavelength tensor modes produced during a slow-roll inflationary regime driven by a single scalar field in a spatially flat Friedmann-Lema\^ıtre-Robertson-Walker background geometry. We investigate the effects on non-local observables such as the effective (averaged) expansion rate and equation of state at second order in cosmological perturbation theory. The coupling between scalar and tensor perturbations induces at second order new tensor backreaction terms beyond the one already present in a de Sitter background. We analyze in detail the effects seen by the class of observers comoving with the inflaton field (taken as a clock) and the class of free-falling observers. In both cases the quantum backreaction is at least $1/ε$ (with $ε$ the slow-roll parameter) larger than the one which can be naively inferred from a de Sitter background. In particular, we compute the effect for a free massive inflaton model and obtain in both cases a quantum correction on the background expansion rate of the order of $H^4/(m^2 M_{Pl}^2)$. A short discussion on the issue of the breakdown of perturbation theory is given.
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.
Starting from the luminosity-redshift relation recently given up to second order in the Poisson gauge, we calculate the effects of the realistic stochastic background of perturbations of the so-called concordance model on the combined light-cone and ensemble average of various functions of the luminosity distance, and on their variance, as functions of redshift. We apply a gauge-invariant light-cone averaging prescription which is free from infrared and ultraviolet divergences, making our results robust with respect to changes of the corresponding cutoffs. Our main conclusions, in part already anticipated in a recent letter for the case of a perturbation spectrum computed in the linear regime, are that such inhomogeneities not only cannot avoid the need for dark energy, but also cannot prevent, in principle, the determination of its parameters down to an accuracy of order $10^{-3}-10^{-5}$, depending on the averaged observable and on the regime considered for the power spectrum. However, taking into account the appropriate corrections arising in the non-linear regime, we predict an irreducible scatter of the data approaching the 10% level which, for limited statistics, will necessarily limit the attainable precision. The predicted dispersion appears to be in good agreement with current observational estimates of the distance-modulus variance due to Doppler and lensing effects (at low and high redshifts, respectively), and represents a challenge for future precision measurements.
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.
We present a general gauge invariant formalism for defining cosmological averages that are relevant for observations based on light-like signals. Such averages involve either null hypersurfaces corresponding to a family of past light-cones or compact surfaces given by their intersection with timelike hypersurfaces. Generalized Buchert-Ehlers commutation rules for derivatives of these light-cone averages are given. After introducing some adapted "geodesic light-cone" coordinates, we give explicit expressions for averaging the redshift to luminosity-distance relation and the so-called "redshift drift" in a generic inhomogeneous Universe.
Within a genuinely gauge invariant approach recently developed for the computation of the cosmological backreaction, we study, in a cosmological inflationary context and with respect to various observers, the impact of scalar fluctuations on the space-time dynamics in the long wavelength limit. We stress that such a quantum backreaction effect is evaluated in a truly gauge independent way using a set of effective equations which describe the dynamics of the averaged geometry. In particular we show under what conditions the free falling (geodetic) observers do not experience any scalar-induced backreaction in the effective Hubble rate and fluid equation of state.
The standard field-theoretical approach to the slow-roll inflation is introduced. We then show as, in order to calculate the mean square of the canonical gauge invariant quantum fluctuations associated to a generic field, the logarithm of the scale factor has to be used as the time variable in the Fokker-Planck equation in the stochastic approach. Then we compute the growth of different test fields with a small effective mass during slow-roll inflationary models, comparing the results with the one for the gauge invariant canonical fluctuation associated to the inflaton, the Mukhanov variable. We find that in most of the single fields inflationary models such fluctuation grows faster than any test field with a non-negative effective mass, with the exception of hybrid models.
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.
Using our recent proposal for defining gauge invariant averages we give a general-covariant formulation of the so-called cosmological "backreaction". Our effective covariant equations allow us to describe in explicitly gauge invariant form the way classical or quantum inhomogeneities affect the average evolution of our Universe.
We show how to provide suitable gauge invariant prescriptions for the classical spatial averages (resp. quantum expectation values) that are needed in the evaluation of classical (resp. quantum) backreaction effects. We also present examples illustrating how the use of gauge invariant prescriptions can avoid interpretation problems and prevent misleading conclusions.
We prove that the stochastic and standard field-theoretical approaches produce exactly the same results for the amount of light massive scalar field fluctuations generated during inflation in the leading order of the slow-roll approximation. This is true both in the case for which this field is a test one and inflation is driven by another field, and the case for which the field plays the role of inflaton itself. In the latter case, in order to calculate the average of the mean square of the gauge-invariant inflaton fluctuation, the logarithm of the scale factor $a$ has to be used as the time variable in the Fokker-Planck equation in the stochastic approach. The implications of particle production during inflation for the second stage of inflation and for the moduli problem are also discussed. The case of a massless self-interacting test scalar field in a de Sitter background with a zero initial renormalized mean square is also considered in order to show how the stochastic approach can easily produce results corresponding to diagrams with an arbitrary number of scalar field loops in the field-theoretical approach (explicit results up to 4 loops inclusive are presented).
We study a particular nonlinear dispersion relation $ω_p(k_p)$ -- a series expansion in the physical wavenumber $k_p$ -- for modeling first-order corrections in the equation of motion of a test scalar field in a de Sitter spacetime from trans-Planckian physics in cosmology. Using both a numerical approach and a semianalytical one, we show that the WKB approximation previously adopted in the literature should be used with caution, since it holds only when the comoving wavenumber $k\gg aH$. We determine the amplitude and behavior of the corrections on the power spectrum for this test field. Furthermore, we consider also a more realistic model of inflation, the power-law model, using only a numerical approach to determine the corrections on the power spectrum.