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We discuss a recently proposed fit of the 15-year data set obtained from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) in terms of a relic stochastic background of primordial gravitons, produced in the context of the string cosmology pre-big bang scenario. We show that such interpretation cannot be reconciled with a phenomenologically viable minimal version of such scenario, while it can be allowed if one considers an equally viable but generalised, non-minimal version of pre-big bang evolution. Maintaining the $S$-duality symmetry throughout the high-curvature string phase is possible although somewhat disfavoured. The implications of this non-minimal scenario for the power spectrum of curvature perturbations are also briefly discussed., Comment: 19 pages, 3 figures

We first make more precise a recent "Hamiltonian" reformulation of the Hohm-Zwiebach approach to the tree-level, $O(d,d)$-invariant string cosmology equations at all orders in the $\alpha'$ expansion, and recall how it allows to give a simple characterization of a large class of cosmological scenarios connecting, through a non-singular bounce, two duality-related perturbative solutions at early and late times. We then discuss the effects of adding to the action a non-perturbative, $O(d,d)$-breaking, dilaton potential $V(\phi)$. The resulting cosmological solutions, assumed to approach at early times the perturbative string vacuum (with vanishing curvature and string coupling), can stabilize the dilaton at late times and simultaneously approach either a matter-dominated FLRW cosmology or a de-Sitter-like inflationary phase, depending on initial conditions and on the properties of $V(\phi)$ at moderate-coupling. We also identify a general mechanism for generating isotropic late-time attractors from a large basin of anisotropic initial conditions., Comment: 30 pages, 13 figures

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., Comment: 7 pages, no figures. Published in the Special Issue on "Universe: Feature Papers 2023 -- Cosmology", edited by K. Bamba (Universe, MDPI, 2023). Available at: https://www.mdpi.com/2218-1997/9/7/327

The linearized dynamical equation for metric perturbations in a fully general, non-vacuum, background geometry is obtained from the Hamilton variational principle applied to the action up to second order. We specialize our results to the case of traceless and transverse metric fluctuations, and we discuss how the intrinsic properties of the matter stress tensor can affect (and modify) the process of gravity wave propagation even in most conventional geometric scenarios, like (for instance) those described by a FLRW metric background. We provide explicit examples for fluid, scalar field and electromagnetic field sources., Comment: 17 pages, no figures

We compute the modified friction coefficient controlling the propagation of tensor metric perturbations in the context of a generalized cosmological scenario based on a theory of gravity with quadratic curvature corrections. In such a context we discuss the differences between gravitational and electromagnetic luminosity distance, as well as the differences with the standard results based on the Einstein equations. We present numerical estimates of the modified luminosity distance on the cosmic redshift scale typical of Supernovae and standard sirens., Comment: 21 pages, 4 figures, published in General Relativity and Gravitation

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., Comment: 6 pages, 2 figures, Typos corrected, clarifications and a reference added. Version accepted for publication in Physics Letter B

We investigate the electrodynamic in a Bianchi type I cosmological model. This scenario reveals the possibility that photons, during their traveling, can make quantum interference. This effect is only due to the presence of two different axes of expansion in the cosmic evolution. In other word, it is possible to conclude that a purely metrical - or, equivalently, gravitational - phenomenon gives rise up to a quantum effect that manifests itself in the light propagation., Comment: 5 pages, 1 figure, accepted for publication in International Journal of Theoretical Physics

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 JCAP

In this paper we introduce a LTB-Bianchi I (plane symmetric) model of Universe. We study and solve Einstein field equations. We investigate the effects of such model of Universe in particular these results are important in understanding the effect of the combined presence of an inhomogeneous and anisotropic Universe. The observational magnitude-redshift data deviated from UNION 2 catalog has been analyzed in the framework of this LTB-anisotropic Universe and the fit has been achieved without the inclusion of any dark energy., Comment: 9 pages, 1 figure. Accepted for pubblication on Physical Review D

In this article we analyze the electrodynamics in curved space-time in LTB metric. We calculate the most general scale factor in this inhomogeneous Universe. We also study the presence of electromagnetic field bubbles in the Universe., Comment: 9 pages, Accepted for publication in the EPJ C

In the present paper we consider $f(R)$ gravity theories in the metric approach and we derive the equations of motion, focusing also on the boundary conditions. In such a way we apply the general equations to a first order perturbation expansion of the Lagrangian. We present a model able to fit supernovae data without introducing dark energy., Comment: 10 pages, 1 figure

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 JCAP

The beginning of the cosmological phase bearing the direct kinematic imprints of supernovae dimming may significantly vary within different models of late-time cosmology, even if such models are able to fit present SNe data at a comparable level of statistical accuracy. This effect -- useful in principle to discriminate among different physical interpretations of the luminosity-redshift relation -- is illustrated here with a pedagogical example based on the LTB geometry., Comment: 11 pages, 6 figures. To appear in Class. Quantum Grav