String cosmology aims at providing a reliable description of the very early Universe in the regime where standard-model physics is no longer appropriate, and where we can safely apply the basic ingredients of superstring models such as dilatonic and axionic forces, duality symmetries, winding modes, limiting sizes and curvatures, higher-dimensional interactions among elementary extended object. The sought target is that of resolving (or at least alleviating) the big problems of standard and inflationary cosmology like the spacetime singularity, the physics of the trans-Planckian regime, the initial condition for inflation, and so on.

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 to describe in an explicitly gauge invariant form the way classical or quantum inhomogeneities affect the average evolution of our Universe.

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.

The remarkable properties of the recently proposed geodesic light-cone (GLC) gauge allow to explicitly solve the geodesic-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.

Using a recently proposed gauge invariant formulation of light-cone averaging, together with adapted "geodesic light-cone" coordinates, we show how an "induced backreaction" effect emerges, in general, from correlated fluctuations in the luminosity distance and co-variant integration measure. Considering a realistic stochastic spectrum of inhomogeneities of primordial (inflationary) origin we find that both the induced backreaction on the luminosity-redshift relation and the dispersion are larger than naively expected. On the other hand the former, at least to leading order and in the linear perturbative regime, cannot account by itself for the observed effects of dark energy at large-redshifts. A full second-order calculation, or even better a reliable estimate of contributions from the non-linear regime, appears to be necessary before firm conclusions on the correct interpretation of the data can be drawn.

If the observed dark-energy density $ ho_\Lambda$ is interpreted as the net contribution of the energy density of the vacuum, $ ho_\Lambda \equiv ho_V \sim M_V^4$, and the corresponding vacuum length scale $\lambda_V = M_V^-1$ as the cutoff scale controlling the low-energy, effective field-theory limit of gravity, it follows that the conventional cosmological scenario based on the effective gravitational equations may be valid only up to the Tev energy scale. Such a possibility would be strongly disfavored by the existence of a relic background of primordial gravitational radiation of intensity compatible with present (or near future) experimental sensitivities.

The beginning of the cosmological phase bearing the direct kinematic imprints of supernovae (SNe) 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 Lemaˆıtre–Tolman–Bondi geometry.

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.

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.

We discuss the possible influence of a cosmic magnetic field on the macroscopic quantum tunneling process associated, in a cosmological context, to the decay of the "false vacuum." We find a close analogy with the effects of an external magnetic field applied to a Josephson junction in the context of low-temperature/high-temperature superconducting devices.

We discuss the properties of the gas of primordial “stringy” black holes possibly formed in the high-curvature phase preceding the bouncing transition to the phase of standard cosmological evolution. We show that the regime dominated by such a string-hole gas can be consistently described by explicit solutions of the string effective action including first-order alpha' corrections. We present a phase space analysis of the stability of such solutions comparing the results obtained from different actions and including the possibility of O(d,d)-symmetric configurations.

Conventional wisdom, based on kinematic (flat-space) intuition, tell us that a static twin is aging faster than his traveling twin brother. However, such a situation could be exactly inverted if the two twins are embedded in an external gravitational field, and if the (dynamical) distortion of the space-time geometry, due to gravity, is strong enough to compensate the kinematic effect of the relative twin motion.