Maurizio Gasperini

The Pre-Big Bang Scenario in String Cosmology

I review various aspects of the pre-big-bang scenario and of its main open problems, with emphasis on the role played by the dilaton. Since the dilaton is a compelling consequence of string theory, tests of this scenario are direct tests of string theory and also, more generally, of Planck scale physics.

Pre - big bang in string cosmology

The duality-type symmetries of string cosmology naturally lead us to expect a pre-big-bang phase of accelerated evolution as the dual counterpart of the decelerating expansion era of standard cosmology. Several properties of this scenario are discussed, including the possibility that it avoids the initial singularity and that it provides a large amount of inflation. We also discuss how possible tracks of the pre-big-bang era may be looked for directly in the spectral and ”squeezing” properties of relic gravitons and, indirectly, in the distorsion they induce on the cosmic microwave background.

Primordial magnetic fields from string cosmology

Sufficiently large seeds for generating the observed (inter)galactic magnetic fields emerge naturally in string cosmology from the amplification of electromagnetic vacuum fluctuations due to a dynamical dilaton background. The success of the mechanism depends crucially on two features of the so-called pre-big-bang scenario, an early epoch of dilaton-driven inflation at very small coupling, and a sufficiently long intermediate s era preceding the standard radiation-dominated evolution.

Relic Gravitational Waves from String Cosmology

A large class of string-cosmology backgrounds leads to a spectrum of relic stochastic gravitational waves, strongly tilted towards high frequencies, and characterized by two basic parameters of the cosmological model. We estimate the required sensitivity for detection of the predicted gravitational radiation and show that a region of our parameter space is within reach for some of the planned gravitational-wave detectors.

Dilaton production in string cosmology.

We consider the coupled evolution of density, (scalar) metric and dilaton perturbations in the transition from a “stringy” phase of growing curvature and gravitational coupling to the standard radiation-dominated cosmology. We show that dilaton production, with a spectrum tilted towards large frequencies, emerges as a general property of this scenario. We discuss the frame-independence of the dilaton spectrum and of the inflationary properties of the metric background by using, as model of source, a pressureless gas of weakly interacting strings, which is shown to provide an approximate but consistent solution to the full system of background equations and string equations of motion. We combine various cosmological bounds on a growing dilaton spectrum with the bound on the dilaton mass obtained from tests of the equivalence principle, and we find allowed windows compatible with a universe presently dominated by a relic background of dilatonic dark matter.

Average and dispersion of the luminosity-redshift relation in the concordance model

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.

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 Ω(Λ)(z) typically lying in the few-percent range.

Self-sustained inflation and dimensional reduction from fundamental strings

Abstract In a previous paper we have shown that an ideal gas of fundamental strings is not able to sustain, by itself, a phase of isotropic inflation of the Universe. We show here that fundamental strings can sustain, instead, a phase of anisotropic inflation accompanied by the contraction of a sufficient number of internal dimensions. The conditions to be met for the existence of such a solution to the Einstein and string equations are derived, and the possibility of a successful resolution of the standard cosmological problems in the context of this model is discussed.

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 geodesic-deviation equation, and thus to derive an exact expression for the Jacobi map JAB(s,o) connecting a generic source s to a geodesic observer o in a generic space time. In this gauge JAB 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 JAB 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.

Gauge invariant averages for the cosmological backreaction

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.