String cosmology versus standard and inflationary cosmology

This paper presents a review of the basic, model-independent differences between the pre-big bang scenario, arising naturally in a string cosmology context, and the standard inflationary scenario. We use an unconventional approach in which the introduction of technical details is avoided as much as possible, trying to focus the reader's attention on the main conceptual aspects of both scenarios. The aim of the paper is not to conclude in favour either of one or of the other scenario, but to raise questions that are left to the reader's meditation. Warnings: the paper does not contain equations, and is not intended as a complete review of all aspects of string cosmology.Comment: 22 pages, Latex (IOP Style), three figures included using epsfig. To appear in Class. Quantum Grav. (Topical Review Section). Two misprints correcte

Inflation and initial conditions in the pre-big bang scenario

The pre-big bang scenario describes the evolution of the Universe from an initial state approaching the flat, cold, empty, string perturbative vacuum. The choice of such an initial state is suggested by the present state of our Universe if we accept that the cosmological evolution is (at least partially) duality-symmetric. Recently, the initial conditions of the pre-big bang scenario have been criticized as they introduce large dimensionless parameters allowing the Universe to be "exponentially large from the very beginning". We agree that a set of initial parameters (such as the initial homogeneity scale, the initial entropy) larger than those determined by the initial horizon scale, H^{-1}, would be somewhat unnatural to start with. However, in the pre-big bang scenario, the initial parameters are all bounded by the size of the initial horizon. The basic question thus becomes: is a maximal homogeneity scale of order H^{-1} necessarily unnatural if the initial curvature is small and, consequently, H^{-1} is very large in Planck (or string) units? In the impossibility of experimental information one could exclude "a priori", for large horizons, the maximal homogeneity scale H^{-1} as a natural initial condition. In the pre-big bang scenario, however, pre-Planckian initial conditions are not necessarily washed out by inflation and are accessible (in principle) to observational tests, so that their naturalness could be also analyzed with a Bayesan approach, in terms of "a posteriori" probabilities.Comment: 4 pages, Latex, one figure. Many references added. The text has been improved in many points. To appear in Phys. Rev.

Homogeneous magnetic fields in fully anisotropic string cosmological backgrounds

We present new solutions of the string cosmological effective action in the presence of a homogeneous Maxwell field with pure magnetic component. Exact solutions are derived in the case of space-independent dilaton and vanishing torsion background. In our examples the four dimensional metric is either of Bianchi-type III and VI$_{-1}$ or Kantowski-Sachs.Comment: 4 page

Particle production in string cosmology models

We compute spectra of particles produced during a dilaton-driven kinetic inflation phase within string cosmology models. The resulting spectra depend on the parameters of the model and on the type of particle and are quite varied, some increasing and some decreasing with frequency. We use an approximation scheme in which all spectra can be expressed in a nice symmetric form, perhaps hinting at a deeper symmetry of the underlying physics. Our results may serve as a starting point for detailed studies of relic abundances, dark matter candidates, and possible sources of large scale anisotropy.Comment: 20 pages, no figures, latex, RevTe

Electromagnetic Origin of the CMB Anisotropy in String Cosmology

In the inflationary scenarios suggested by string theory, the vacuum fluctuations of the electromagnetic field can be amplified by the time-evolution of the dilaton background, and can grow large enough to explain both the origin of the cosmic magnetic fields and of the observed CMB anisotropy. The normalization of the perturbation spectrum is fixed, and implies a relation between the perturbation amplitude at the COBE scale and the spectral index $n$. Working within a generic two-parameter family of backgrounds, a large scale anisotropy $\Delta T/T\simeq 10^{-5}$ is found to correspond to a spectral index in the range $n\simeq 1.11 - 1.17$.Comment: 11 pages, LATE

Fully Anisotropic String Cosmologies, Maxwell Fields and Primordial Shear

We present a class of exact cosmological solutions of the low energy string effective action in the presence of a homogeneous magnetic fields. We discuss the physical properties of the obtained (fully anisotropic) cosmologies paying particular attention to their vacuum limit and to the possible isotropization mechanisms. We argue that quadratic curvature corrections are able to isotropize fully anisotropic solutions whose scale factors describe accelerated expansion. Moreover, the degree of isotropization grows with the duration of the string phase. We follow the fate of the shear parameter in a decelerated phase where, dilaton, magnetic fields and radiation fluid are simultaneously present. In the absence of any magnetic field a long string phase immediately followed by radiation is able to erase large anisotropies. Conversely, if a short string phase is followed by a long dilaton dominated phase the anisotropies can be present, in principle, also at later times. The presence of magnetic seeds after the end of the string phase can induce further anisotropies which can be studied within the formalism reported in this paper.Comment: 19 pages in Revtex style, 14 Encapsulated figure

Kantowski-Sachs String Cosmologies

We present new exact solutions of the low-energy-effective-action string equations with both dilaton $\phi$ and axion $H$ fields non-zero. The background universe is of Kantowski-Sachs type. We consider the possibility of a pseudoscalar axion field $h$ ($H=e^\phi (dh)^{*}$) that can be either time or space dependent. The case of time-dependent $h$ reduces to that of a stiff perfect-fluid cosmology. For space-dependent $h$ there is just one non-zero time-space-space component of the axion field $H$, and this corresponds to a distinguished direction in space which prevents the models from isotropising. Also, in the latter case, both the axion field $H$ and its tensor potential $B$ ($H=dB$) are dependent on time and space yet the energy-momentum tensor remains time-dependent as required by the homogeneity of the cosmological model.Comment: 23 pages, REVTEX, 6 figures available on reques

Constraints on pre-big bang models for seeding large-scale anisotropy by massive Kalb-Ramond axions

We discuss the conditions under which pre-big bang models can fit the observed large-scale anisotropy with a primordial spectrum of massive (Kalb--Ramond) axion fluctuations. The primordial spectrum must be sufficiently flat at low frequency and sufficiently steeper at high frequency. For a steep and/or long enough high-frequency branch of the spectrum the bounds imposed by COBE's normalization allow axion masses of the typical order for a Peccei--Quinn--Weinberg--Wilczek axion. We provide a particular example in which an appropriate axion spectrum is obtained from a class of backgrounds satisfying the low-energy string cosmology equations.Comment: 11 pages, revtex, two figures included using epsfig. An updated collection of papers on the pre-big bang scenario is available at http://www.to.infn.it/~gasperi

Duality in String Cosmology

Scale factor duality, a truncated form of time dependent T-duality, is a symmetry of string effective action in cosmological backgrounds interchanging small and large scale factors. The symmetry suggests a cosmological scenario ("pre-big-bang") in which two duality related branches, an inflationary branch and a decelerated branch are smoothly joined into one non-singular cosmology. The use of scale factor duality in the analysis of the higher derivative corrections to the effective action, and consequences for the nature of exit transition, between the inflationary and decelerated branches, are outlined. A new duality symmetry is obeyed by the lowest order equations for inhomogeneity perturbations which always exist on top of the homogeneous and isotropic background. In some cases it corresponds to a time dependent version of S-duality, interchanging weak and strong coupling and electric and magnetic degrees of freedom, and in most cases it corresponds to a time dependent mixture of both S-, and T-duality. The energy spectra obtained by using the new symmetry reproduce known results of produced particle spectra, and can provide a useful lower bound on particle production when our knowledge of the detailed dynamical history of the background is approximate or incomplete.Comment: 6 pages, no figures, latex2e using ltwol2e.sty. Based on talks at the 44'th annual meeting of the Israel Physical Society, Apr 8, 1998, Rehovot, Israel, and ICHEP98, 23-29 July, Vancouver, BC, Canada, and second conf. on Quantum Aspects of Gauge Theories, Supersymmetry and Unification, Sept 21-26, 1998, Corfu, Greece. To be published in the proceeding

Time Gauge Fixing and Hilbert Space in Quantum String Cosmology

Recently the low-energy effective string theory has been used by Gasperini and Veneziano to elaborate a very interesting scenario for the early history of the universe (``birth of the universe as quantum scattering''). Here we investigate the gauge fixing and the problem of the definition of a global time parameter for this model, and we obtain the positive norm Hilbert space of states.Comment: 13 pages, Plain TEX, no figure