Pre-big bang bubbles from the gravitational instability of generic string vacua

TL;DR

This work reframes early-un-universe cosmology by positing asymptotic past triviality: a generic bath of gravitational and dilatonic waves in a tree-level string framework can gravitationally collapse into multiple pre-big bang bubbles, each becoming a local, dilaton-driven inflationary patch in the string frame. The authors derive a perturbative strength criterion based on the variance of the incoming news function to predict collapse and illustrate transitions to cosmological-like regimes with detailed spherically symmetric Einstein-dilaton models, Kasner-like singularities, and exact solutions. They connect weak-field data to strong-field cosmology, explore the structure of singularities via Kasner exponents, and use Bayesian reasoning to discuss fine-tuning and naturalness of initial conditions, arguing that selection effects can favor universes like ours. The framework yields potential observational signatures through anisotropies imprinted on the big-bang hypersurface and provides a structured path for future mathematical and phenomenological investigations into pre-big bang cosmology and exit dynamics.

Abstract

We formulate the basic postulate of pre-big bang cosmology as one of ``asymptotic past triviality'', by which we mean that the initial state is a generic perturbative solution of the tree-level low-energy effective action. Such a past-trivial ``string vacuum'' is made of an arbitrary ensemble of incoming gravitational and dilatonic waves, and is generically prone to gravitational instability, leading to the possible formation of many black holes hiding singular space-like hypersurfaces. Each such singular space-like hypersurface of gravitational collapse becomes, in the string-frame metric, the usual big-bang t=0 hypersurface, i.e. the place of birth of a baby Friedmann universe after a period of dilaton-driven inflation. Specializing to the spherically-symmetric case, we review and reinterpret previous work on the subject, and propose a simple, scale-invariant criterion for collapse/inflation in terms of asymptotic data at past null infinity. Those data should determine whether, when, and where collapse/inflation occurs, and, when it does, fix its characteristics, including anisotropies on the big bang hypersurface whose imprint could have survived till now. Using Bayesian probability concepts, we finally attempt to answer some fine-tuning objections recently moved to the pre-big bang scenario.

Figures (5)

• Figure 1: Symbolic sketch of the birth of many pre-big bang bubbles from the gravitational instability of a generic string vacuum made of a stochastic bath of classical incoming gravitational and dilatonic waves. Each local Einstein-frame collapse of sufficiently strong waves forms a cosmological-like space-like singularity hidden behind a black hole. The parts of those classical singularities where the string coupling grows inflate, when viewed in the string frame, and generate ballooning patches of space (here schematized as the stretching of one spatial dimension) which are expected to evolve into many separate quasi-closed Friedmann hot universes.
• Figure 2: A representation of pre-big bang bubbles similar to that of Fig. \ref{['fig1']}, but in 2+1 dimensions. The different horizontal planes represent different instants in the evolution from the asymptotic trivial past to the Friedmann phase. Two inflationary bubbles characterized by two different initial horizon sizes (both large in string units) are shown to lead to Universes of very different homogeneity scale at the time at which the Hubble radius reaches string-scale values ($\ell_s = {\cal O}(10^{-32}\, {\rm cm})$).
• Figure 3: Schematic representation of the space-time generated by the collapse of a spherically symmetric pulse of dilatonic waves. An incoming pulse of scalar news $N(v)$, which grows by ${\cal O}(1)$ on an advanced-time scale $\ell_i$, collapses to a space-like singularity ${\cal B}$ after having formed an apparent horizon ${\cal A}$ hidden behind the event horizon ${\cal H}$. In the vicinity of ${\cal A}$ and ${\cal H}$, there is an abrupt transition between a weak-field region (dark shading) where the perturbation series (\ref{['eqn4.1a']})--(\ref{['eqn4.1c']}) holds, and a strong-field one (light shading) where the cosmological-like expansion (\ref{['appen1']})--(\ref{['appen3']}) holds.
• Figure 4: Geometric representation of the Einstein-frame Kasner exponents $(\lambda_1, \lambda_2, \lambda_3; \gamma)$ of Einstein-dilaton cosmological singularities. The three $\lambda$'s, such that $\sum_a \lambda_a =1$ are the orthogonal distances to the three sides of an equilateral triangle. The constraint $\gamma = \pm \sqrt{2}\, \sqrt{1 - \sum_a \lambda^2_a}$ restricts the representative $\Lambda$ of $\lambda_a$ to stay on a two-sided disk circumscribed around the triangle. The pure-Einstein cases ($\gamma = 0$) correspond to the circumscribing circle. In the spherically symmetric case ($\lambda_2 = \lambda_3$), $\Lambda$ runs over a bissectrix of the triangle. The basic parameter $\alpha$ of Eqs. (\ref{['phi']}) and (\ref{['lam']}) runs over a full real line (shown folded on the right of the figure ) and is mapped to the bissectrix via horizontal lines.
• Figure 5: Geometrical representation of the link between the two-sided disk of Fig. \ref{['fig4']} on which the Einstein-frame Kasner exponents $\lambda_a$ live, and the sphere, $\sum_a \alpha^2_a=1$, on which the string-frame Kasner exponents $(\alpha_1, \alpha_2, \alpha_3)$ live. The map $\alpha_a \rightarrow \lambda_a$ is a stereographic projection, from the center $(\alpha_a^c)= (1,1,1)$. The upper side of the disk comes from the projection of the polar cap $\sigma \equiv (\sum_a \alpha_a) -1 > 0$ located on the same side as $\alpha^c$, while the lower side of the disk comes from projection of the antipolar cap $\sigma < 0$. The points $\alpha_+$ on the polar cap, and $\alpha_-$ on the antipolar cap, are both projected on the same point $\Lambda$ of the disk. The tangents to the sphere issued from $\alpha^c$ touch the sphere along the circle limiting the disk (on which $\sigma=0$).