String Theory and Pre-big bang Cosmology

TL;DR

This work argues that string theory naturally leads to a pre-big bang cosmology in which the Universe starts from a perturbative vacuum with vanishing curvature and coupling and evolves toward a high-curvature, high-$g_s$ phase that undergoes a bounce into standard cosmology. The approach relies on scale-factor duality and the dilaton’s dynamics, supplemented by higher-order string corrections to enable a smooth transition to the post-big bang era, thereby avoiding trans-Planckian issues and initial singularities. A key prediction is a blue spectrum for tensor perturbations with a high-frequency peak, while scalar perturbations can be generated by a curvaton mechanism via axion fluctuations, yielding a nearly scale-invariant curvature spectrum under suitable conditions. Observationally, a detectable high-frequency gravitational-wave background and specific CMB polarization signals would provide critical tests of the pre-big bang scenario and its string-theoretic underpinnings.

Abstract

In string theory, the traditional picture of a Universe that emerges from the inflation of a very small and highly curved space-time patch is a possibility, not a necessity: quite different initial conditions are possible, and not necessarily unlikely. In particular, the duality symmetries of string theory suggest scenarios in which the Universe starts inflating from an initial state characterized by very small curvature and interactions. Such a state, being gravitationally unstable, will evolve towards higher curvature and coupling, until string-size effects and loop corrections make the Universe "bounce" into a standard, decreasing-curvature regime. In such a context, the hot big bang of conventional cosmology is replaced by a "hot big bounce" in which the bouncing and heating mechanisms originate from the quantum production of particles in the high-curvature, large-coupling pre-bounce phase. Here we briefly summarize the main features of this inflationary scenario, proposed a quarter century ago. In its simplest version (where it represents an alternative and not a complement to standard slow-roll inflation) it can produce a viable spectrum of density perturbations, together with a tensor component characterized by a "blue" spectral index with a peak in the GHz frequency range. That means, phenomenologically, a very small contribution to a primordial B-mode in the CMB polarization, and the possibility of a large enough stochastic background of gravitational waves to be measurable by present or future gravitational wave detectors.

Figures (5)

• Figure 1: One-loop graph for a point particle (left) and a closed string (right). In the left picture the world-line of a physical point particles (solid curve) splits into a "world-loop" (dashed curve) representing a virtual particle-antiparticle pair generated by the quantum fluctuations of the vacuum. In the right picture, where the world-lines are replaced by cylindrical "world-sheet" surfaces, the same process is illustrated for the case of a closed string.
• Figure 2: Example of smooth transition between a phase of pre-big bang inflation and the standard radiation-dominated evolution. The figure gives a qualitative illustration of the evolution in time (from $-\infty$ to $+\infty$) of the string coupling parameter $g_s= \exp(\phi)$, of the spacetime curvature scale $H^2= \dot a^2/a^2$, of the effective energy density $\rho \exp(\phi)$ and pressure $p \exp(\phi)$ of the gravitational sources, and of the effective dilaton potential $V$. Note that the pre-big bang phase is characterized by growing curvature and negative pressure, the post-big bang phase by decreasing curvature and positive pressure.
• Figure 3: Example of pre-big bang evolution represented in the E-frame, where the scale factor $a_E$ is shrinking and the Hubble parameter $H_E$ is negative, unlike in the string-frame representation of Fig. \ref{['fig2']}. The figure also illustrates the evolution (with respect to the conformal time parameter $\eta$) of the E-frame energy density $\rho_E$ and of the string coupling parameter $g_s =\exp(\phi)$. The plots are obtained from Eq. (\ref{['14']}) with $a_0=0.8$, $\phi_0=0$, $\rho_0=1$, $\eta_0=1$.
• Figure 4: Comparison between the time evolution of the Hubble horizon $c/H$ (dashed lines) and of the scale factor $a(t)$ (solid curves) in the conventional inflationary scenario (left) and in models of pre-big bang inflation (right). For the pre-big bang phase we have plotted the evolution of both the expanding string-frame scale factor $a(t)$ and the contracting E-frame scale factor $a_E(t)$. The vertical axis is the time axis, and the shaded areas represent causally connected spatial sections of Hubble size $c/H$ at various epochs. The evolution from the end of inflation, $t_f$, to the present epoch, $t_0$, is the same in both cases. However, during inflation (i.e. from $t_i$ to $t_f$) the Hubble horizon is constant (or slightly increasing) in conventional models (left), while it is shrinking in pre-big bang models (right). As a consequence, the size of the initial inflationary patch may be very large (in string or Planck units) for a phase of pre-big bang inflation, but not larger than the horizon itself, as illustrated in the figure.
• Figure 5: The figure shows, on a logarithmic scale, the typical spectral energy density $\Omega_g h^2$ of a cosmic background of primordial gravitational waves produced in the context of $(a)$ minimal models of pre-big bang inflation (growing, or "blue", spectra) and $(b)$ standard models of slow-roll inflation (flat and decreasing, or "red", spectra). See 26 for technical details on the properties of these spectra. The figure also shows the maximal background intensity allowed by present data on the CMB polarization, and the planned sensitivities expected to be reached in the near future by Earth-based gravitational detector such as Advanced LIGO and by space interferometers such as LISA and BBO.