Superstring Cosmology

TL;DR

The paper surveys how dualities in string/M-theory shape cosmology, from high-dimensional Kasner-type backgrounds to four-dimensional FRW and Bianchi universes. It develops a comprehensive framework based on toroidal compactifications, non-linear sigma-models, and SL(d,R)/SO(d) and O(d,d)/O(d) cosets to reveal S-, T-, and U-dualities as organizing principles. By deriving dual actions and exploiting symmetry-generated solutions, it connects NS-NS and RR sectors, axions, and moduli to inflationary scenarios like the pre-big bang and to brane interpretations within M-theory. The work highlights how dualities constrain cosmological dynamics, generate new solutions, and potentially yield observable imprints in perturbation spectra. Overall, it provides a cohesive, symmetry-driven roadmap for constructing and analyzing string cosmologies across dimensions and sectors.

Abstract

Aspects of superstring cosmology are reviewed with an emphasis on the cosmological implications of duality symmetries in the theory. The string effective actions are summarized and toroidal compactification to four dimensions reviewed. Global symmetries that arise in the compactification are discussed and the duality relationships between the string effective actions are then highlighted. Higher-dimensional Kasner cosmologies are presented and interpreted in both string and Einstein frames, and then given in dimensionally reduced forms. String cosmologies containing both non-trivial Neveu-Schwarz/Neveu-Schwarz and Ramond-Ramond fields are derived by employing the global symmetries of the effective actions. Anisotropic and inhomogeneous cosmologies in four-dimensions are also developed. The review concludes with a detailed analysis of the pre-big bang inflationary scenario. The generation of primordial spectra of cosmological perturbations in such a scenario is discussed. Possible future directions offered in the Horava-Witten theory are outlined.

Figures (15)

• Figure 1: String frame scale factor, $a$, as a function of conformal time, $\eta$, for flat $\kappa=0$ FRW cosmology in dilaton-vacuum solution in Eq. (\ref{['dila']}) with $\xi_*=0$ (dashed-line), $\xi_*=\pi$ (dotted line) and dilaton-axion solution in Eq. (\ref{['axia']}) with $r=\sqrt{3}$ (solid line). The $(+)$ and $(-)$ branches are defined in Section \ref{['Section9.1']}.
• Figure 2: Dilaton, $e^\varphi$, as a function of conformal time, $\eta$, for flat $\kappa=0$ FRW cosmology in dilaton-vacuum solution in Eq. (\ref{['dilphi']}) with $\xi_*=0$ (dashed-line), $\xi_*=\pi$ (dotted line) and dilaton-axion solution in Eq. (\ref{['axiphi']}) with $r=\sqrt{3}$ (solid line). The $(+)$ and $(-)$ branches are defined in Section \ref{['Section9.1']}.
• Figure 3: Hubble rate in the string frame, $H$, as a function of proper cosmic time, $t$, for flat $\kappa=0$ FRW cosmology in dilaton-vacuum solution in Eq. (\ref{['dila']}) with $\xi_*=0$ (dashed-line), $\xi_*=\pi$ (dotted line) and dilaton-axion solution in Eq. (\ref{['axia']}) with $r=\sqrt{3}$ (solid line). The $(+)$ and $(-)$ branches are defined in Section \ref{['Section9.1']}.
• Figure 4: String frame scale factor, $a$, as a function of conformal time, $\eta$, for closed $\kappa=+1$ FRW cosmology in dilaton-vacuum solution in Eq. (\ref{['dila']}) with $\xi_*=0$ (dashed-line), $\xi_*=\pi$ (dotted line) and dilaton-axion solution in Eq. (\ref{['axia']}) with $r=\sqrt{3}$ (solid line).
• Figure 5: Dilaton, $e^\varphi$, as a function of conformal time, $\eta$, for closed $\kappa=+1$ FRW cosmology in dilaton-vacuum solution in Eq. (\ref{['dilphi']}) with $\xi_*=0$ (dashed-line), $\xi_*=\pi$ (dotted line) and dilaton-axion solution in Eq. (\ref{['axiphi']}) with $r=\sqrt{3}$ (solid line).