String Kaluza-Klein cosmologies with RR-fields

TL;DR

The paper constructs 4D FRW cosmologies by reducing a 5D black hole arising from a transformed 5-brane in type IIB string theory. RR-fields are generated via an $SL(2,\mathbb{R})$ transformation and carried through a sequence of toroidal and temporal compactifications, yielding FRW spacetimes with nontrivial RR content. The RR-fields qualitatively affect the dilaton dynamics and the early expansion, enhancing but not producing viable inflation across most parameter ranges; the extremal limit exhibits delicate behavior and often retains singular features in the string frame. Overall, RR fields enrich the cosmological model space but do not solve the standard inflationary challenges in this setup, while highlighting the interplay between duality, compactification, and cosmology in string theory.

Abstract

We construct 4-dimensional cosmological FRW--models by compactifying a black 5-brane solution of type IIB supergravity, which carries both magnetic NS-NS-charge and RR-charge. The influence of nontrivial RR-fields on the dynamics of the cosmological models is investigated.

Figures (2)

• Figure 1: $\zeta\equiv\ddot{a}/a=\dot{H}\, + H^{2}$ for several SO(2)-rotations. (Rotation angles in degrees, 0 means zero RR-charge, 90 means zero NS-NS charge.) The spatial section was assumed to be flat ($k=0$) and the time parameters were chosen to be $t_{-}=1$ and $t_{+}=4$.
• Figure 2: The extremal limit for pure NS-NS-charge (2a) and the extremal limits for pure RR-charge for $k=+1$ (2b), $k=-1$ (2c) and $k=0$ (2d).