Cosmology from string theory

We explore the cosmological content of Salam-Sezgin six-dimensional supergravity, and find a solution to the field equations in qualitative agreement with observation of distant supernovae, primordial nucleosynthesis abundances, and recent measurements of the cosmic microwave background. The carrier of the acceleration in the present de Sitter epoch is a quintessence field slowly rolling down its exponential potential. Intrinsic to this model is a second modulus which is automatically stabilized and acts as a source of cold dark matter, with a mass proportional to an exponential function of the quintessence field (hence realizing varying mass particle models within a string context). However, any attempt to saturate the present cold dark matter component in this manner leads to unacceptable deviations from cosmological data—a numerical study reveals that this source can account for up to about 7% of the total cold dark matter budget. We also show that (1) the model will support a de Sitter energy in agreement with observation at the expense of a miniscule breaking of supersymmetry in the compact space; (2) variations in the fine structure constant are controlled by the stabilized modulus and are negligible; (3) “fifth” forces are carried by the stabilized modulus and are short range; (4) the long time behavior of the model in four dimensions is that of a Robertson-Walker universe with a constant expansion rate $(w=-1/3)$. Finally, we present a string theory background by lifting our six-dimensional cosmological solution to ten dimensions.

Figure 1

The upper panel shows the evolution of $Y$ as a function of $u$. Today corresponds to $z=0$ and for primordial nucleosynthesis $z\approx {10}^{10}$. We set the initial conditions $Y(-30)=0$ and $Y^{\prime }(-30)=0.08$; we take $A:B:C=11:0.3:0.1$. The second panel shows the evolution of ${\Omega }_Y$ (solid line), ${\Omega }_{\mathrm{mat}}$ (dot-dashed line), and ${\Omega }_{\mathrm{rad}}$ (dashed line) superposed over experimental best fits from SDSS and WMAP observations [13, 14]. The curves are not actual fits to the experimental data but are based on the particular choice of the $Y$ evolution shown in the upper panel, which provides eyeball agreement with existing astrophysical observations. The lower panel shows the evolution of the equation of state $w_Y$ superposed over the best fits to $\mathrm{WMAP}+\mathrm{SDSS}$ data sets and $\mathrm{WMAP}+\mathrm{SNGold}$ [14]. The solution of the field equations is consistent with the requirement from primordial nucleosynthesis, ${\Omega }_Y<0.045$ (90% CL) [12], it also shows the established radiation and matter dominated epochs, and at the end shows an accelerated dS era.