Kantowski-Sachs String Cosmologies

We present new exact solutions of the low-energy-effective-action string equations with both dilaton $\phi$ and axion $H$ fields non-zero. The background universe is of Kantowski-Sachs type. We consider the possibility of a pseudoscalar axion field $h$ ($H=e^\phi (dh)^{*}$) that can be either time or space dependent. The case of time-dependent $h$ reduces to that of a stiff perfect-fluid cosmology. For space-dependent $h$ there is just one non-zero time-space-space component of the axion field $H$, and this corresponds to a distinguished direction in space which prevents the models from isotropising. Also, in the latter case, both the axion field $H$ and its tensor potential $B$ ($H=dB$) are dependent on time and space yet the energy-momentum tensor remains time-dependent as required by the homogeneity of the cosmological model.Comment: 23 pages, REVTEX, 6 figures available on reques

Spatially Homogeneous String Cosmologies

We determine the most general form of the antisymmetric $H$-field tensor derived from a purely time-dependent potential that is admitted by all possible spatially homogeneous cosmological models in 3+1-dimensional low-energy bosonic string theory. The maximum number of components of the $H$ field that are left arbitrary is found for each homogeneous cosmology defined by the Bianchi group classification. The relative generality of these string cosmologies is found by counting the number of independent pieces of Cauchy data needed to specify the general solution of Einstein's equations. The hierarchy of generality differs significantly from that characteristic of vacuum and perfect-fluid cosmologies. The degree of generality of homogeneous string cosmologies is compared to that of the generic inhomogenous solutions of the string field equations.Comment: 16 pages, Latex, assumptions clarified, calculations unchanged, published in Phys. Rev.

Is there chaos in string cosmology?

Bianchi type IX, 'Mixmaster' universes are investigated in low-energy-effective-action string cosmology. We show that, unlike in general relativity, there is no chaos in these string cosmologies for the case of the tree-level action. The characteristic Mixmaster evolution through a series of Kasner epochs is studied in detail. In the Einstein frame an infinite sequence of chaotic oscillations of the scale factors on approach to the initial singularity is impossible, as it was in general relativistic Mixmaster universes in the presence of a massless scalar field. A finite sequence of oscillations of the scale factors described by approximate Kasner metrics is possible, but it always ceases when all expansion rates become positive. In the string frame the evolution through Kasner epochs changes to a new form which reflects the duality symmetry of the theory. Again, we show that chaotic oscillations must end after a finite time. The need for duality symmetry appears to be incompatible with the presence of chaotic behaviour as $t \to 0$. We also obtain our results using the Hamiltonian qualitative cosmological picture for Mixmaster models. We also prove that a time-independent pseudoscalar axion field $h$ is not admitted by the Bianchi IX geometry.Comment: 49 pages, Revtex 3.0, 4 postscript figures, typos in references corrected, one reference adde