Quantum cosmology at finite temperature in superstring theory

 By

 Lihui LIU

 (10 septembre 2012)

 

Quantum cosmology at finite temperature in superstring theory.pdf

Summary

This thesis is dedicated to the study of cosmology induced by superstring theory at finite temperature.
The thermal string scenario has the aim of establishing a unified framework for describing
cosmological evolution, with gravity quantized, and matter contents derived from first principles.
The cosmological solutions of string theory are determined by the low energy effective action.
The latter only accommodates static solutions at tree level, while nontrivial cosmological evolution is obtained when corrections from thermal and quantum effects are taken into account.
We restrict our attention to the weak coupling regime. In such cases the thermal and quantum effects back-react on the initially flat static spacetime background through an effective potential
computed up to one loop level, which is a Colemann-Weinberg effective potential. It turns out that this setup describes a universe filled with an ideal string gas in quasi-static evolution, and the Colemann-Weinberg effective potential is just the Helmholtz free energy density of the string gas.
The resulting cosmological evolution can be divided into three stages characterized by the
scale of temperature. They are namely:
1) the Hagedorn era where the temperature is of order
string scale, and the free energy density diverges due to the exponential growth of degeneracies with mass level;
2) the standard cosmology era where the temperature goes below the electroweak
phase transition scale, and the nucleosynthesis takes place giving birth to the matter contents of the current universe;
3) the intermediate era which is between the above two, where the spacetime
metric evolves in the pattern of a radiation-dominated universe (radiation-like), moduli can be stabilized, and the hierarchy for supersymmetry breaking scale is generated.
The issue of moduli stabilization in the intermediate era is intensively studied. At certain
points in the moduli space, extra massless states emerge, and the Helmholtz free energy density, or the effective potential, develops local minima. The latter provide moduli attractors. The depth of the local minima is time dependent, which induces scalar masses reducing with cosmological evolution. This makes the coherent scalar oscillations dilute before nucleosynthesis, and the cosmological moduli problem is avoided. Specific models are studied, where attention is given to moduli stabilization by non-perturbative effects.

We first studied cosmology induced by a maximally supersymmetric heterotic string gas. The free energy density reaches local minima where perturbative string states of nonzero winding and momentum numbers become massless, giving rise to non-Abelian gauge symmetry enhancement.
This can stabilize all heterotic moduli but the dilaton, i.e. the internal metric, the internal B-field and Wilson lines, among which the internal metric components are attracted to the string scale.
Through the type I/heterotic string S-duality this mechanism can be mapped to the type         I side.
In particular it is found that the dual type I moduli are stabilized by either non perturbative
BPS D-string states or by perturbative open string states, where the internal geometric moduli are stabilized at the scale , with  the type I string coupling in ten dimensions. Enhanced gauge symmetries at moduli attractors on the heterotic side are also sent to the type I dual side.
Although these enhancements of type I gauge symmetry are non-perturbative effects, they should be treated on equal footing with the gauge group induced by perturbative states.
The second case is the cosmology induced by a gas of type II string compactified on Calabi-Yau three-folds. Moduli attractors are found to be at the loci where some 2-spheres or 3-spheres in the Calabi-Yau space shrink to zero size leading the Calabi-Yau space to a singular configuration.
These can be either conifold loci or some non Abelian gauge symmetry loci. In type IIA description, in the case of shrinking 2-spheres, the extra massless states arise from BPS D2-branes wrapping
these 2-cycles. In case of shrinking 3-spheres, the extra massless states are not yet identified, but their existence can be inferred from the change in moduli space dimension, and further confirmed by analyzing the low energy effective action. This mechanism can lift the whole Kähler moduli space, while in the complex structure moduli space, the flat directions lifted are those associated to the shrinking 3-spheres that can be blown up into 2-spheres. The universal hypermultiplet moduli, which contains the dilaton, cannot be lifted by this mechanism. An explicit example is analyzed where all Kähler moduli are stabilized at the intersection of a conifold locus and a non-Abelian locus. By virtue of the type II/heterotic string duality, the moduli in the dual heterotic string are stabilized, where remarkably, the axio-dilaton modulus is stabilized at order 1 in the unit of string length.