Late-time Cosmology with String Gases Scott Watson Department of Physics Brown University watson@het.brown.edu

Challenges for Cosmology Dark Energy / Cosmological Constant Dark Matter Viable Inflation model (or alternative) Singularities String Theory? Extra Dimensions (3+1+6) Massless Moduli (a.k.a “Determining the Landscape”)

Why Three Large Dimensions? Brandenberger-Vafa Scenario + oscillators The mass spectrum of the string: Winding Modes (Prevent Expansion) Momentum Modes (Prevent Contraction) Strings intersect in at most 3 spatial dimensions!!!

Too Much Symmetry? O(d,d) Symmetry Action for massless modes of NS sector O(d,d) Symmetry String Spectrum (Quantum Considerations) O(d)xO(d) Symmetry

Moduli Space of Toriodal Compactification d2 moduli (metric and NS flux) No potentials in low energy theory We want to generate potential using massive string modes.

String Gas Cosmology Generate potential for massless string modes by including backreaction of massive string modes. (Brandenberger, Vafa) and (Tseytlin, Vafa) All spatial dimensions taken toriodal (For generalization see hep-th/0204099), Action for massless modes of NS sector with gas of string modes, Winding modes: Momentum modes: Pressure Vanishes at Self-dual Radius

Stabilization at the self dual radius Assuming that the 6 compactified dimensions begin at the self-dual point, we find that they remain frozen for all times as the other 3 dimensions grow large. Only constraint on dilaton is that gs~small Our result holds for all initial values of f given this constraint. 3d expanding 6d stabilized

Anisotropy and dilaton play vital role in stabilization

Late-time Cosmology Scale of dimensions 3+1 growing large d compact

Successes of String Gas Approach Explanation for origin of 3+1+6 universe Isotropization is natural result of dynamics (hep-th/0207168, Brandenberger and GSW) 6d Stabilized near self dual radius (hep-th/0307044 , Brandenberger and GSW) Stable to linear perturbations ( long wavelength hep-th/0312097, Brandenberger and GSW ) ( small wavelength hep-th/0402015, GSW ) Possibility of Cold Dark Matter from remnant strings in the extra dimensions (hep-th/0402225, Gubser and Peebles) String Gas approach can be extended to late time cosmology (hep-th/0403075 , Battefeld and GSW)

Upshot Higher dimensional perspective is different. (e.g. pressure and anisotropy are missing?) Non-perturbative physics important NOT just massless modes.

String Higgs Effect At special places in the landscape massive states become massless and should be included in low energy effective action Generate “trapping” potential by their coupling to the other massless states (Should include ALL massless states hep-th/9401139 )

Worldsheet Perspective Space-time perspective Worldsheet perspective Demand couplings preserve conformal invariance

Vectors from compactification Low energy degrees of freedom, Compactification on S1 Vectors from compactification Radius of extra dimensions (Radion) Low energy degrees of freedom, Chiral Gauge Theory Low energy states do not carry winding and momentum charge Exact theory given by Dilaton-Gravity-U(1) Chiral Gauge theory Bad news for BGC,

Enhanced Gauge Symmetry At self dual radius there are additional massless states Four vectors Eight Scalars Additional states carry winding and momentum charge

String Higgs Effect Self dual radius is point of enhanced gauge symmetry (ESP) Exactly marginal deformation Near self dual radius theory given by dilaton-gravity coupled to Yang-Mills This theory describes EXACTLY the dynamics E.g. T-duality is gauge rotation about an axis of one of the SU(2)’s.

String Higgs Effect in Cosmology (hep-th/0404177, GSW) For generic location in the moduli space low energy theory given by dilaton-gravity coupled to chiral gauge theory As we approach ESP should include additional states Time dependent mass for additional states

String Higgs Effect in Cosmology Particle Production near ESP States easy to produce at ESP. Additional states lead to backreaction on sigma

Moduli Trapping This is another realization of Moduli Trapping (hep-th/0403001, Kofman, et. al.) Figure from hep-th/0403001

Comments and Conclusions Dimensionality as result of string dynamics Cosmology and non-perturbative physics may offer solution to string theory landscape. Many applications of moduli trapping (Reheating, Dark Matter, Cyclic/Ekpyrotic, Brane Inflation models, etc…) Interesting alternative to LCDM (Gubser, Peebles; SW, Battefeld)