1. Late-time Cosmology with String Gases
Scott Watson Department of Physics Brown University

2. 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”)

3. 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!!!

4. 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

5. 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.

6. 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/ ),
Action for massless modes of NS sector with gas of string modes,
Winding modes:
Momentum modes:
Pressure Vanishes at Self-dual Radius

7. 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

8. Anisotropy and dilaton play vital role in stabilization

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

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

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

12. 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/ )

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

14. 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,

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

16. 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.

17. 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

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

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

20. 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)