Transcript Decompactification and Stabilization of Extra Dimensions

Late-time Cosmology
with String Gases
Scott Watson
Department of Physics
Brown University
[email protected]
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
The mass spectrum of the string:
+ oscillators
Momentum Modes
(Prevent Contraction)
Winding Modes
(Prevent Expansion)
Strings intersect in at most 3 spatial dimensions!!!
Too Much Symmetry?
Action for massless modes of NS sector
O(d,d) Symmetry
String Spectrum (Quantum Considerations)
O(d)xO(d) Symmetry
Moduli Space
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
3+1 growing large
Scale of
dimensions
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
Compactification on S1
Vectors from compactification
Radius of extra dimensions (Radion)
Low energy degrees of freedom,
Chiral Gauge Theory
Bad news for BGC,
Low energy states do not carry winding and momentum charge
Exact theory given by Dilaton-Gravity-U(1) Chiral Gauge theory
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.
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R
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)