1. Observing Cosmic Superstrings
or, How Gravity Wave Observers
Could Prove String Theory
Mark Wyman
Cornell University
With Levon Pogosian, Ira Wasserman, Henry Tye, and Ben Shlaer
Pogosian, Tye, Wasserman, MW, Phys. Rev. D68 (2003) (hep-th/ )
Pogosian, MW, Wasserman, JCAP 09 (2004) 008 (astro-ph/ )
MW, Pogosian, Wasserman, Phys. Rev. D72 (2005) (astro-ph/ )
Tye, Wasserman, MW, Phys. Rev. D71 (2005) (astro-ph/ )
Shlaer and MW, hep-th/

2. First, Some History …

3. I. Inflation Horizon and Flatness Problems Horizon Problem:
Spatial Scale L today: fraction H0 of “horizon”
Expansion -> fraction HaL = (Ha/H0) H0L at an earlier time
Standard Cosmology: Ha decreases with time. Extrapolate back to large scale, M: T ~ M, r ~ M4

4. I. Inflation Horizon and Flatness Problems Flatness Problem:
Spatial curvature
1 - W = 0 unstable fixed point

5. I. Inflation The Solution!
Ha increased by at least 1029 M/MP during a “pre-Big Bang” epoch -->
(Horizon scale today) < (Horizon scale before inflation)
Expansion flattens the universe, so k -> 0 naturally
At the end of Inflation, Universe reheats, standard Big-Bang cosmology begins.
Needed: Very flat “Inflaton” Potential (Fine Tuning?)

6. II. Cosmic Strings Cosmic String Defect for U(1) Symmetry
Kibble Mechanism for Symmetry Breaking:
Regions Larger than H-1 Are Out of Causal Contact!
Cosmic String Defect for U(1) Symmetry
(Fig. From Gangui)

7. Cosmic Strings Gm: Key Dimensionless Parameter
G = Newton’s constant ( = c = 1)
m = string tension
Gm ~ string tension in Planck units
~ gravitational coupling of string = size of
metric perturbation.

8. How do Strings Interact?
nothing:
probability 1-P
reconnection:
probability P
P = 1 for non-string-theory
cosmic strings
Simulations suggest that
approximately

9. String Network Evolution: Scaling
Simplest One-Scale Model: Energy Lost in Loops (Kibble)
But since this is hard to picture ….

10. In the
Matter-
dominated
Era
Movie by
Paul
Shellard

11. Brane Inflation: New Source for Cosmic Strings?
(Tye and Sarangi 2002, Jones, Stoica, and Tye 2002)
Annihilation of Inflating Branes Can Produce Strings (Actual 1-D Objects or “Wrapped” Higher-D Objects)
Kibble Mechanism Applies --> But Not in Compact Dimensions (R < H-1) (or more complicated explanations!)
Brane Dynamics Exclude Domain Walls and Monopoles; Allow Only Strings
(Since = 1)
Predicts: few x
Not Ruled Out; Potentially Detectable
extra
anti-
brane
extra
brane

12. Strings vs. Data: Review
Wilkinson Microwave Anisotropy Probe
Strings
Alone: Strings FAIL
(Albrect, Battye, & Robinson, PRL 79 (1997) 4736)
Sloan Digital Sky Survey
Strings
Strings ARE allowed
at a subdominant level:
Question: how much?
(Bouchet, Peter, Riazuelo, Sakellariadou,
PRD 65 (2002) )

13. Cosmic String Observables:
Cosmological Limits already in Place:
Precision CMB Observation Limits
Pulsar Timing
Possible Direct Windows:
Gravity Waves: Possible LIGO and LISA sources!
Gravitational Lensing: One Observed Already?!

14. Our Modeling Parameters
Standard Cosmological Parameters: As, ns, h, WBh2, WMh2, t
Cosmic String Model “Weight”
Incoherently add String and Adiabatic Power Spectra:
Vary 7 Parameters using Markov Chain Monte Carlo (+ overall P(k) normalization and “string wiggliness”, a)

15. Method Compute Adiabatic Cl’s with CMBWarp
Compute String CL’s and string & adiabatic P(k)’s with a modified form of CMBFAST
Nonlinear P(k) fitting with Halofit
Incoherently add String and Adiabatic contributions
Use WMAP and SDSS Likelihood Functions with MCMC to find PDFs
CMBWarp: Jimenez et al, PR D70 (2004) (astro-ph/ )
Halofit: Smith et al MNRAS 341 (2003) 1311
SDSS: Tegmark et al, PR D69 (2004) (astro-ph/ )
WMAP: Verde et al, ApJ Supp. 148 (2003) 135 (astro-ph/ )
Strings: Gangui et al PR D64 (2001) 43001; Pogosian et al, PR D60 (1999) 83504

16. Method Compute Adiabatic Cl’s with CMBWarp
This is
not simple!
Compute Adiabatic Cl’s with CMBWarp
Compute String CL’s and string & adiabatic P(k)’s with a modified form of CMBFAST
Nonlinear P(k) fitting with Halofit
Incoherently add String and Adiabatic contributions
Use WMAP and SDSS Likelihood Functions with MCMC to find PDFs
CMBWarp: Jimenez et al, PR D70 (2004) (astro-ph/ )
Halofit: Smith et al MNRAS 341 (2003) 1311
SDSS: Tegmark et al, PR D69 (2004) (astro-ph/ )
WMAP: Verde et al, ApJ Supp. 148 (2003) 135 (astro-ph/ )
Strings: Gangui et al PR D64 (2001) 43001; Pogosian et al, PR D60 (1999) 83504

17. WMAP and SDSS Bounds: Summary

18. WMAP and SDSS Bounds: Summary

19. WMAP and SDSS Bounds: Overall String Power
Usual Parameters: basically unchanged
CS fractional power f < 0.14 (95% c.l.)
also: “test” of adiabatic model

20. WMAP and SDSS Bounds: Direct Limits on String Tension
Fix parameters at WMAP values
Define

21. String Wiggliness String Gravity: No Useful Limit string wiggliness
NO TIME HERE!!
string wiggliness

22. B-Mode Polarization Odd parity: vector, tensor, and lensing E to B
Adiabatic: Tensor mode fraction, r = 0.1 in graph
Strings: f = in graph; 2 different alpha values

23. String B-Mode in Context
Plot by Bruce Winstein

24. GW Background: Pulsar Timing
String Loops Make Lots of Gravity Waves!
Lommen, Backer ‘KTR’ ‘01 Data;
Vilenkin / Damour ‘04 Analysis:
(But … Somewhat Model Dependent)

25. Gravity Wave Bursts from Cusps and Kinks

26. Gravity Waves from Cosmic Strings
a ~ 50Gm
LIGO I
Advanced
LIGO
cusps
kinks h
Damour and Vilenkin 2001
Cosmic strings could be the very bright GW sources, over a wide range of Gm
cosmological.
bounds
LISA
cusps
kinks h
Old Calculations:
P = 1
(100% interaction
probability)

27. But in String Theory, P < 1 …
most pessimistic
Bursts from cusps
LIGO, LIGO 2, ….
Analysis / Plot from Damour and Vilenkin, Phys. Rev. D71 (2005) , hep-th/

28. And for LISA:
most pessimistic

29. String Cusps Typically, several times per oscillation a cusp
will form somewhere on a cosmic string (Turok 1984).
For zero-width strings, the instantaneous velocity of the tip approaches c …

30. String Cusps
But finite size / self-interaction effects MAY change this ….
red: zero width approx.
Movie by Ken Olum

31. Gravitational Lensing by a String

32. Conical Spacetime (c = 1):
(Gm = string mass per unit length ~1022 g/cm)
Deficit Angle

33. CSL-1: A Detection? (Sazhin et al, 2002) z = 0.46 Separation ~ 20 Kpc
~ 1.9 ”
--> Gm ~ few x 10-7

34. To be tested in February …
What we’d love to see

35. Cosmic Superstrings: How Are They Different?
Multi-m networks: F, D, (p,q) bound states
p F-strings + q D-strings = (p,q) string
Scaling? Tension Distribution??
(MW, Wasserman, Tye, astro-ph/ )

36. Distinctive Gravitational Lensing
Distinctive, but probably very rare
with B. Shlaer, hep-th/

37. New Interaction Physics
(Note: Hide Dynamics / Cosmology
in conformal time, 
SAY: alpha = p,q species
N = number density
P, q possibly negative …. ?
N eta^2 ----> scaling
Speak of WHAT P IS LIKE!
Interaction Rules:
p and q must be coprime to be stable
(k,0) and (0,k) strings decay instantly Become k (1,0) or (0,1) strings
All interactions lose energy
Rules From Jackson, Jones, & Polchinski (2004)

38. N+1 Length Scales, One Velocity
Multiple tensions:
L, v evolved as in Two Scale Model
Densities evolve via …
Dilution (2H) and straightening
Self-interaction
Reactions and Breakup as in previous slide
Omega: Fraction of critical density in CS
REMIND what F is
L = one - scale model
n.b.: for F = 0

39. N+1 Length Scales, One Velocity
Multiple tensions:
L, v evolved as in Two Scale Model
Densities evolve via …
Dilution (2H) and straightening
Self-interaction
Reactions and Breakup as in previous slide
P: self-interaction parameter; F: inter-string-interaction parameter (massive simplification of collision physics)
Omega: Fraction of critical density in CS
REMIND what F is
L = one - scale model

40. Possible Catastrophes
Low P + reactions: leads to frustration (over-density, string domination)
Low F: many tensions go to scaling …
A Multi-Tension UV Catastrophe:

41. Networks DO Scale convergence test Cosmological scale factor, a
Conformal time
Cosmological scale factor, a

42. Few Tensions are Populated

43. Few Tensions are Populated
(0,1) (1,0) (1,1)
N(
Tension

44. Conclusions Cosmic String power: ~10% or less
Tension Limit: G < (few) x 10-7
Cusps (and Kinks?) COULD be a major LIGO / LISA GW Source
(p,q) Network interpretation:
Few String tensions: scaling: coherence?
Gravitational Lensing? We’ll see in February …

45. Filling Out the Model … When F = 0 … (no inter-string interactions)
Reported often recently; natural in our model
When F = 0 … (no inter-string interactions)

46. Filling Out the Model … When F = 0 … (no inter-string interactions)
High tensions populated: BAD NEWS
--- tells importance of interaction terms, non-flat spectrum
END HERE, say: Thank you. <applause> Are there any questions?
When F = 0 … (no inter-string interactions)

47. String Theory: New Source for Cosmic Strings?
(Tye and Sarangi 2002, Jones, Stoica, and Tye 2002)
Annihilation of Inflating Branes Can Produce Strings (Actual 1-D Objects or “Wrapped” Higher-D Objects)
Kibble Mechanism Applies --> But Not in Compact Dimensions (R < H-1)
Brane Dynamics Exclude Domain Walls and Monopoles; Allow Only Strings
(Since = 1)
Predicts: few x
Not Ruled Out; Potentially Detectable

48. Strings can be a subdominant contribution to Structure Formation
What Kind of
Strings can be a subdominant contribution to Structure Formation
Bouchet et al, PR D65 (2002) 21301; Pogosian et al, D68 (2003) (hep-th/ )

49. II. Old-Style Cosmic Strings
GUT Strings Alone Cannot Account for
Structure Formation, CMB Power Spectra Shapes
WMAP dta
strings
Albrecht, Battye, Robinson 1997
WMAP data

50. II. Cosmic Strings
Data do allow strings as a subdominant contribution -- Gm < 10-6
But where do we get lighter strings?
Bouchet et al, PR D65 (2002) 21301; Pogosian et al, D68 (2003) (hep-th/ )

51. String Theory: Brane Inflation
Early-universe D-Brane collisions can successfully model inflation
Brane attraction can be weak = inflationary potential
Brane collision may provide natural model for reheating

52. Cosmic Superstrings: How Are They Different?
Multi-m networks: D,F, (p,q)
Intercommutation Probability P < 1?
(Sakellariadou 2004:
Scaling Without Intercommutation?
(MW, Wasserman, Tye, In preparation)

53. String Theory to the Rescue ….

54. Are They Detectable?
Vilenkin & Damour 2001, 2004
Maybe …