Observing Cosmic Superstrings
Observing Cosmic Superstrings
Mark WymanCornell University
With Levon Pogosian, Ira Wasserman, Henry Tye, and Ben Shlaer
Pogosian, Tye, Wasserman, MW, Phys. Rev. D68 (2003) 023506 (hep-th/0304188)Pogosian, MW, Wasserman, JCAP 09 (2004) 008 (astro-ph/0403268)
MW, Pogosian, Wasserman, Phys. Rev. D72 (2005) 023513 (astro-ph/0503364)Tye, Wasserman, MW, Phys. Rev. D71 (2005) 103508 (astro-ph/0503506)
Shlaer and MW, hep-th/0509177
or, How Gravity Wave Observers
Could Prove String Theory
First, Some History …
I. InflationHorizon and Flatness Problems
• 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, ~ M4
Horizon Problem:
I. InflationHorizon and Flatness Problems
• Spatial curvature
• 1 - = 0 unstable fixed point
Flatness Problem:
I. InflationThe 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?)
II. Cosmic Strings
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)
Cosmic Strings
G = Newton’s constant ( = c = 1) = string tension
G ~ string tension in Planck units ~ gravitational coupling of string = size of
metric perturbation.
G Key Dimensionless Parameter
How do Strings Interact?
reconnection:probability P
nothing:probability P
Simulations suggest that approximately
P = 1 for non-string-theorycosmic strings
String Network Evolution: Scaling
But since this is hard to picture ….
Simplest One-Scale Model: Energy Lost in Loops (Kibble)
In theMatter-dominatedEra
Movie byPaulShellard
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Brane Inflation:New Source for Cosmic Strings?
• 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 3 - 2 = 1)
• Predicts: few x • Not Ruled Out; Potentially Detectable
(Tye and Sarangi 2002, Jones, Stoica, and Tye 2002)
extra brane
extraanti-brane
Wilkinson Microwave Anisotropy Probe
Strings
Sloan Digital Sky SurveyStrings
Strings vs. Data: Review
Alone: Strings FAIL
Strings ARE allowedat a subdominant level:
Question: how much?
(Albrect, Battye, & Robinson, PRL 79 (1997) 4736)
(Bouchet, Peter, Riazuelo, Sakellariadou, PRD 65 (2002) 021301)
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?!
Our Modeling Parameters• Standard Cosmological Parameters: As, ns, h, Bh2, Mh2,
• 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”,
)
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) 023005 (astro-ph/0404237)Halofit: Smith et al MNRAS 341 (2003) 1311SDSS: Tegmark et al, PR D69 (2004) 103501 (astro-ph/0310723)WMAP: Verde et al, ApJ Supp. 148 (2003) 135 (astro-ph/0302217)Strings: Gangui et al PR D64 (2001) 43001; Pogosian et al, PR D60 (1999) 83504
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) 023005 (astro-ph/0404237)Halofit: Smith et al MNRAS 341 (2003) 1311SDSS: Tegmark et al, PR D69 (2004) 103501 (astro-ph/0310723)WMAP: Verde et al, ApJ Supp. 148 (2003) 135 (astro-ph/0302217)Strings: Gangui et al PR D64 (2001) 43001; Pogosian et al, PR D60 (1999) 83504
This is not simple!
WMAP and SDSS Bounds: Summary
WMAP and SDSS Bounds: Summary
WMAP and SDSS Bounds: Summary
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
WMAP and SDSS Bounds:Direct Limits on String Tension
• Fix parameters at WMAP values
• Define
• String Gravity:
• No Useful Limit
String Wiggliness
string wiggliness
B-Mode Polarization
• Odd parity: vector, tensor, and lensing E to B
• Adiabatic: Tensor mode fraction, r = 0.1 in graph
• Strings: f = 0.1 in graph; 2 different alpha values
String B-Mode in Context
Plot by Bruce Winstein
GW Background: Pulsar Timing
Lommen, Backer ‘KTR’ ‘01 Data;Vilenkin / Damour ‘04 Analysis:
String Loops Make Lots of Gravity Waves!
(But … Somewhat Model Dependent)
Gravity Wave Burstsfrom Cusps and Kinks
Gravity Waves from Cosmic Strings
~ 50G
LIGO I
Advanced LIGO
cusps kinks
h
Damour and Vilenkin 2001
LISA
cuspskin
ks
h
cosmological.bounds
Cosmic strings could be the very bright GW sources, over a wide range of G
Old Calculations:P = 1(100% interactionprobability)
Bursts from cusps
Analysis / Plot from Damour and Vilenkin, Phys. Rev. D71 (2005) 063510, hep-th/0410222
LIGO, LIGO 2, ….
But in String Theory, P < 1 …
most pessimistic
And for LISA:
most pessimistic
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 …
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String Cusps
But finite size / self-interaction effects MAY change this ….
Movie by Ken Olum
red: zero width approx.
Gravitational Lensing
by a String
Conical Spacetime (c = 1): (G = string mass per unit length ~1022
g/cm)
Deficit Angle
CSL-1: A Detection?
z = 0.46
Separation ~ 20 Kpc ~ 1.9 ”
(Sazhin et al, 2002)
--> G ~ few x 10-7
To be tested in February …
What we’d love to see
• Multi- networks: F, D, (p,q) bound states
• p F-strings + q D-strings = (p,q) string
•Scaling? Tension Distribution?? (MW, Wasserman, Tye, astro-ph/0503506)
Cosmic Superstrings: How Are They Different?
Distinctive Gravitational Lensing
Distinctive, but probably very rare
with B. Shlaer, hep-th/0509177
New Interaction Physics
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
(Note: Hide Dynamics / Cosmology in conformal time,
Rules From Jackson, Jones, & Polchinski (2004)
• 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
N+1 Length Scales, One Velocity
n.b.: for F = 0
• 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)
N+1 Length Scales, One Velocity
Possible Catastrophes
• Low P + reactions: leads to frustration (over-density, string domination)
• Low F: many tensions go to scaling …
A Multi-Tension UV Catastrophe:
Networks DO Scale
convergencetest
Cosmological scale factor, a
Conformal time
Few Tensions are Populated
N(
Tension
Few Tensions are Populated
N(
Tension
(0,1) (1,0) (1,1)
Conclusions
• Cosmic String power: ~10% or lessTension 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 …
Filling Out the Model …
When F = 0 … (no inter-string interactions)
Filling Out the Model …
When F = 0 … (no inter-string interactions)
String Theory:New Source for Cosmic Strings?
• 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 3 - 2 = 1)
• Predicts: few x • Not Ruled Out; Potentially Detectable
(Tye and Sarangi 2002, Jones, Stoica, and Tye 2002)
What Kind of
Strings can be a subdominant contribution to Structure FormationBouchet et al, PR D65 (2002) 21301; Pogosian et al, D68 (2003) 023506 (hep-th/0304188)
QuickTime™ and aTIFF (LZW) decompressor
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QuickTime™ and aTIFF (LZW) decompressor
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II. Old-Style Cosmic Strings
WMAP dta
stringsAlbrecht, Battye, Robinson 1997
WMAP data
GUT Strings Alone Cannot Account forStructure Formation, CMB Power Spectra Shapes
II. Cosmic Strings
Data do allow strings as a subdominant contribution -- G
But where do we get lighter strings?Bouchet et al, PR D65 (2002) 21301; Pogosian et al, D68 (2003) 023506 (hep-th/0304188)
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
Cosmic Superstrings: How Are They Different?
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• Multi- networks: D,F, (p,q)
• Intercommutation Probability P < 1? (Sakellariadou 2004:
• Scaling Without Intercommutation? (MW, Wasserman, Tye, In preparation)
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String Theory to the Rescue ….
Are They Detectable?Vilenkin & Damour 2001, 2004
Maybe …