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) 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

First, Some History …

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

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

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?)

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)

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.

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

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

In the Matter- dominated Era Movie by Paul Shellard

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 3 - 2 = 1) Predicts: few x Not Ruled Out; Potentially Detectable extra anti- brane extra brane

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) 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, 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)

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) 1311 SDSS: 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 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) 023005 (astro-ph/0404237) Halofit: Smith et al MNRAS 341 (2003) 1311 SDSS: 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

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 Wiggliness String Gravity: No Useful Limit string wiggliness NO TIME HERE!! 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 String Loops Make Lots of Gravity Waves! Lommen, Backer ‘KTR’ ‘01 Data; Vilenkin / Damour ‘04 Analysis: (But … Somewhat Model Dependent)

Gravity Wave Bursts from Cusps and Kinks

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)

But in String Theory, P < 1 … most pessimistic Bursts from cusps LIGO, LIGO 2, …. Analysis / Plot from Damour and Vilenkin, Phys. Rev. D71 (2005) 063510, hep-th/0410222

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 …

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

Gravitational Lensing by a String

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

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

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

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/0503506)

Distinctive Gravitational Lensing Distinctive, but probably very rare with B. Shlaer, hep-th/0509177

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)

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

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

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 convergence test Cosmological scale factor, a Conformal time Cosmological scale factor, a

Few Tensions are Populated

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

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 …

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)

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)

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 3 - 2 = 1) Predicts: few x Not Ruled Out; Potentially Detectable

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) 023506 (hep-th/0304188)

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

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) 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? Multi-m networks: D,F, (p,q) Intercommutation Probability P < 1? (Sakellariadou 2004: Scaling Without Intercommutation? (MW, Wasserman, Tye, In preparation)

String Theory to the Rescue ….

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