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30 YEARS OF COSMIC STRINGS
Alex Vilenkin
Tufts Institute of Cosmology
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30 YEARS OF COSMIC STRINGS
String evolution
Detection (bounds)
FOCUS ON:
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30 YEARS OF COSMIC STRINGS
Superconducting strings VortonsSemilocal stringsString formation Strings in GUTsStrings in condensed matter …
LEAVE OUT:
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1970 1975 1980 1985 1990 1995 2000 2005 2010
Strings areseeds ofgalaxies!
Strings are dead!
Cosmicsuper-strings!
A BRIEF HISTORYP
ub
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tio
ns
per
yea
r
Kibble 1976
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OLD STRING EVOLUTION SCENARIO
• Distance between strings:
• Loop sizes:
• Loops decay by gravitational radiation:
ttd ~)(
ttl ~)(
Kibble (1976), A.V. (1981)
G
l~ Mass per unit
length of string
.1~~
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THE FIRST COSMIC STRING REVOLUTION
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High-resolution simulations: the loops are tiny
Bennett & Bouchet (1990)Allen & Shellard (1990)
310
(below theresolution)
Small-scale wiggles
0.6 3.0~ rad. matter
Loop sizes are set by the scale of wiggles.
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SCENARIOS:
is determined by gravitational back-reaction:
G50~ Bennett & Bouchet (1990)
.2 ,)(~ nG n Siemens & Olum (2001)Siemens, Olum & A.V. (2002)
No scaling:
.0 Vincent, Hindmarsh & Sakellariadou (1997)
Observational predictions are sensitive to !
(“standard model”)
ttl ~)(
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THE SECOND COSMIC STRING REVOLUTION
(still in progress!)
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Small-scale wiggles and loops are resolved!
Ringeval, Sakellariadou & Bouchet (2005):
.17~/ 0max t
Olum & Vanchurin (2006):
.200~/ 0max t
Shellard & Martins (2005): .6~/ 0max t
Most of the energy goes Into loops with .
Requires a cutoff.
Loop formation on scales .
tl /
tl /
0~ l
.)( 2/5 ltnl
0l
Scaling peak in loop productiondevelops atafter a long transient regime.
tl 1.0~
Radiation era
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1.0~ after a long transient regime.
ttl ~)(
Flat-space exact simulation
Vanchurin, Olum & A.V. (2005)
1000/ 0max t
tl /
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The picture that seems to emergeis close to the old string scenario:
.1.0~ 0.3,~
Broad distribution of loops and small-scale wiggles.
(?)
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Analytic models:
Kibble (1985)Bennett (1986)Copeland, Kibble & Austin (1992)Martins & Shellard (1996) Copeland, Kibble & Steer (1998)Polchinski & Rocha (2006)
To reach full understanding, we will need to combine numerical and analytic techniques.
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COSMIC SUPERSTRINGS
Reconnection probability may be small: .110 3 p
Jackson, Jones & Polchinski (2004)
Witten (1985)Sarangi & Tye (2002)Majumdar & A. Davis (2002)
F, D and FD strings; FD networks.Copeland, Myers & Polchinski (2004)Dvali & A.V. (2004)
Metastable, but the lifetime can be >> 1010 yrs.
In models of brane inflation: .611 1010 G
Jones, Stoica & Tye (2003)
[Similar range in hybrid inflation GUT models]Jeannerot & Postma (2005)
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How does affect string evolution?1p
Sakellariadou & A.V. (1990)Sakellariadou (2005)
.1 ps
Avgoustidis & Shellard (2006)
Simple argument suggests
Numerical evidence is inconclusive.
But in any case, for p << 1 there is a large number of strings per Hubble volume.
Direct observational test of string theory.
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EVOLUTION OF FD-NETWORKSVachaspati & A.V. (1987)McGraw (1998)Tye, Wasserman & Wyman (2005)
Simple models
Scaling: ttd ~)(2/~/ GFD
depends on energy dissipation.
Spergel & Pen (1997)Copeland & Saffin (2005)Hindmarsh & Saffin (2006)
Global string network simulations
01.01.0~ 1/ FD
If the dominant energy lossis gravitational radiation:
G~1/1~/ GFD
Goldstone radiation
String domination
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UrrestillaGauge strings
U(1)xU(1)
.25~/ 0max t
Scaling: Loop production?05.0~,~)( ttd
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OBSERVATIONAL BOUNDS
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STRING SIGHTINGS:
Sazhin et. al. (2003)
Cowie & Hu (1987)
Schild et. al. (2004)
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GRAVITATIONAL RADIATION
Stochastic GW background & GW bursts from cusps.
Vachaspati & A.V. (1984) Hogan & Rees (1984) Caldwell & Allen (1992)Battye, Caldwell & Shellard (1996) …
Comparable power in bursts andin low harmonics.
1110~ GBursts may be detectable for .
Better for p << 1.
LIGO search is underway!
Damour & A.V. (2000,2005)Siemens et. al. (2006)Hogan (2006)
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BOUNDS FROM PULSAR OBSERVATIONS
8 yrs: 710G Kaspi, Taylor & Ryba (1994)
17 yrs: 1010G Lommen (2002)Hogan (2006)
(disputed)
PTA: 2/38105.1 pG Jenet et. al. (2006)
Full PTA 1110~ G
(Pulsar Timing Array)
(20 pulsars for 5 yrs)
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Implications of large loops )1.0~(
Nucleosynthesis bound:
.10 7G Vanchurin, Olum & A.V. (2005)
Reionization:
8103 G Olum & A.V. (2006)
loops seed early galaxy formation.
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CMB BOUNDS
CMB anisotropies
7103 G Pogosian, Wasserman & Wyman (2006)
CMB polarization
B-type polarization due to vector perturbations induced by strings.
98 1010~ G may be detectable.Seljak & Slosar (2006)
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Bad news: GUT-scale strings are ruled out.
)10( 8G
Good news: strings can be detected well belowthe GUT scale.
We are not likely to detect strings through gravitational lensing or CMB anisotropies.
Gravitational waves, CMB polarization
Constraint is much weaker for global strings:
.103 7G
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CONCLUSIONS
A new generation of string simulations is underway.Strong indications of loop scaling; (?) important observational implications.
The strongest present bound on strings:
8105.1 G (PTA)
The most promising detection methods:pulsar timing, GW bursts, CMB polarization. May get to in ~ 5 yrs.1110~ G
1.0~
The field is as vibrant as ever!