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Is the Universe held together with cosmic string?
Mark HindmarshDept. of Physics & Astronomy
Sussex University
Collaborators:
N. Bevis, M. Kunz, J. Urrestilla [astro-ph/0605018,astro-ph/0702223,0704.3800]
+ A. Liddle [0711.1842]
S. Borsanyi [0712.0300], P. Safn [hep-th/0605014], P. Salmi [0712.0614]
G. Vincent & N.Antunes, [hep-ph/9708427]
G Vi t & M S k ll i d [ t h/9612135]
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G Vi t & M S k ll i d [ t h/9612135]
Is the Universe held together with cosmic string? PMF, University of Ni s, 29/8/08
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Introduction
Cosmic strings a are linear distributions of mass-energy in the universe.
Mass per unit length , tension T . Normally = T c2
Dynamics: acceleration curvature : wave equation, In theories of high energy physics they may be
Fundamental (string theory): zero width
Solitonic (eld theory): non-zero width
Made in the early universe? b t 10 36 s, 1020 kg/m, w
If formed still here: O(1) innite string unknown distribution of cl
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Two models of a universe lled with string
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Observational signals from strings
Small theoretical disagreement (factor 10)
Cosmic Microwave Background, density perturbations aLarge theoretical disagreement (factor 10lots )
Gravitational radiation b
Cosmic rays c Gravitational lensing d
a Zeldovich (1980); Vilenkin (1981); Kaiser & Stebbins (1984); Landriau & Shellard (2004); W
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Danger! Natural Units
= c = kB = 1
[Mass] GeV 10 27 kg proton mass
[Length] GeV 1 10 15 m proton size
[Time] GeV 1 10 24 s proton light crossing time
[Temperature] GeV 1013 K proton pair creation temperature
M 1 / G 101
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Quantum Field Theory in a Nutshell
Quantum elds can behave either like particles or classical waves.
E.g. electromagnetic eld can behave either as a photon or a radio wave:
e
e
e
e
ClassicalHigh occupation numberLow occupation number
Quantum0 00 00 00 00 00 00 0
1 11 11 11 11 11 11 1
0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1
0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0
1 1 1 1 1 1 11 1 1 1 1 1 11 1 1 1 1 1 11 1 1 1 1 1 11 1 1 1 1 1 11 1 1 1 1 1 101010 0 0 00 0 0 0
0 0 0 01 1 1 11 1 1 11 1 1 1
Cl i l b h i ibl l f b ( i 0 1 2 )
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Cosmic string zoo: eld theory
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String theory in a nutshell
Fundamental object is a string . Strings may be open or closed. Particles are tiny strings.
Different particles - different vibration modes. Strings may also be macroscopic. Super strings have supersymmetry :
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Cosmic string zoo: string theory
Fundamental strings F-strings
Extended objects D-branes
IIA (IIB): 2, 4, 6, 8 (1, 3, 5, 7, 9 ) dimensions F-strings end on D-branes, ( D1 = D-string )
Bound states, junctions: ( p,q)-strings & more a
Formation: D3-D3, tachyon eld theory b
Evolution: analytic & numerical modelling c a C l d M P l hi ki (2004) Fi j hi L bl d T
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Formation of strings (Kibble-Zurek) (2+1)D model
Real scalar eld (x , t ), symmetry . Lagrangian density:
L=
1
22
1
2( )2
V (), V () = V 0
1
22 (T )2 +
T (t) is a control parameter(e.g. temperature, inaton)
2 (T > T c ) < 0, 2 (T < T c ) > 0Phase transition at T = T c .Field eqn. (Minkowski space)
2 2 2 (T)+1
3 = 0
T>T c
v +v
V T
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Formation of strings in 2D: numerical simulation
+ (t) 2 + ( 2 2 (t)) = 0Initial conditions : (
x
) Gaussian random variable on each lattice site
(Loading ...)
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Gauge eld theories: Abelian Higgs model
S = d4 x D D + V () + 14e2 F F
Complex scalar eld (x , t ), vector eld A (x , t )Covariant derivative D = + iA .
Potential V () =12 (||
2
v2)
2.
Relativistic Ginzburg-Landau
T V
T l ( A 0 ) ld i
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Vortex solutions in the Abelian Higgs model
Static nite energy (2D) cylindrically symmetric:
= vf ()ei , A = a()
Energy density:
= |D i |2 + V + 12B2
Magnetic eld:
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Visualising Abelian Higgs string simulations
(Loading ...)
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Computing 1976 to 2008
Kibble, J. Phys A (1976): Topology of cosmic domains and strings
Best 1976: Cray 1 120 MHz 64-bit vector processor, 250 MFlops , 8 M583 requires 7.8 MB
Our simulations on Cosmos 152 1.6GHz Itanium2, 790 GFlops , 456G3
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COSMOS
UK National Cosmology Computer 148 1.6Ghz Itanium II 444 Gb
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Parallel simulations of eld theories: LATeld
Public C++ library of objects for parallel classical lattice elds a
Rewrite of MDP/FermiQCD b
Objects:Lattice: Takes care of boundary conditions and domain decompositionField: Template - can have real, complex, user-dened object.
Site: Accesses elements of eld
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Abelian Higgs model simulations: string length scale
Scaling : L/V 2
Network scale: = (V/L )Hence
Lattice spacing: x = 0 .5Time step: t = 0 .1
Volume: 10243
Matter era
20
30
40
50
60
70
80
1024 3 data = 0.267t 45.3
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String network scaling hypothesis
String network characteristic scale (=
V/L , i.e. average curvatu
Network scaling hypothesis: = x t (x constant O(1)) String energy density: s / 2
Total energy density: t 1/Gt2
:
String density fraction: s G/x 2Grand Unication: G 10 6
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Modelling cosmic superstrings
Field theory model with junctions a
SU (2)
U (1)
Z 3
(global symmetry)
0 10 20 30 40 50 60 700
10
20
30
40
0 5
1
/ d t
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Wilkinson Microwave Anisotropy Probe
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Strings and the Cosmic Microwave Background
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Angular power spectrum C
Multipole moments:
a lm = R d T ( n )Y lm (n )Angular power spectrum:
C l = 12 l +1 P m |a lm | 2
Anisotropy power:l(l + 1) C l / (2 )
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Explanation - Ination
Energy density of Universe dominated by homogeneous scalar eld (
Scalar eld equation: + 3 H + V () = 0
Friedmann equation: H 2 = 8G3 (V () + 12 2 )
Slow roll
|
| |
|: overdamped evolution
Accelerated expansion: a(t) thuge , Quantum uctuations in eld:
( ) (t) + (t )
V
( )
( )t,x
t _
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Ination + strings: just 7 (or 6) numbers
C = C inf (H 0 , b , m , , A s , n s ) + C string (G)
Parameter CDM +strings HZ+strings
H 0 (km/s/MPc) 73 82 82100b 4.2 3.7 3.7m 24.0 17.9 17.9
0.092 0.11 0.111010 A2s 22 20 20n s 0.958 1.00 1f 10 0.099 0.099
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Abelian Higgs string C s vs. WMAP3 and BOOMERanG
Multipole moments:
a lm = R d T ( n )Y lm ( n )
Angular power spectrum:
C l =1
2l + 1
l
Xm = l
|a lm | 2
A i t200
0
200
1000
2000
3000
4000
5000
6000
l ( l + 1 ) C
l / 2
[ K
2 ]
String contribInflation bestInflation+striWMAP (binnBOOMERAN
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Results slide for string-o-philes
Fit to CMB data (WMAP3, Boomerang, CBI, ACBAR, VSA) a
G = (0 .65 0.10) 10 6
Ingredients for a stringy universe:
Hubble parameter H 0 = 82 km s 1 Mpc 1
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Results slide for string-o-phobes
Fit to CMB (7 parameters) a
+ Hubble Key Project ( H 0 = 72 8 km s 1 Mpc 1 )
+ D abundance & Big Bang Nucleosynthesis ( b h2 = 2 .14
0.20
G < 0.7 10 6 (95%)
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Conclusions
Strings are common in high energy physics theories
If strings were every formed, they would still be here. Field theory calculations of string Cosmic Microwave Background signal Results:
(CMB only t) G = 0 .65 0.10 10 6
(n s = 1 , high b h (CMB + Hubble + BBN) G < 0.7 10
6 (95% C.L.)
Strings improve CMB in range 300 < < 700:
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