Mark Hindmarsh- Is the Universe held together with cosmic string?

8/3/2019 Mark Hindmarsh- Is the Universe held together with cosmic string?

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Is the Universe held together with cosmic string? PMF, University of Ni s, 29/8/08

Is the Universe held together with cosmic string?

Mark HindmarshDept. of Physics & Astronomy

Sussex University

[email protected]

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]



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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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Is the Universe held together with cosmic string? PMF, University of Ni s, 29/8/08 M

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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Mark Hindmarsh- Is the Universe held together with cosmic string?