Cosmo – Tahoe – September 2006 CMB constraints on inflation models with cosmic strings Mark Hindmarsh Neil Bevis (Sussex) Martin Kunz (Geneva) Jon Urrestilla

Cosmo – Tahoe – September 2006

CMB constraints on inflation models with cosmic strings

Mark Hindmarsh

Neil Bevis (Sussex) Martin Kunz (Geneva)

Jon Urrestilla (Tufts, Sussex)

in preparation – MCMC WMAP3, polarisation astro-ph/0605018 – CMB TT calculations

astro-ph/0403029 – global textures



Introduction: inflation & strings

• Simplest model of the early Universe: inflationa

• General relativity + scalar field (quantum fluctuations)b

• String defectsc may be formed at end of hybrid inflationd

• Also at later thermal phase transitionse

• String/M-theory: strings from D + anti D-brane collisionsf

• Strings very important in SUSY F- & D-term inflationg

a) Starobinsky (1980); Sato (1981); Guth (1981); Hawking & Moss (1982); Linde (1982); Albrecht & Steinhardt (1982)

b) Mukhanov & Chibisov (1981); Hawking (1982); Starobinsky (1982); Guth & Pi (1982); Hawking & Moss (1983); Bardeen, Steinhardt, Turner (1983)

c) Hindmarsh & Kibble (1994); Vilenkin & Shellard(1994); Kibble (2004)d) Yokoyama (1989); Kofman,Linde,Starobinski (1996)e) Kibble (1976); Zurek (1996); Rajantie (2002)f) Jones, Stoica, Tye (2002); Dvali & Vilenkin (2003); Copeland, Myers, Polchinski (2003)g) Jeannerot (1995); Rocher & Sakellariadou (2006); Battye, Garbrecht, Pilaftsis (2006)


Strings in the early universe

• Form at t∼10−36 sec

• Observe at t0 ∼1017 sec.

• Scaling hypothesis: dimensional analysis based on physical

scales

• Once formed strings maintain a constant density parameter

Ωs

• With string tension μ, Ωs ∼ Gμ ∼10−6 for GUT scale strings


Observational signals of strings

Robust:

• Cosmic Microwave Background fluctuationsa

Uncertain (orders of magnitude):

• Gravitational radiationb

• Cosmic raysc

• Gravitational lensingd

• Baryon asymmetrye

a) Zel'dovich (1980); Vilenkin (1981); Kaiser & Stebbins (1984); Landriau & Shellard (2004); Wyman et al (2005); Bevis et al (2006)

b) Vachaspati & Vilenkin (1985); Hindmarsh (1990); Damour & Vilenkin (2000,2001,2005)c) Bhattarcharjee (1990); Sigl (1996); Protheroe (1996); Berezhinksi (1997); Vincent, M.H.,

Antunes (1998)d) Vilenkin (1984); Hindmarsh (1989); de Laix & Vachaspati (1996,1997)e) Bhattarcharjee, Kibble, Turok (1982); Brandenburger, Davis, M.H. (1991); Brandenburger,

Davis, Trodden (1994); Jeannerot (1996); Sahu, Bhattarcharjee, Yajnik (2004);Jeannerot & Postma (2005)


Uncertainty: energy loss

Scenario 1 (based on Nambu-Goto approximation & modelling)

• Long strings - loops - gravitational radiation

Scenario 2 (based on Classical Field Theory approximation)

• Long strings - tiny loops/massive radiation - high energy

particles

Need better understanding of coupling between large & small scales


Approximations

String/M-theory

(Energy << Mstring)

|

Quantum field theory(High occupation number)

|

Classical field theory(Low curvature string trajectory)

|

Ideal (Nambu-Goto) strings(Phenomenogical from simulations)

|

Moving segment model, VOS model

This work

Landriau & Shellard 2004

Wyman et al 2005


Strings in classical field theory

Standard Model of particle physics: spontaneous gauge symmetry-breaking

Simplest field theory with gauge SSB also has string-like classical solutions

Abelian Higgs model:

Energy-momentum tensor:

Gravitational perturbations proportional to:

CMB power spectrum proportional to:

μ: string tension

Ad: defect amplitude


Simulations: Lagrangian density

QuickTime™ and a decompressor

are needed to see this picture.


Simulations: energy density

QuickTime™ and a decompressor

are needed to see this picture.


Theory:

Lattice:

Times:

Final string curvature radius:

Simulations: the details

Visualisation runs:

Lattice:

Times:

Final string curvature radius:

Classical lattice field theory in parallel: www.latfield.org


Cut to the chase: TT spectrum

Normalisation at l=10:

This (astro-ph/0605018)

Wyman et al 2005

Landriau & Shellard 2004

Moving segment model

Nambu-Goto simulations


Bevis et al. 2004 - Global textures

Global O(4) textures - 3D classical field theory simulations

Unequal Time Correlator (UETC) methoda

CMBeasyb modified to accommodate sources of energy-momentum

Data: WMAP first year (and ACBAR, CBI, VSA)

MCMC fit – using modified CosmoMC - 7 parameters

Inflationary contribution uncorrelated with defects

a) Pen, Seljak, Turok (1997); Durrer, Kunz, Melchiorri (2001)b) Doran (2004)


Bevis et al. - defect degeneracy

WMAP 1yr + VSA + CBI + ACBAR data

Degeneracy involving Ad

2, As

2 (obviously) and bh2, h, ns allowing high defect fractions.

fd = fractional defect contribution at l=10

But large fd incompatible withKirkman et al. value of bh2

and Hubble Key Project value of hde

gene

racy


Defect degeneracy v. BBN & HKP

68%

95%

68%

95%

WMAP 1yr

WMAP 1yr+

BBN+

HKP

Detection of textures removed by BBN & HKP priorsfd,10 < 13% (95%)


String CMB from field theory

Cls for cosmic strings using field evolution simulations (astro-ph/0605018)c.f. Wyman et al. (2005, Err 2006) using moving segment modelc.f. global texturec.f. data: 3 year WMAP

Normalised to l=10

Cosmic strings (Wyman et al.)

Cosmic strings (Bevis et al.)

Global textures (Bevis et al.)


WMAP 3rd year (astro-ph/0603451)BOOMERanG (astro-ph/0507494)

CBI (astro-ph/0402359)VSA (astro-ph/0402498)

ACBAR (astro-ph/0212289)

MCMC: inflation + strings v. CMB


MCMC with “all” CMB data

Strings are favoured by the data - 2 sigma detection!

68%

95%


MCMC with WMAP3 data

Strings are favoured by the WMAP3 data, at between 1 and 2 sigma level

68%

95%


WMAP - why strings?


WMAP - why strings?


WMAP - why strings?


“All” CMB + BBN + HKP

WMAP 3rd year (astro-ph/0603451)BOOMERanG (astro-ph/0507494)

CBI (astro-ph/0402359)VSA (astro-ph/0402498)

ACBAR (astro-ph/0212289)+

BBN (astro-ph/0302006) HKP(astro-ph/0012376)


“All” CMB + BBN + HKP

“all” CMB

“all” CMB + BBN + HKP


WMAP normalization at l=10: 10 = 2.0 x 10-6 (astro-ph/0604018)

NB Moving segment model must be normalised from a simulation

“all” CMB

< 0.22

< 0.96 x 10-6

Constraints on string tension

“all” CMB + BBN + HKP

< 0.10

< 0.7 x 10-6

WMAP-3 only

< 0.19

< 0.9 x 10-6

Wyman et al. (2005,6): < 0.27 x 10-6 (astro-ph/0604141)

(moving segment model, WMAP-1 and SDSS, 10 = 1.1 x 10-6)

Fraisse 2006: < 0.26 x 10-6 (astro-ph/0603589)

(moving segment model, WMAP-3)


Polarization


Polarization

Tensors@ r=0.3

EE lensed


Conclusions

• First cosmic string CMB power spectra from classical field theory

• Normalisation to WMAP3 at l=10:

• First likelihood analysis for string CMB from classical field theory

• CMB data has a moderate preference (2-sigma) for strings

• Including of BBN and HKP priors reduces significance (1.5-sigma)

• Upper bound of 10% contribution to TT from strings at l=10

• Parallel N-dimensional field theory simulations: www.latfield.org

To do:• Fitting to SDSS data, inflation tensors• Low Higgs coupling (D-term inflation)• Other field theories (e.g. semilocal strings)

COSMO 2007COSMO 2007

University of Sussex, Brighton, U.K.

August 21-25 2007

University of Sussex, Brighton, U.K.

August 21-25 2007

Documents

Cosmo – Tahoe – September 2006 CMB constraints on inflation models with cosmic strings Mark Hindmarsh Neil Bevis (Sussex) Martin Kunz (Geneva) Jon Urrestilla