cosmo – tahoe – september 2006 cmb constraints on inflation models with cosmic strings mark...
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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
Cosmo – Tahoe – September 2006
Cosmo – Tahoe – September 2006
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)
Cosmo – Tahoe – September 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
Cosmo – Tahoe – September 2006
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)
Cosmo – Tahoe – September 2006
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
Cosmo – Tahoe – September 2006
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
Cosmo – Tahoe – September 2006
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
Cosmo – Tahoe – September 2006
Simulations: Lagrangian density
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are needed to see this picture.
Cosmo – Tahoe – September 2006
Simulations: energy density
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Cosmo – Tahoe – September 2006
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
Cosmo – Tahoe – September 2006
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
Cosmo – Tahoe – September 2006
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)
Cosmo – Tahoe – September 2006
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
Cosmo – Tahoe – September 2006
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%)
Cosmo – Tahoe – September 2006
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.)
Cosmo – Tahoe – September 2006
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
Cosmo – Tahoe – September 2006
MCMC with “all” CMB data
Strings are favoured by the data - 2 sigma detection!
68%
95%
Cosmo – Tahoe – September 2006
MCMC with WMAP3 data
Strings are favoured by the WMAP3 data, at between 1 and 2 sigma level
68%
95%
Cosmo – Tahoe – September 2006
“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)
Cosmo – Tahoe – September 2006
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)
Cosmo – Tahoe – September 2006
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)