1. 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

2. Introduction: inflation & strings Simplest model of the early Universe: inflation a General relativity + scalar field (quantum fluctuations) b String defects c may be formed at end of hybrid inflation d Also at later thermal phase transitions e String/M-theory: strings from D + anti D-brane collisions f Strings very important in SUSY F- & D-term inflation g 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)

3. Cosmo – Tahoe – September 2006 Strings in the early universe Form at t ∼ 10 −36 sec Observe at t 0 ∼ 10 17 sec. Scaling hypothesis: dimensional analysis based on physical scales Once formed strings maintain a constant density parameter Ω s With string tension μ, Ω s ∼ G μ ∼ 10 −6 for GUT scale strings

4. Cosmo – Tahoe – September 2006 Observational signals of strings Robust: Cosmic Microwave Background fluctuations a Uncertain (orders of magnitude): Gravitational radiation b Cosmic rays c Gravitational lensing d Baryon asymmetry e 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)

5. 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

6. Cosmo – Tahoe – September 2006 Approximations String/M-theory (Energy << M string ) | 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

7. 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 A d : defect amplitude

8. Cosmo – Tahoe – September 2006 Simulations: Lagrangian density

9. Cosmo – Tahoe – September 2006 Simulations: energy density

10. 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

11. 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

12. Cosmo – Tahoe – September 2006 Bevis et al. 2004 - Global textures Global O(4) textures - 3D classical field theory simulations Unequal Time Correlator (UETC) method a CMBeasy b 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)

13. Cosmo – Tahoe – September 2006 Bevis et al. - defect degeneracy WMAP 1yr + VSA + CBI + ACBAR data Degeneracy involving A d 2, A s 2 (obviously) and  b h 2, h, n s allowing high defect fractions. f d = fractional defect contribution at l=10 But large f d incompatible with Kirkman et al. value of  b h 2 and Hubble Key Project value of h degeneracy

14. Cosmo – Tahoe – September 2006 Defect degeneracy v. BBN & HKP 68% 95% 68% 95% WMAP 1yr + BBN + HKP Detection of textures removed by BBN & HKP priors f d,10 < 13% (95%)

15. Cosmo – Tahoe – September 2006 String CMB from field theory C l s for cosmic strings using field evolution simulations (astro-ph/0605018) c.f. Wyman et al. (2005, Err 2006) using moving segment model c.f. global texture c.f. data: 3 year WMAP Normalised to l=10 Cosmic strings (Wyman et al.) Cosmic strings (Bevis et al.) Global textures (Bevis et al.)

16. Cosmo – Tahoe – September 2006 WMAP 3 rd 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

17. Cosmo – Tahoe – September 2006 MCMC with “all” CMB data Strings are favoured by the data - 2 sigma detection! 68% 95%

18. Cosmo – Tahoe – September 2006 MCMC with WMAP3 data Strings are favoured by the WMAP3 data, at between 1 and 2 sigma level 68% 95%

19. Cosmo – Tahoe – September 2006 WMAP - why strings?

20. Cosmo – Tahoe – September 2006 WMAP - why strings?

21. Cosmo – Tahoe – September 2006 WMAP - why strings?

22. Cosmo – Tahoe – September 2006 “All” CMB + BBN + HKP WMAP 3 rd 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)

23. Cosmo – Tahoe – September 2006 “All” CMB + BBN + HKP “all” CMB “all” CMB + BBN + HKP

24. 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)

25. Cosmo – Tahoe – September 2006 Polarization

26. Cosmo – Tahoe – September 2006 Polarization Tensors @ r=0.3 EE lensed

27. 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)

28. COSMO 2007 University of Sussex, Brighton, U.K. August 21-25 2007 University of Sussex, Brighton, U.K. August 21-25 2007