Gravitational Waves from Topological Defects Richard Battye Jodrell Bank Centre for Astrophysics University of Manchester in collaboration with Sotiris Sanidas & Ben Stappers Horizon size GW (BATTYE & SHELLARD 1997) Sources of Primordial Gravitational Waves (BATTYE & SHELLARD 1997) Sources of Primordial Gravitational Waves EPTA/ NanoGRAV e- Planck (BATTYE & SHELLARD 1997) Topological defects Symmetry Breaking Transition : G -> H π0(G/H) ≠ I Domain Walls π1(G/H) ≠ I Cosmic strings π2(G/H) ≠ I Monopoles π3(G/H) ≠ I Textures Symmetry can be global or local Strings in the Abelian-Higgs Model LAGRANGIAN : VORTEX FIELD CONFIGURATION MASS / UNIT LENGTH CORE WIDTH VORTEX FIELD CONFIGURATION Gravitational effects - all proportional to Gµ CMB anisotropies - ΔT/T ~ Gµ Gravitational Waves 2 2 - hGW ~ Gµ or Ωgh ~ (Gµ) ``Naturalness’’ ! INFLATION CMB NORMALIZATION eg. ! STRINGS (AND OTHER TOPOLOGICAL DEFECTS) GUT SCALE PHASE TRANSITION If strings form at a GUT scale phase transition then THEY AUTOMATICALLY HAVE THE RIGHT AMPLITUDE OF CMB ANISOTROPIES They may also be a signature of string theory ! (LINDE 1994, Hybrid Inflation COPELAND et al 1994) INFLATON DIRECTION DESTABILIZED AT PHASE TRANSITION & FORMATION OF STRINGS Nambu String Simulations LINE APPROXIMATION : - IMPOSE RECONNECTION - IGNORE RADIATION CONFIRMS THE SCALING ASSUMPTION MAKE MEASUREMENTS OF - CORRELATION LENGTH - SMALL SCALE STRUCTURE (STRING WIGGLES) - LOOP PRODUCTION & DISTNS - UETC (UNEQUAL TIME CORRELATOR) (ALLEN & SHELLARD 1990) CMB anisotropies from strings USM STRING SPECTRUM DESCRIBING NAMBU SIMULATIONS (POGOSIAN ET AL, BATTYE ET AL) SPECTRUM FROM A-H SIMULATIONS (BEVIS ET AL) NEITHER LOOK LIKE THE WMAP/PLANCK DATA – CONSTRAIN A SUBDOMINANT COMPONENT ! Planck 2015 results f10 = fractional contribution to C10 NG = Nambu Goto AH = Abelian-Higgs SL = Semi-local strings TX = Textures Constraints on cosmic strings from pulsars -philosophy • There is significant uncertainty: due to lack of detailed understanding of string networks - observers/experimentalists are conservative - they don’t like theories that are moving targets • PGW : sensitive to many more things - loop distribution - radiation mechanism • Modelling v simulations – a quagmire ! • Our philosophy is to be reasonably conservative Present & future constraints on primordial gravitational waves from pulsars GW energy density Strain or amplitude of metric perturbation per log frequency 2 -8 Jenet et al 2006 : Ωgwh < 2 x 10 2 -9 Van Haasteren et al 2011- EPTA : Ωgwh < 5.6 x 10 2 -10 EPTA, NanoGRAV, IPTA – improvements recently published : Ωgwh ~ 5 x 10 2 -12 SKA : Ωgwh ~10 Modelling the string network • Network parameters - ξ = correlation length / t Scaling balance defines the amount - (β = string wiggliness = µeff / µ) of energy lost by the - v = r.m.s. velocity network - (p = intercommutation probability) Change from radiation to matter era • Loop distribution : a number of options - Single loop production size = αt - (Log-normal distribution) - Two sizes = t and t Loop distribution defines α1 α2 the spectral shape Goldstone Boson Radiation (BATTYE & SHELLARD 1994) Lagrangian : where Energy density isosurfaces for a straight string time Goldstone boson radiation Spectrum of radiation, Pn Gravitational Radiation Very similar to Goldstone boson radiation! eg. - GB radiation - Grav radiation Power : where q = 4/3 - cusps & q = 5/3-2 - kinks Timescale for loop decay: Spectrum of Radiation Nambu EOM: Evolution leads to cusps Open question: what are the effects of backreaction EOM becomes- Radiaition also defines Assertion, either : the spectral shape (i) where (ii) q > 2 Cosmic string spectrum (CALDWELL, BATTYE, SHELLARD 1996) Very sensitive to q & n Matter era * loops Radiation era loops frequency Pulsar LISA & timing LIGO Parameters : where BATTYE, GARBRECHT Conservative estimate & MOSS (2006) ! Radiation era spectrum can be computed where ! this is a lower bound of the signal at pulsar frequencies - e-LISA probes this regime with one caveat ! use this to establish a conservative upper bound ! need measured values for Conservative constraint of string tension BATTYE, GARBRECHT & MOSS (2006) (McHUGH ET AL 1996) (JENET ET AL 2006) (Discredited !) (VAN LOMMEN ET AL 2002) Cosmic string spectra : 1 Varying α for fixed Gµ/c2 Varying Gµ/c2 for fixed α Dashed line is α=ΓGµ/c2 Analytic approximation to frequency of maximum signal Cosmic string spectra : 2 Cosmic string spectra : 3 Impact of particle annihilations Pulsars e-LISA Present ultra-conservative limits LIGO α=ΓGµ/c2 EPTA for different (q,n*) n*=1 typically Most conservative Expected LEAP (SANIDAS, BATTYE & STAPPERS 2012) Specific choices of loop production size α Gµ/c2 bound 0.1 6.5 x 10-11 0.05 8.8 x 10-11 0.01 7.0 x 10-10 ΓGµ/c2 5.3 x 10-7 10% 0.1 & 90% ΓGµ/c2 4.1 x 10-8 10-9 1.9 x 10-8 -7 2 Most conservative is 5.3 x 10 when α ~ ΓGµ/c (Using limits from the European Pulsar Timing Array – EPTA in van Haasteren et al 2011) (SANIDAS, BATTYE & STAPPERS 2012) Future limits (SANIDAS, BATTYE & STAPPERS 2013) New EPTA limit (LENTATI et al 2015) Updated limits EPTA NanoGRAV Gµ < 1.3 x10-7 Gµ < 3.3 x10-8 Lentati et al 2015 Arzounmanian et al 2015 e-LISA Worst case scenario String spectrum satuirating NanoGRAV limit Best case scenario .