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

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