Forecast constraints on cosmic strings from future CMB, pulsar timing and gravitational wave direct detection experiments

Sachiko Kuroyanagi Univ. of Tokyo

RESCEU (RESearch Center for the Early Universe)

12 Nov 2012Based on

S. Kuroyanagi, K. Miyamoto, T. Sekiguchi, K. Takahashi, J. Silk, PRD 86, 023503 (2012) + arXiv:1210.2829 [astro-ph]

Cosmic string？One dimensional topological defect

generated in the early universe

2: Cosmic superstrings

Generation mechanism

→ could provide some insight into fundamental physics

1: Phase transition

Cosmological size D-strings or F-strings remains after inflation

spontaneous symmetry breaking

Cosmic strings become loops via reconnection.

Scaling law

Loops lose energy by emitting gravitational waves.

Evolution of cosmic strings

Cosmic String Networks approach a self-similar solution, which always looks same at the Hubble scale.

energy density

a: scale factor

∝a-4

∝a-3

∝a-2 X

Cosmic strings

The energy density of cosmic strings ∝a-2 ?

Observational Probe

1. Direct detection Ground：Advanced-LIGO、KAGRA、

Virgo、IndIGO (2017-)

Space：eLISA/NGO (2022?)、DECIGO (2027)

eLISA image (http://elisa-ngo.org/)

KAGRA image (http://gwcenter.icrr.u-tokyo.ac.jp/)

2. Pulsar timing : SKA (2020)

PTA image (NRAO)

3. CMB temperature fluctuation +B-mode polarization : Planck, CMBpol

DECIGO image, S. Kawamura et al, J. Phys.: Conf. Ser. 122, 012006 (2006)

Current constraints on cosmic string parameters

・CMB temperature fluctuation: Gμ<~10-7

Pulsar timing: Gμ<~10 -9

Direct detection (LIGO GWB): Gμ<~10-6

3 parameters to characterize cosmic string

・Gμ(= μ/Mpl2)：tension (line density)

・α：initial loop size L～αH-1

・p：reconnection probability

for loopsα=0.1, p=1

What about future constraints？

for infinite strings・Gravitational lensing: Gμ<~10-6

・Gravitational waves

Phase transition origin: p=1Cosmic superstring: p<<1

Gravitational wave signalsStrong GW emission from singular points

called kinks and cusps

kink cusp

Gravitational wave background (GWB): superposition of small GWs coming from the early epoch

Rare Burst: GWs with large amplitude coming from close loops

→ direct detection + pulsar timing

→ direct detection

Gμ=10-7, α=10-16, p=1

How many cosmic string bursts are coming to the earth per year?(plotted as a function of the amplitude for the fixed frequency @220Hz)

← amplituderate

(pe

r ye

ar) →

Gμ=10-7, α=10-16, p=1

How many cosmic string bursts are coming to the earth per year?(plotted as a function of the amplitude for the fixed frequency @220Hz)

← amplituderate

(pe

r ye

ar) →

LIGO～220Hz

220 oscillations per second= 7×109 oscillations per year

Gμ=10-7, α=10-16, p=1

GWB

small amplitudebut numerous

Gμ=10-7, α=10-16, p=1

How many cosmic string bursts are coming to the earth per year?(plotted as a function of the amplitude for the fixed frequency @220Hz)

rate

(pe

r ye

ar) →

← amplitude

LIGO～220Hz

220 oscillations per second= 7×109 oscillations per year

Gμ=10-7, α=10-16, p=1

GWB

Gμ=10-7, α=10-16, p=1

How many cosmic string bursts are coming to the earth per year?(plotted as a function of the amplitude for the fixed frequency @220Hz)

← amplitude

LIGOh～10-25@ f ～220Hz

rate

(pe

r ye

ar) →

GWB

Gμ=10-7, α=10-16, p=1

How many cosmic string bursts are coming to the earth per year?(plotted as a function of the amplitude for the fixed frequency @220Hz)

← amplitude

LIGOh～10-25@ f ～220Hz

rare burst

rate

(pe

r ye

ar) →

GWB

Gμ=10-7, α=10-16, p=1

How many cosmic string bursts are coming to the earth per year?(plotted as a function of the amplitude for the fixed frequency @220Hz)

← amplitude

LIGOh～10-25@ f ～220Hz

rare burst

distant (old)

near (new)

rate

(pe

r ye

ar) →

Parameter dependences of the rateGμ↑

α↓

p ↓ number density ↑

lifetime↓ number density ↓

amplitude of GWs ↑

GW power

Γ: numerical constant ～50-100

（initial loop energy）（energy release rate per time）

Lifetime of loops ＝

lifetime↓ number density ↓

＝

Parameter dependences of the rateGμ

α

p

The parameter dependences of the large burst (rare burst) and small burst (GWB) are differentbecause they are looking at different epoch of the Universe

→ give different information on cosmic string parameters

GWB

rare burst

Gμ

α

p

frequency frequency

frequency

frequency

Spectrum of the GWB

Accessible parameter region (for p=1)

dotted：Burst

solid：GWB

dotted：Burst

solid：GWB

Advanced-LIGO can detect both rare bursts and GWB

★Gμ=10-7, α=10-16, p=1

black ：Burst only

red：Burst + GWB

Example: Gμ=10-7, α=10-16, p=1Adv-LIGO 3year

Constraint from direct detection experiments

Kuroyanagi et. al. PRD 86, 023503 (2012)different parameter dependence= different constraints on parameters

log10 Gµ

log10

-7.05

-7

-6.95

-16.2 -16 -15.8

log10

log10 p

-16.2

-16

-15.8

-0.08 -0.06 -0.04 -0.02 0

log10 Gµ

log10 p

-7.05

-7

-6.95

-0.08 -0.06 -0.04 -0.02 0

Before marginalized over

Strong degeneracy seen in constraint from GWB

since the observable is only ΩGW

Kuroyanagi et. al. arXiv:1202.3032

black ：Burst only

dotted: GWB only

red：Burst + GWB

Kuroyanagi et. al. PRD 86, 023503 (2012)

Example: Gμ=10-7, α=10-16, p=1Adv-LIGO 3year

Constraint from direct detection experiments

Signals in the CMBB-mode polarizationtemperature fluctuation

Gμ Gμ

p p

black : LIGO Burst onlyred : LIGO Burst + GWB

blue: LIGO +Planckgreen: LIGO+CMBpolorange: CMB pol only

Gμ=10-7, α=10-16, p=1Adv-LIGO 3year + CMB B-mode

If we combine CMB constraints...

Kuroyanagi et al. arXiv:1210.2829

Constraints from pulsar timing and space direct detection mission

frequency

ampl

itude

of G

WB

inflationcusps on loops kinks on infinite strings

cosmic string

pulsar timing

direct detection

oldnew

observing GWs from different epochs

dotted：Burst

solid：GWB

Pulsar timing (SKA) + Advanced-LIGO burst search

★Gμ=10-9, α=10-9, p=1

Direct detection + Pulsar timing Gμ=10-9, α=10-9, p=1Adv-LIGO 3year (burst only)

+ SKA 10year Kuroyanagi et al. arXiv:1210.2829

Parameter constraint by eLISA Gμ=10-9, α=10-9, p=1eLISA 3year(burst only)

Kuroyanagi et al. arXiv:1210.2829

Summary• Future CMB and GW experiments can be a powerful tool to

probe cosmic strings.

• If signals are detected, it would determine cosmic string parameters, which can provide us with hints of fundamental physics such as particle physics or superstring theory.

• Two different kinds of GW observation (rare burst and GWB) provide different constraints on cosmic string parameters and lead to better accuracy in determining parameters.

• Combination of different experiments (CMB, Pulser timing, direct detection) also helps to get stronger constraints.

• Space GW missions are more powerful to prove cosmic strings.

Initial number density of loops

Estimation of the GW burst rate

depends on α and p

Evolution of infinite strings・velocity-dependent one-scale model

energy conservation

energy discarded to loopsfor small p: c → cp

＝（length of infinite string discarded to loops）

(initial length of loops = αti）

length L, velocity v

random walk of straight strings

acceleration due to the curvature of the strings

damping due to the expansion

momentum parameter:

i

GW power

Initial loop length＝

（initial loop energy）（energy release rate per time）Lifetime of the loop ＝

loop evolution

Γ: numerical constant ～50-100

＝

Loop length at time t

（energy of loop at time t =μl） ＝（initial energy of the loop =μαti）ー（enegry released to GWs =PΔt）

From the energy conservation law

ti： time when the loop formed

Estimation of the GW burst rate

i

depends on Gμ and α

GW burst rate emitted at t～t+dt from loops formed at ti～ti+dti

θm

Beaming

∝(loop length at t)1/3

∝(loop length at t)-1Time interval of GW emission Loop number

GW amplitude from loop of length l

Estimation of the GW burst rate

Generation mechanism 1: phase transitionThe Universe has experienced symmetry breakings.

If you consider U(1) symmetry breaking...

High energy vacuum remains at the center

π

π/2π/2

3π/2

3π/2

3π/2

ππ

0

0

Hubble volume= causal region

03π/2

π/2π

Tension Gμ~ the energy scale of the phase transition

Cosmological size D-strings or F-strings remains after inflation in superstring theory

→ Cosmic strings could give some insight into fundamental physics

Difference from phase transition origin・low reconnection probability (p) because of the extra dimension

D-string: p=0.1-1F-string: p=10-3-1

・broad values of Gμ depending on the inflation scale and the extra

internal degrees of freedom(・Y-junction　・mixed strings with different Gμ)

Phase transition origin: p=1

Generation mechanism 2: Cosmic superstrings

Cosmic strings become loops when they collide and form a network composed by loops and infinite strings

Scaling law

Loss of infinite string length by generation of loops

Loops lose energy by emitting gravitational waves and shrink

Evolution of cosmic strings

Increase of infinite string length by the Hubble expansion

Higher reconnection rate more efficient generation of loops

more energy release by the emission of GWs

Evolution of cosmic strings

energy density

a: scale factor

∝a-4

∝a-3

∝a-2

The network keeps O(1) number of infinite strings in the Hubble horizon

X

α：initial loop size L～αH-1

p：reconnection probability

→ cosmic strings does not dominate the energy density of the Universe.

Initial number density of loops

Loop number generated per unit timeTo satisfy the scaling law, infinite strings should lose O(1) Hubble length per 1 Hubble time. So they should reconnect O(1) times per Hubble time

To reconnect O(1) times per Hubble time, number of infinite strings per Hubble volume should be ~ p-1

→total length of infinite strings ~p-1H-1~p-1t

Number of loops＝

N =p−1t

αt=

1pα

（length to lose）(initial length of loops）

L~H-1

V~H-3

Estimation of the GW burst rate

Fisher information matrix

Burst

log(Likelihood)

αー

N

h

Observable：amplitude vs number

N is predictable by the rate dR/dh

If  the  likelihood  shape  is  sensi5ve  to  the  parameter        =  easy  to  es5mate  the  parameter

Constraint on parameters

Constraint on parametersFisher information matrix

GWB Observable：ΩGW

log(Likelihood)

αー

If  the  likelihood  shape  is  sensi5ve  to  the  parameter        =  easy  to  es5mate  the  parameter