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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