2015/04/07 EHQG seminar@Nagoya U.

Cosmic strings andtheir future detectability
YAMAUCHI, Daisuke
Research Center for the Early Universe (RESCEU),
U. TokyoCosmic strings… are something likerubber bands, which
 Are 1-dimensional objects

 Have a tension
 Are VERY USEFUL!

Cosmic strings… are something likerubber bands, which
 Are 1-dimensional objects

 Have a tension
 Are VERY USEFUL!
Hiramatsu+Sendouda+Takahashi+DY+Yoo,
1307.0308

Cosmic strings
Phase transition
Scalar field settles down
to true vacuum due toHubble friction
Strings begin to appear
Hiramatsu+Sendouda+Takahashi+DY+Yoo,
1307.0308

[Exercise 1]
V[φ]Field space
Since the correlation cannot establish
on scales greater than the causal horizon,
the sign must be randomly chosen!

-φ0+φ0φy
Plus!
Minus!

Real spacex

[Exercise 1]V[φ]-φ0+φ0Field space

φPlus!
Minus!

Real space

[Exercise 2]
V[φ]Field space The phase θ must berandomly chosen.

-φ0+φ0φ2 φ1+iφ2=φ0eiθ

φ1yθ=πReal space

θ=0x
θ=3π/2

[Exercise 2]
V[φ]Field space The phase θ must be
randomly chosen.

-φ0+φ0φ2 φ1+iφ2=φ0eiθ

φ1yθ=πReal space

θ=0x
θ=3π/2

COSMIC STRING Inner structure～1/myx[Nielsen+Olsen (1973)]

String tension: energy-density per unit lengthμ～(phase transition energy)2

Why are cosmic strings still interesting?

Cosmic strings have a potential to reveal
the high-energy physics during phase transition!
For GUT scale…

GN μ = 10-6 (μ/(10-3Mpl)2)

Contents
1.Introduction
2.Basic properties String network dynamics
 Reconnection
 String gravity

3.Observational prospects
4.Discussion

comoving box

Question1
How does string
network evolve?
 Comoving : Lstr∝a(t) ?
 Scaling: Lstr∝1/H(t) ?
 Anything else ?

Hubble length whensimulation starts.
Hiramatsu+Sendouda+Takahashi+DY+Yoo, 1307.0308

Q1 : How does a string network evolve?

正解
Comoving evolution

Scaling evolution

不正解Scaling
t=t2

t=t1

1/H(t1)
1/H(t2)
 Number of strings inside the Hubble volume is always O(1)!
 Length of a string is always given by Hubble length 1/H.

ScalingL∝η∝1/H[Hiramatsu+DY+Yoo+, 1307.0308]

L∝η∝1/H

Scaling is the stable attractor!
Scaling is the general property!
Normalized conformal time η

Normalized conformal time η Number of strings inside the Hubble volume is always O(1)!
 Length of a string is always given by Hubble length 1/H.

Normalized correlation length

Normalized correlation length[Bevis+, 1005.2663]

Scaling～1/H(t) ～1/H3(t)ρstring(t)ρcr(t)
Energydensity=μ×L(t)×nstring (t)(3/8πGN)H2(t)～ GNμ = const.

 Cosmic strings do not dominate thesubsequent Universe due to their latetime evolution.
 Scaling behavior is an attractor solution.

ρcrρstringtime

Q2 : What happens when 2 strings collide?
正解
reconnection
pass-through不正解[cf. Salmi+, 0712.1204]

Reconnection
Reconnection almost
always happens! (P～1)
But in some case,a junction may form:[Hiramatsu+DY+Steer, in progress]

Loop formation and energy loss
When a string crosses itself, a loop separate from the string.
The energy of long strings is converted into small string loops,
which eventually shrink due to GW & scalar radiation.

String gravity
The nonvanishing energy-momentum
tensor, Tαβ, modifies the spacetime
metric gαβ through the Einstein eq.
For static straight sting lying along z-axis,

T 00 = T zz = μ δ2(x-xstr)
Txx = Tyy = 0[Vilenkin (1981)]

[Vilenkin (1981)]

Conical structure
The spacetime around a straight cosmic string is “locally” flat.

[Vilenkin+Shellard textbook]

An angular wedge of width Δ=8πGμ is removed fromthe space and the remaining edges identified.

Take-home message
 We can obtain the robust predictions because…

1. Scaling

2. Reconnection

3. Conical structure

SOME LOOPHOLES[Lazarides+Shafi(1984), Shafi+Vilenkin(1984), Yokoyama (1988),…]When do strings form?
Scaling starts.
Inflation era

Radiation dominated era
Strings form.

Standard cosmic strings are produced at thephase-transition during radiation-dominated era.
The scaling can be achieved just after
the formation.

[Lazarides+Shafi(1984), Shafi+Vilenkin(1984), Yokoyama (1988),…]When do strings form?
Strings form.
Inflation era
They are diluted and the meanseparation expands exponentially
until end of inflation.

Scaling starts.
Radiation dominated era
The network enters the scaling regime
at the later epoch because L>>1/H andthe collision cannot occur.

[Lazarides+Shafi(1984), Shafi+Vilenkin(1984), Yokoyama (1988),…]When do strings form?
Strings form.
Inflation era
They are diluted and the mean
separation expands exponentially
until end of inflation.

Scaling starts.
Radiation dominated era
The network enters the scaling regime
at the later epoch because L>>1/H andthe collision cannot occur.

Cosmic superstrings :Observable remnants of string theory
 Fundamental strings, which are elementary objects in string
theory, could stretch to macroscopic scale by the expansion ofthe Universe (without suffering instability).
Stringy inflation
D-branes

anti D-branes

Same as cosmic strings
Strings form.

[original:Witten(1985)] [Sarangi+Tye(2002), Jones+(2003), Dvali+Vilenkin(2004)]

Cosmic superstrings :Observable remnants of string theory
 There are several differences from the standard cosmic strings:
 Reconnection probability P

For standard strings

P～1P

For cosmic superstringsP << 1 Appearance of bound states Multiple tension network
…
[original:Witten(1985)] [Sarangi+Tye(2002), Jones+(2003), Dvali+Vilenkin(2004)]

Contents
1.Introduction
2.Basic properties String network dynamics
 Reconnection
 String gravity

3.Observational prospects
4.Discussion

Observational prospects for stringsCosmic Microwave BackgroundGravitational waves

Weak/strong gravitational lensing
21cm line
…

Observational prospects for stringsCosmic Microwave BackgroundGravitational waves

Weak/strong gravitational lensing
21cm line
…

Observational prospects for stringsCosmic Microwave BackgroundGravitational waves

Weak/strong gravitational lensing
21cm line
…

Cosmic strings on the CMB skystring[Planck(2013)XXV]

Simulated CMB sky from only cosmic strings(δT/T)/GμCMB temperature anisotropies

string

WARM

Cosmic strings create line-like
discontinuities in the CMB signal(through Integrated Sachs-Wolfe).
[Kaiser+Stebbins (1984), Gott III(1985)]

COLDPlanck(2013)XXV[For curved strings, DY+, 1004.0600,
For kinks/cusps, Takahashi+DY+, 0811.4698]

[For curved strings, DY+, 1004.0600]

CMB temperature anisotropies
Last scattering surface

Doppler
shiftidentify

Cosmicstring As the string moves acrossthe line of sight, the CMB
photons are boosted
towards the observer.

A relative CMB temp
shift across the string[Kaiser+Stebbins (1984), Gott III(1985)]

Delayed scaling scenario

Cosmic superstrings[Kamada+DY+, 1407.2951][DY+, 1006.0687]

Gμ=3×10-7

standard
delayedMultipole moment lPower spectrum l(l+1) ClTT/2π

Power spectrum l(l+1) ClTT/2π

CMB temperature power spectrum

Multipole moment l

The observations of the acoustic oscillation in the CMB haveexcluded strings as the dominant source of the CMB anisotropies:

GNμ < 1.3×10-7 (95%CL, P=1) [Planck(2013)XXV]

[DY+Sendouda+Takahashi, 1309.5528]

Detectability from future CMB obs.
(1) String-induced temprature 3-point functions= (SSS-type) + (PS-type) + (SP-type)
Planck(2013)
bispectrum
Planck(2013)
power spectrum[contour of (S/N)=1]

[DY+Sendouda+Takahashi, 1309.5528]

Detectability from future CMB obs.
(1) String-induced temprature 3-point functions= (SSS-type) + (PS-type) + (SP-type)

We could detect
the superstring-induced
bispectrum with GNμ~10-8Planck(2013)
bispectrumPlanck(2013)
power spectrum

GNμ~10-7 for standard
cosmic strings[contour of (S/N)=1]

[Kamada+Miyamoto+DY+Yokoyama, 1407.2951]

Detectability from future CMB obs.
(2) String-induced B-mode polarization
The presence of delayed-scaling strings improves the fit tothe BICEP2+POLARBEAR data, although more data are required.

δχ2=-9 [+2dof][Namikawa+DY+Taruya, 1205.2139, 1308.6068]

Detectability from future CMB obs.
(3) String-induced CMB lensing:can provide a evidence for the intervening strings
along a line of sight by measuring the spatial patternsof the deformation of the photon path.

Foreground cosmic strings

Primary CMB map@last scattering surface

[Namikawa+DY+Taruya, 1205.2139, 1308.6068]

Detectability from future CMB obs.
(3) String-induced CMB lensing
Strings continuously generate vector and tensor pert. evenat late time, which induce the parity-odd mode signal.
Curl mode power spectrum

Planck (current)
GNμ < 3×10-8 (P/10-3)[95%C.L., curl-mode]GNμ = 10-8
P = 10-3 (superstrings)

FutureGNμ < 2×10-9(P/10-3)[(S/N)=1, curl-mode][For parity-even mode for CMB lensing, DY+Takahashi+Sendouda+Yoo, 1110.0556]

Observational prospects for stringsCosmic Microwave BackgroundGravitational waves

Weak/strong gravitational lensing
21cm line
…

Gravitational waves from strings
Oscillating loops of string
can generate a potentiallyobservable GW.
GW burstsignal: GW with shot duration [<1s]∝|t-tc|1/3time

Stochastic background: produced by superposition ofbursts from a string network.

e.g. KAGRA

[LIGO+Virgo collaborations, 0910.5772]

Stochastic background :ΩGW=(1/ρc)dρGW/dlogf

[LIGO+Virgo collaborations, 1310.2384]

ε=(initial loop length)/50GNμConstraints on
tension and initial loop length Note : the amplitude of
GW strongly depends on
the loop distribution.

P=10-3 (cosmic superstrings)

GW burst
search The allowed parameters:(P=10-3 case)GNμ < 10-11(long loop model)

GNμ < 3×10-8(small loop model)

Tension GNμ[For delayed-scaling strings, Deno+DY+Yokoyama, in progress…]

Contents
1.Introduction
2.Basic properties String network dynamics
 Reconnection
 String gravity

3.Observational prospects
4.Discussion

Can we see bound states in a network?
When two (type-I or super-)strings collide, boundstates and Y-junctions would be produced.

• Nearly parallel• Low relative velocity

It is open question whether the (type-I) string network candynamically create the bound states.

But 3-dim simulation requires heavy
computational costs…
 2-dim toy model : Impose translation sym along z-axis
Easy to produce
a bound statez yxmerits••••

Reduce the computational costs
Restrict the spatial degree-of-freedom
Enhance the production rate of bound states
May lead to the maximum fraction of bound stateAnyway, you can see bound states!
Type-I string network in 2-D
simulations have the boundstates!
 The evolution of thenetwork with bound states

 How large is the fraction ofhigher winding strings ?

[Hiramatsu+DY, work in progress…]

Summarytimeformation

evolutionobservation

Cosmic strings are line-like objects, which are expected
to be produced
 at PT after inflation via SSB(for standard ones)
 at PT during inflation via SSB(for delayed-scaling ones)
 at the end of stringy inflation(for superstrings)

Summary
timeformation

evolutionobservation

A cosmic string network has the unique properties:

 Scaling attractor
Reconnection
Conical structure
Thanks to these, we can obtain the robust predictions.

Summary
timeformation

evolutionobservation

The presence of cosmic strings would leave a varietyof traces such as Cosmic microwave background Gravitational waves
 Weak/strong gravitational lensing[DY+Namikawa+Taruya 1205.2139, Yoo+DY+ 1209.0903]

 21cm line [Square Kilometre Array]

FutureModeling for loop distributions• The constraint from GW amplitude strongly
depends on it!

Formulation for strong lensing• E.g. double images

Bound states / Y-junctions• Observational consequence?

Thank you!

Summary
Anyway,…

Cosmic strings are fun!

Direct detection : strong lensing
The string with the deficit angle creates the double
image with the very similar amplitude with a separation
angle of order Gμ.