CMB, phase transition, modified gravity

Rikkyo University

Takashi Hiramatsu

Gasshuku, 7-9 Sep 2016 @ Miura-Kaigan

2/39CMB bipectrum

UTAP (prof. Suto) → RESCEU (1yr) → ICRR (2yr) → YITP (6.5yr) → Rikkyo (now)

Career

3/39CMB bipectrum

UTAP (prof. Suto) → RESCEU (1yr) → ICRR (2yr) → YITP (6.5yr) → Rikkyo (now)

Career

Experiences

24 Sep 2007 : Northernmost point in Japan26 Nov 2010 : Westernmost point in Japan27 Nov 2010 : Southernmost point in Japan20 Sep 2011 : Easternmost point in Japan08 Dec 2012 : Conquered all prefectures

4/39CMB bipectrum

UTAP (prof. Suto) → RESCEU (1yr) → ICRR (2yr) → YITP (6.5yr) → Rikkyo (now)

Career

Experiences

15721.5 / 20198.5 km (77.8%)3510 / 4751 stations (73.9%)116 / 202 lines (57.4%)

24 Sep 2007 : Northernmost point in Japan26 Nov 2010 : Westernmost point in Japan27 Nov 2010 : Southernmost point in Japan20 Sep 2011 : Easternmost point in Japan08 Dec 2012 : Conquered all prefectures

Achivement (solely JR)

5/39CMB bipectrum

Research field

CMB

Modified gravity

Large-scale structure

Phase transition

Ryo Saito (YITP)Atsushi Naruko (TITech)Misao Sasaki (YITP)

Kazuya Koyama (Portsmouth)Atsushi Taruya (YITP)

Atsushi Taruya (YITP)

Daisuke Yamauchi (Kanagawa)Daniele Steer (APC)Junichi Yokoyama (RESCEU)Kenichi Saikawa (DESY)Masahiro Kawasaki (ICRR)

CMB bispectrum

Takashi Hiramatsu

Collaboration with Ryo Saito (YITP), Atsushi Naruko (TITech), Misao Sasaki (YITP)

Gasshuku, 7-9 Sep 2016 @ Miura-Kaigan

Rikkyo University

7/39CMB bipectrum

8/39CMB bipectrum

Collision term ofThomson scattering(only for photons)

Dodelson, “Modern cosmology”, (Academic press)Matsubara, “Uchuron no Butsuri” (Tokyo Univ.)

Photon/Neutrino

CDM/Baryon

Photon's Thomson scatteringterm is derived from Boltzmann eq.of baryons.

Gravity

Boltzmann eqs.

Continuity/Euler eqs.

Perturbed Einstein eqs.

9/39CMB bipectrum

Seljak, Zaldarriaga, APJ 469 (1996) 437

suppressed by tight-couplingbetween baryons-photons

directly solving

Line-of-sight formula

10/39CMB bipectrum

CosmoLib : Huang, JCAP 1206 (2012) 012CMBFAST : Seljak, Zaldarriaga, APJ469 (1996) 437CAMB : Lewis, Challinor, APJ538 (2000) 473

CLASS II : Blas, Lesgourgues, Tram, JCAP 1107 (2011) 034existing codes

Rel

ativ

e er

ror

from

CA

MB

(%)

parameters

11/39CMB bipectrum

Tensor TT Tensor TE Tensor EE, BB

All kinds of spectra are consistent to those computed by CAMB with ~1%

12/39CMB bipectrum

LinearBoltzmann eqs.

2nd-order Boltzmann eqs.

Line-of-sight formula CAMB, CMBfast, Class, CosmoLib,...

CMBquick, SONG, CosmoLib2

2nd-orderline-of-sight formula

cmb2nd cmb2nd(future work)

CMBquick : Pitrou, Uzan, Bernardeau, JCAP 07 (2010) 003]SONG : Petinarri et al., JCAP 1304 (2013) 003CosmoLib2 : Huang, Vernizzi, PRL 110 (2013) 101303

13/39CMB bipectrum

Source x ISWSource x LensingSource x Time-delaySource x Deflection

ISW x ISW

ISW x Time-delayISW x Lensing

We find totally 7 combinations that contribute to

[Source] x [gravitational] [ISW] x [gravitational]

TD

L

D

R.Saito, Naruko, Hiramatsu, Sasaki, JCAP10(2014)051 [arXiv:1409.2464]

ISW

Temp. fluc. on LSS

1st-order LOS = [Source on LSS] + [ISW]

14/39CMB bipectrum

e.g. source x lensing

[source] x [gravitational]

15/39CMB bipectrum

Bispectrum templates

Verde et al., MNRAS 313 (2000) L141Gangui et al., APJ 430 (1994) 447

Komatsu, Spergel, PRD63 (2001) 063002

Estimating the magnitude of NG

templatessignals

Komatsu, Spergel, PRD63 (2001) 063002

is detemined by minimising

16/39CMB bipectrum

Local Equilateral Orthogonal Folded

Source x ISW 1.25(-3) 1.24(0) 4.11(-2) 3.93(-1)

Source x Lensing 8.86(0) -4.57(-1) -2.83(+1) 4.35(+1)

Source x Time-delay 2.82(-1) 4.35(-1) -3.45(-1) 6.93(-1)

Source x Deflection 1.82(-2) 1.76(-1) -3.00(-1) 5.27(-1)

ISW x ISW 1.31(-4) 5.19(-2) 1.13(-1) 1.64(-3)

ISW x Lensing 7.63(-2) 1.60(-1) -6.19(-1) 1.01(0)

ISW x Time-delay -1.84(-1) -1.48(-1) 1.33(-1) -2.59(-1)

(Single-template fitting)

- Lensing effect ([Src x Lens] + [ISW x Lens]) dominates as expected.- The whole lensing effect leads to

m309e

17/39CMB bipectrum

Remapping approarch

Neglecting the thickness of LSS

Taylor expansion

Leading contribution to lensing bispectrum

Lensing potential Hu, PRD 62 (2000) 043007

Goldberg, Spergel, PRD 59 (1999) 103002

Zaldarriaga, PRD 62 (2000) 063510

Review : Lewis, Challinor, PR 429 (2006) 1

5 perms.

Last

-sca

tter

ing

surf

ace

CMB lensing

18/39CMB bipectrum

Recovery of remapping approach

5 perms.

Remapping approach

Local Equilateral Orthogonal Folded

Remapping 8.94(0) -2.40(-1) -2.91(+1) 4.48(+1)m309e

Local Equilateral Orthogonal Folded

Curve-of-sight 8.93(0) -2.97(-1) -2.89(+1) 4.45(+1)m309e

We, for the first time, justify the remapping approach as a scheme to estimatethe lensing effect. In the other words, the effect of LSS width is so tiny.

19/39CMB bipectrum

A : Source or ISWB : GravitationalTensor Curve-of-sight

Leading contributions

20/39CMB bipectrum

Source x ISWSource x LensingSource x Time-delaySource x Deflection

ISW x ISW

ISW x Time-delayISW x Lensing

Source x ISWSource x LensingSource x Time-delaySource x Deflection

Source x ISWSource x LensingSource x Time-delaySource x Deflection

ISW x ISW

ISW x Time-delayISW x Lensing

ISW x Deflection

ISW x ISW

ISW x Time-delayISW x Lensing

ISW x Deflection

Totally,we have 7+7+7+8=29 kinds of fNL.

21/39CMB bipectrum

(Single-template fitting)

m320c

PRELIMINARY

Local Equilateral Orthogonal Folded

Source x ISW -2.14(-1) 1.42(-2) 3.69(-1) -5.64(-1)

Source x Lensing -6.65(-1) 1.23(-1) 1.66(0) -2.52(0)

Source x Time-delay -3.68(-2) -1.17(-3) 5.27(-2) -8.17(-2)

Source x Deflection -1.53(-2) -5.50(-2) 1.39(-1) -2.34(-1)

ISW x ISW -1.75(-3) 1.58(-3) 9.20(-3) -1.36(-2)

ISW x Lensing -5.17(-3) -6.34(-3) 3.47(-2) -5.58(-2)

ISW x Time-delay 4.89(-2) 2.24(-3) -5.00(-2) 7.79(-2)

22/39CMB bipectrum

(Single-template fitting)

m320c

PRELIMINARY

Local Equilateral Orthogonal Folded

Source x ISW 3.38(-7) -3.32(-5) -1.34(-5) 8.46(-6)

Source x Lensing 1.09(-5) 2.71(-4) 2.31(-5) 6.40(-5)

Source x Time-delay 6.05(-5) 4.03(-5) -3.95(-5) 7.57(-5)

Source x Deflection 4.34(-9) -3.40(-5) -6.80(-6) -1.98(-6)

ISW x Lensing 1.32(-3) -3.09(-2) -2.45(-2) 2.65(-2)

ISW x Time-delay -1.12(-4) -3.53(-4) 1.57(-4) -3.72(-4)

ISW x Deflection -9.25(-5) 3.62(-3) 2.96(-3) -3.24(-3)

23/39CMB bipectrum

(Single-template fitting)

m320c

PRELIMINARY

Local Equilateral Orthogonal Folded

Source x ISW 1.16(-7) 6.96(-7) -4.67(-6) 7.47(-6)

Source x Lensing -8.31(-7) -1.97(-5) -3.01(-6) -2.59(-6)

Source x Time-delay -1.60(-5) -3.91(-7) 1.43(-5) -2.22(-5)

Source x Deflection 3.00(-7) 4.66(-5) 7.52(-6) 5.52(-6)

ISW x ISW -6.39(-5) -6.39(-4) 7.63(-4) -1.41(-3)

ISW x Lensing -7.64(-5) 1.36(-3) 1.02(-3) -1.07(-3)

ISW x Time-delay 1.39(-5) 5.79(-5) -1.77(-4) 2.94(-4)

ISW x Deflection 1.80(-5) -3.59(-3) -1.82(-3) 1.50(-3)

24/39CMB bipectrum

(Single-template fitting)

m320c

PRELIMINARY

Local Equilateral Orthogonal Folded

Scalar x Scalar 9.05(0) 1.46(0) -2.94(+1) 4.59(+1)

Scalar x Tensor -8.89(-1) 7.83(-2) 2.21(0) -3.39(0)

Tensor x Scalar 1.18(-3) -2.74(-2) -2.14(-2) 2.30(-2)

Tensor x Tensor -1.25(-4) -2.78(-3) -2.04(-4) -7.07(-4)

25/39CMB bipectrum

New CMB Boltzmann code implemeting 'curve'-of-sight formulas

* 1st-order scalar and tensor are completed. (TT, TE, EE, BB)

* Different schemes from CAMB, but consistent within O(1)%

* Implemented “curve”-of-sight formulas (2nd-order line-of-sight) for scalar and tensor temperature fluctuations.

* Implemented Komatsu-Spergel bispectrum estimator.

* Implemented 2nd-order equations only for gravity and matter. (skipped today)

* Implemented remapping approximation.

26/39CMB bipectrum

- Implement pure 2nd-order Boltzmann equations for radiation (cf. SONG, CosmoLib2)

- Implement the curve-of-sight formulas for polarisation

- 2nd-order gravitational waves, magnetic field from [1st-order]2

- y-distortion to photon's distribution function ?

To-do

Applications ?

SONG : Petinarri et al., JCAP 1304 (2013) 003CosmoLib2 : Huang, Vernizzi, PRL 110 (2013) 101303

e.g. Saga et al., PRD 91 (2015) 024030 Saga et al., PRD 91 (2015) 123510

Cosmic strings coupled with scalar matter field

Takashi Hiramatsu

Collaboration with Daisuke Yamauchi (RESCEU), Daniele Steer (APC)

Gasshuku, 7-9 Sep 2016 @ Miura-Kaigan

Rikkyo University

28/39

Vacuum I

GUT ?

Temerature fall

Standard model

GUT transition Electroweak transition

Now

Vacuum II

29/39

Cosmic strings

Solitonic objects associating with the phase transitions, whose interior is occupied by the false vacuum.

0-dim : monopole1-dim : cosmic string2-dim : domain wall

could give a clue of GUT ? could be a probe for the baby Universe

TH, Kawasaki, Saikawa, PRD 85 (2012) 105020 etc.

TH, Eto, Kamada, Ookouchi, Kobayashi, JHEP01 (2014) 165

TH et al., PRD 88 (2013) 085021

TH, Kawasaki, Takahashi, JCAP 06 (2010) 008

cosmological evolution of TD network

- Type-I cosmic strings network- Axionic strings (by Saikawa)- Charge distribution of Q-balls

- Constraint on supersymmetric models based on dynamical simulations- Superconducting strings

colliding string simulations

31/39Cosmic strings with matter

Network simulation with thermal effecfts

Simulation of colliding strings

32/39Cosmic strings with matter

* Its realisability and observability in cosmological context is discussed by Witten.

Model Lagrangian

another scalar field

Witten, NPB 249 (1985) 557

Conserved corrent :

33/39Cosmic strings with matter

Field equations

Axially-symmetric case

Solve them as 1-dim boundary-value problem with CGS+SOR

self-coupling of

self-coupling of

effective mass of

:

:

:

:

depend on

winding number :

34/39Cosmic strings with matter

- Prepare 2 stable straight strings.- Lorentz boost (velocity+rotation)- Embedding them to simulation box with some separation so that superposition is justified :

- Leap-Frog scheme- 2nd-order finite difference- Grid size :

Strategy

Numerical methods

35/39Cosmic strings with matter

36/39Cosmic strings with matter

In some cases, the current promotes for strings to be bounded.

Superconducting No currents

m445c m706c

37/39Cosmic strings with matter

x-bridge blowed-up undistinguishable

38/39Cosmic strings with matter

“Really” stable pairs

Dynamically-unstable

pairs

Parallel-Parallel Parallel-Antiparallel

39/39Cosmic strings with matter

* Not all cases are safe the SS network cannot be well developed ? * If developed, the network contains a variety of strings, condensed, non-condensed, and bounded strings. * If bound states are popular and doubly-reconnection takes place well, the network is prevented from scaling ?

* Vacuum D is really responsible for the stability of the 'bridge' ?

Discussion

To-do