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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