第6回観測的宇宙論ワークショップ @弘前大学
10:05 - 10:35, 24th. Oct, 2017

モンテカルロ法による宇宙論的観測と整合的な修正重力理論の分類+GW170817& GRB170817Aのインパクト
Shun Arai (Cosmology group in Nagoya University, D1)
Based on Shun Arai and Atsushi Nishizawa in progress.

Outline in this talk・Introduction

・Model extraction based on consistency withcurrent cosmic expansion

e.g. Horndeski theory

・Gravitational Waves (GW) observations
as a probe of Horndeski theory

SA and A.Nishizawa. in preparation

impact of GW170817 &GRB170817A・Summary

Outline in this talk・Introduction

・Model extraction based on consistency withcurrent cosmic expansion

e.g. Horndeski theory

・Gravitational Waves (GW) observations
as a probe of Horndeski theory
impact of GW170817 &GRB170817A

・Summary

Model extraction consistent with current
cosmic expansion

Observations of gravity cosmological scale
redshift

0.1
0.1~1
~2
8~30
1100z

the present universe
New!

cosmic expansion

GW
Type-Ia supernovae
LSS
EoR + small scale issues
CMBInflation
The creation of the universe

HModel extraction consistent with current
cosmic expansion

Observational constraints on cosmic expansion histories
O.Farooq et al. Astrophys. J. 835 (2017)

Simon et al. (2005)
Moresco et al. (2012)
Zhang et al. (2012)

Hobs
' 17%
Hobs
@ z ⇠ 0.1

Model extraction consistent with current
cosmic expansion

Horndeski theory

G. Horndeski, 1974
T. Kobayashi, M.Yamaguchi, and J.Yokoyama 2011

The most generic theory with a scalar whose EoM
contains only up to 2nd order spacetime derivatives.
Z
5X
4 p
SHorn = d xg
Li
i=2L2 = G2 ( , X),

X⌘;µ;µ /2

Model extraction consistent with currentcosmic expansion

α-parameterization
E.Bellini & I.Sawicky JCAP 2014
In ADM formalism

R :3d Ricci scalar↵M↵K↵B↵T

1 dM 2↵M ⌘HM 2 dt

Kineticity of scalar“Braiding” between scalar and tensor
2↵⌘cphase velocity of tensor
TT1Model extraction consistent with current
cosmic expansion

α-parameterization
E.Bellini & I.Sawicky JCAP 2014

Model extraction consistent with current
cosmic expansion

Flow of the model extraction
SA and A.Nishizawa. in preparation

Model extraction consistent with current
cosmic expansion

Set-upSA and A.Nishizawa. in preparation

・time-dependence of (t)nopa22(t) = Mpl H0 a0 + a1 H0 tLB + (H0 tLB )2tLB ⌘Z z
0a0 ⌘ 0dz 0H⇤CDM (z 0 ) · (1 + z 0 )3

H⇤CDM (z) = H0 ⌦m0 (1 + z) + 1

⌦m0

1/2

・approximation of the Horndeski functions(app)
Gi, X, X,2gi⇢ , gi⇢ (⇢,=2, X (i = 2, 3, 4, 5)or X)

Model extraction consistent with current
cosmic expansion

Criteria for model extraction
SA and A.Nishizawa. in preparation

1. Consistency|1

H/H⇤CDM | <Hobs /Hobs

Hobs⌘ 20%
Hobs

2. Stability

Avoiding ghost and gradient instabilities. i.e. Q > 0, c > 0
2

for a quadratic action asS(2)

=Z

3

dtd x

X

=scalar,tensor

Q ˙

22c (@ )2

Outline in this talk・Introduction

・Model extraction based on consistency withcurrent cosmic expansion

e.g. Horndeski theory

・Gravitational Waves (GW) observations
as a probe of Horndeski theory
impact of GW170817 &GRB170817A

・SummaryGW observation as a probe of Horndeski theory

Modification of GW propagation
I. D. Saltas et. al PRL 2014
A.Nishizawa arXiv:1710.04825

0002 22 22hij + (2 + ⌫)Hhij + (cT k + a µ )hij = a⌫time variation of theeffective Planck mass

ij

time dependent gravitational couplingcTpropagation speed of GW

Lorentz symmetry/Equivalence principleµgraviton mass

massive gravity (Shinji-Mukohyama’s talk)additional sources of GW

Non-minimal coupling with other fields

GW observation as a probe of Horndeski theory

Solution of modified GW propagation
at cosmological scale

A.Nishizawa arXiv:1710.04825

Source-less system=0solutions that alters in cosmological time scale:h = CMG hGR CMG ⌘ e D e ik T
1D⌘2amplitudephaseT ⌘Z ⌧d⌧0Z ⌧⇢(1d⌧ 0 ⌫HcT )⌧ : conformal time

a2 µ2
2k 2

luminosity distancearrival time difference
e.g. GW and GRBGW observation as a probe of Horndeski theory

α & cT in Horndeski theory
E.Bellini & I.Sawicky JCAP 2014M⇤2 (z) ⌘ 2(G4⌫⌘
cT22d ln M⇤d ln a2XG4X + XG5

˙ HXG5X )dt = ad⌧dAȦ ⌘dt= ↵M (z)1 ⌘ ↵T =⇣2XM⇤2

H = H/a2G4X

2G5(¨˙ H)G5X⌘・in GR, ⌫ = 0 cT = 1・ G4 or G5 themselves can achieve accelerating universe“self acceleration” L.Lombriser & A.Taylor, JCAP 2016

・GW properties are only involved with G4 and G5

GW observation as a probe of Horndeski theory

Different expansion histories
SA and A.Nishizawa. in preparation

GW observation as a probe of Horndeski theory

Model distribution
SA and A.Nishizawa. in preparation

GW observation as a probe of Horndeski theory

Impact of GW170817 & GRB170817A
APJLett. 848:L13 2017

GW observation as a probe of Horndeski theory

Observational bounds from GW (preliminary)
10

SA and A.Nishizawa. in preparation

010-1

|D|
|D|

10-3

10-4

Permitted

10-2

10-5

10-6

10-7 -16
10G4,G5 only
+G2+G2 small+G3Cov.Gal
10-14

10-12

10-10

10-8
|∆T|

10-6

10-4

10-2100

Summary

Summary of my talk・We developed the numerical formulation to classify themodels in the Horndeski theory based on α parameterization.
・Applying our method to GW observation, we obtain thedistributions of the models in αT-αM plane.
・Considering the current observation of GW170817
and GRB170817A, the Horndeski theory hardly accountfor cosmic acceleration and GW propagation at thesame time.

comments : quintessence or f(R) gravity survive so far!

Back UpGW observation as a probe of theories of gravity

Self Acceleration

SHorn =Z

22pM⇤ (t)cT (t)4d xgR + ...
2⌦(t)in the language of the EFTdM⇤2⌫⌘ 2M⇤ H dt
1G.Gubitosi et al. 2013 J.Gleyzes et al. 2013

N.B 1. We here use the notation as same as EFT of DE.
N.B 2. This way of acceleration is ONLY seen in the Jordan frame.

˙⌦(t)&1H⌦(t)L.Lombriser & A. Taylor JCAP 2016

Lombriser & Taylor 2016
L.Lombriser & A.Taylor JCAP 2016˙⌦(t)&1H⌦(t)˙⌦(t)↵˙ T= ↵M +H⌦(t)
H(1 + ↵T )They carefully consider models thathave non-linear screening mechanism
but still give general discussion ofHorndeski theory