Modified Gravity after GW170817 - CERN

Taishi Katsuragawa (桂川大志)

Institute of Astrophysics, Central China Normal University

2017/12/25（Mon.）@東京大学本郷

新テラスケール研究会

Modified Gravity after GW170817

(华中师范大学)

Gravitational Wave

Albert Einstein predicted the existence of gravitational waves (GW) in 1916.

2017/12/25 新テラスケール研究会「Modified Gravity after GW170817」桂川大志 2

http://einstein-annalen.mpiwg-berlin.mpg.de/related_texts/sitzungsberichte

Propagate at speed of light

Gravitational Wave



Ripples of space-time

http://einstein-annalen.mpiwg-berlin.mpg.de/related_texts/sitzungsberichte

Detection of Gravitational Wave


‒ Einstein’s final homework (?)

‒ First detection (GW150914)

‒ Announced in 11 Feb. 2016


https://www.youtube.com/watch?v=an-9JHTpiLA

We Did It! ‒ Nobel Prize in physics awarded for discovery of GW, in 2017

New “Window”

We have relied on observations with EM radiation

‒ To provides us with complementary view of the Universe

‒ Neutrinos in recent years

GW is completely different phenomenon

‒ Because GWs interact very weakly with matter, not like EM radiation, it gives us clear view of the Universe

‒ GWs carry information about cosmic events that is not carried by EM radiation

e.g.) Colliding black hole (BH)

‒ GW is new window to observe the Universe


Sources of GWs


ContinuousFrom orbiting binary system or massive spinning object that have steady frequency

StochasticRandom signal by large number of weak and independent sources e.g.) Cosmological background from inflation

BurstGenerated from supernova in short time

InspiralProduced during final stage of binary systems where orbiting pairs of compact objects merge into one

• Binary BH

• Binary neutron star (NS) etc.

[B. P. Abbott et al (2016)]

Detections So Far...


http://www.ligo.org/detections.php

5 binary BH mergers and

1 binary NS merger were detected

GW170817 and Multi-Messenger era

First detection of binary NS

‒ Observed by the LIGO and Virgo detectors on 17 August 2017

First EM counterpart

‒ Gamma-ray burst (GRB 170817A)

‒ Optical astronomical transient (AT 2017gfo)


This GW observation would give us new insights of physics in both matter and gravity sector.

→ EOS in NS, GRB, Astrophysics etc.

What about gravity sector?

→ Testing gravitational theory

→ Constraint on modified gravities

6 pages IntroductionDawn of Multi-messenger era, Test of GR


4 pages Short Review of GW170817EM counter-part, Constraint on GW speed

9 pages Constraint on Modified GravityHorndeski theory, Tensor speed excess

5 pages Future Direction(Personal opinion on) Polarization, Screening Mechanism

Contents

Basic Properties

Chirp mass , mass ratio , spin 𝜒


Low-spin or High spin?

• Chirp mass is well constrained

• Degeneracy b/w mass ratio and spin

[B. P. Abbot et al. (2017)]

Short GRB Detection

Short GRB (GRB 170817A) was detected after GW170817



Deference in arrival time

Δ𝑡 = (+1.74 ± 0.05) [s]

b/w GW and GRB

Distance

𝐷 = 40 [Mpc] ~ 3 × 1015[s]

Speed of GW is very close to that of light

1.7

3 × 1015∼ 10−15

Constraint on Speed of GW

This delay gives us constraint on speed of GW.

Difference in arrival time : Δ𝑡 = (𝐷/𝑐𝑇) − (𝐷/𝑐)


Upper bound: GW is faster, time lag 0[s] → 1.7[s]

Lower bound: GW is slower, time lag 10[s] → 1.7[s]

Assume GRB emitted 0~10[s] after GW

Model Dependence of GRB?

• Lags much longer than 10[s] are proposed

• −100~1000[s] in exotic scenarios?

Constraint on speed of GW


Constraint on Gravitational Theory

In general relativity (GR), speed of GW is same as speed of light

However, alternative theories of gravity predict different scenario


We can convert the constraint on speed of GW into constraint on gravitational theories

‒ So many theories and models...

‒ Quintessence, Brans-Dicke, F(R) gravity, K-essence, Covariant Galileon, f(Gauss-Bonnet) etc.

I review the analysis in Horndeski theory today.






Contents

Dark Energy

The late-time accelerated expansion of the Universe

→ Unknown energy source, called Dark Energy (DE)

The simplest candidate is cosmological constant.‒ Cosmological constant problem

‒ DE is not necessarily cosmological constant (w<-1/3)


Gravity Matter

Modification of gravity sector Modification of matter sector

In both cases, newly introduced modifications explain the late-time acceleration.

Alternative ways to explain dark energy

How to Modify Gravity

GR is unique theory

‒ 4-dimensional space-time

‒ General covariance

‒ Metric theory

‒ Second-order EOM


Need to give up some assumptions,

‒ Higher Dimension

‒ Violation of Lorentz invariance

‒ Add degrees of freedom

• Massive gravity (5 DOF)

• Scalar-Tensor (2+1 DOF)

• Vector-Tensor, Tensor-Vector-Scalar (TeVeS) etc

[Weinberg (1964)], [Lovelock (1971)] etc.

Scalar-Tensor Theory and F(R) Gravity

To add scalar field to GR (Scalar-Tensor theory)


Quintessence [Caldwell, Dave and Steinhardt (1998)]

Brans-Dicke theory [Jordan (1959)], [Brans and Dicke (1961)]

F(R) Gravity [Buchdahl (1970)] etc.

Equivalent

https://texclip.marutank.net/#s=%5Cbegin%7Balign*%7D%0D%0AS%20%3D%20%5Cfrac%7B1%7D%7B2%5Ckappa%5E%7B2%7D%7D%20%20%5Cint%20d%5E%7B4%7Dx%20%5Csqrt%7B-g%7D%20%5Cleft%5B%20%5Cphi%20R%20%0D%0A-%20%5Cfrac%7B%5Comega_%7BBD%7D%7D%7B%5Cphi%7D%20%5Cnabla%5E%7B%5Cmu%7D%20%5Cphi%20%5Cnabla_%7B%5Cmu%7D%20%5Cphi%20%5Cright%5D%0D%0A%5Cend%7Balign*%7D%0D%0A

https://texclip.marutank.net/#s=%5Cbegin%7Balign*%7D%0D%0AS%20%3D%20%5Cfrac%7B1%7D%7B2%5Ckappa%5E%7B2%7D%7D%20%20%5Cint%20d%5E%7B4%7Dx%20%5Csqrt%7B-g%7D%20%5Cleft%5B%20%5Cphi%20R%20%0D%0A-%20%5Cfrac%7B%5Comega_%7BBD%7D%7D%7B%5Cphi%7D%20%5Cnabla%5E%7B%5Cmu%7D%20%5Cphi%20%5Cnabla_%7B%5Cmu%7D%20%5Cphi%20%5Cright%5D%0D%0A%5Cend%7Balign*%7D%0D%0A

Generalization of Scalar-Tensr theory

Many developments in Scalar-Tensor theory,

starting from simple theories to generalized ones


K-essence [Chiba, Okabe, Yamaguchi (2000)]

Kinetic Gravity Braiding [Deffayet, Pujolas, Sawicki, Vikman (2010)]

Covariant Galileon [Deffayet, Esposito-Farese, Vikman (2009)]

→ Generalized Galileon = Horndeski’s theory

[Deffayet et al. (2011)] [Horndeski (1974)]

Horndeski Theory

Horndeski Theory [Horndeski (1974)]


‒ 4 arbitrary functions 𝐺𝑖(𝜙, 𝑋)

‒ The most general scalar-tensor theory which produces second-order EOM

‒ No Ostrogradski instability

https://texclip.marutank.net/s=%5Cbegin%7Balign*%7D%0D%0A%5Cmathcal%7BL%7D_%7B4%7D%20%3D%20G_%7B4%7D(%5Cphi%2C%20X)R%0D%0A%2B%20G_%7B4%2CX%7D%20%5Cleft%5B%20(%5CBox%20%5Cphi)%5E2%20-%20(%5Cnabla_%7B%5Cmu%7D%20%5Cnabla_%7B%5Cnu%7D%20%5Cphi)(%5Cnabla%5E%7B%5Cmu%7D%20%5Cnabla%5E%7B%5Cnu%7D%20%5Cphi)%20%5Cright%5D%0D%0A%5Cend%7Balign*%7D

https://texclip.marutank.net/s=%5Cbegin%7Balign*%7D%0D%0A%5Cmathcal%7BL%7D_%7B4%7D%20%3D%20G_%7B4%7D(%5Cphi%2C%20X)R%0D%0A%2B%20G_%7B4%2CX%7D%20%5Cleft%5B%20(%5CBox%20%5Cphi)%5E2%20-%20(%5Cnabla_%7B%5Cmu%7D%20%5Cnabla_%7B%5Cnu%7D%20%5Cphi)(%5Cnabla%5E%7B%5Cmu%7D%20%5Cnabla%5E%7B%5Cnu%7D%20%5Cphi)%20%5Cright%5D%0D%0A%5Cend%7Balign*%7D

Structure of Horndski Theory

(Hopefully) Easy-to-understand picture


Horndeski includes

‒ GR

‒ Quintessence/K-essence

‒ Kinetic Gravity Braiding

‒ Brans-Dicke theory, F(R) gravity etc.

‒ Covariant Galileon

‒ Gauss-Bonnet coupling etc.

Speed of GW in Horndeski Theory

Tensor mode


𝑀𝑝 running 𝛼𝑀 : Variation rate of effective 𝑀𝑝

Tensor speed excess 𝛼𝑇 : GW propagates at 𝑐𝑇2 = 1 + 𝛼𝑇

[Ezquiaga and Zumalacárregui (2017)]

[Bellini and Sawicki (2014)] etc.

Lagrangian

Constraint on Horndeski Theory

The GW speed constrains 𝐺4 and 𝐺5.



Or fine-tuning b/w 𝐺4 and 𝐺5 for cancellation 𝛼𝑇 ≈ 0.‒ Cancellation at the level of cosmological solution is broken by

perturbations

The Horndeski theories are ruled out unless they satisfy

Strongly constrained

Viable Scalar-Tensor Theories after GW170817.

Summary of the viable (left) and nonviable (right) Scalar-Tensor theories after GW170817








Contents

Six Polarizations in GW

In general metric theory of gravitation,

GW has possible six polarizations (ELLWW framework)


(b) Cross(a) Plus

(c) Breathing

(d) Longitudinal

(e) Vector-x (f) Vector-y [Nishizawa et.al (2009)]

[Newman and Penrose (1962)], [Eardley et. al (1973)]

Polarizations in Modified Gravity

Due to additional DOF, modified gravity theories predict additional polarization of GW.


Observation of extra polarization modes can directly test gravitational theory

Theory Polarization

General Relativity +, ×

Brans-Dicke theory +, ×, b

F(R) gravity +, ×, b, l

Horndeski theory +, ×, b, (l)

Massive gravity +, ×, b, x, y

Constraint on Polarization

GW170814


Screening Mechanism

Viable modified gravities possess screening mechanismto avoid the Solar-System constraints


For example, chameleon mechanism

Chameleon Mechanism

𝑉eff

𝑉

Large 𝜌+

Small 𝜌−

𝜅𝜙

𝑚+2

𝑚−2

(for dust)

In high-density region,

scalar field is heavy

and suppressed.

In low-density region,

scalar field is light and

acts as DE.

Scalaron mass

[Khoury and Weltman, (2004)]


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Modified Gravity after GW170817 - CERN

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