Gravitational waves from the early...

Gravitational waves from the early Universe

Sachiko Kuroyanagi (Nagoya University)

26 Aug 2017

Summer Institute 2017

Part 1

gravity = distortion of the spacetime

General relativity（1916）

What is a Gravitational Wave?

without object with object

space(3) + time(1) = 4

The spacetime distortion propagates as waves

What is a Gravitational Wave?

2 years later

= Gravitational wave

We have detected gravitational waves. We did it!

11 Feb 2016

Hanford Washington

Livingston, Louisiana

Detection on 14 Sep 2015

It was from a binary black hole

GWs from Black hole binary 1.3billion light years away

36 + 29 = 62 solar mass black hole

mirror1

mirror２ beam splitter

leser

same phase

photodetector

strong signal

Detection with a interferometer

4km

4km

different phase

mirror1


leser

photodetector

weak signal

If a gravitational wave pass through …

Fabry-Perot interferometer

multiple reflections → effectively increase the length

mirror1


leser

different phase

weak signal

photodetector

Note: what is strain?

strain

D0×h = (4km×200)×10-21 ~ 10-15m~ size of atomic nucleus

LIGO:

Fabry-Perot↓

h1 12

h

D0

Dmax/min = D0[1±12h]

GW150914

GW151226

GW170104

More detections

36Msun + 29Msun

All from black hole binaries

14Msun + 7.5Msun

31Msun + 19Msun

Observation run 2: 30 Nov 2016 - 25 Aug 2017

Observation run 1: 12 Sep 2015 - 19 Jan 2016

Event rate

~900Mpc

~400Mpc

→ Hints for black hole formation history Test of strong gravity

More GW sources are expected

New window of observation has just opened !

Astrophysical

・Neutron star binaries

・Supernovae

・Pulsars

Astrophysical Cosmological

・Neutron star binaries

・Supernovae

・Pulsars

・Inflation

・Reheating

・Phase transitions

・Cosmic strings

↑ My talk

New window of observation has just opened !

More GW sources are expected

Observing the early Universe

light was emitted 13.4 billion years ago31.9 billion light-year away now

new galaxies

old galaxies

The most distant galaxy (March 2016): GN-z11

The further the galaxy, the older the signal

→0.4 billion years after the birth

lights from 13.8 billion years agoCosmic Microwave background (CMB) The oldest signal:

→0.38 million years after the birth

？

photons are scattered by electrons

high

low3K

3000KThe temperature of the Universe was high in the past

Can we see further? → No (currently)

electronphoton

？Can we see further? → Gravitational waves can!

Gravitational waves do not interact with electrons

Inflation nowCosmic Microwave Background

light

gravitational waves

380,000 years 13.8 billion years

cosmic phase transitions

reheating

observer

Only gravitational waves can directly bring us the information of the early Universe!

log(time)

Advantages of gravitational wave observation

→ Full of information on high energy physics!

Multi wavelength observation of GWs

Sensitivities of gravitational wave experiments

GWs from inflation

LIGO-India (2024)

KAGRA (2018)Advanced-LIGO (2015)

Advanced-VIRGO (2017)

Ground-based interferometers

Test run with room temperature has done in March 2016Cryogenic test run is planned in March 2018full design sensitivity in 2022

3km

Started observation on 1st August 2017full design sensitivity in 2021

full design sensitivity in 2019

Interferometers in space

LISA

B-DECIGO

ESA + NASAlaunch in 2034pathfinder (test for technology) in 2015→ better sensitivity than expected

proposed in Japan2020’s

DECIGO

1millon km

2030’s 40’s?Triangle formation × 4

→ better angular resolution correlation analysis for GW background

How to detect a stochastic background

GWs from the early Universe

stra

in

time [s]

→ random phase no directional dependence→ very similar to noise

Cross Correlationdetector1 detector2

s: observed signalh: gravitational wavesn: noise

no correlations → 0

GW signal

s2(t) = h(t) + n2(t)s1(t) = h(t) + n1(t)

We need multiple detectors

Pulsar timing array

B-mode polarization in CMB

Pulsar (= rotating neutron star) → precise period GWs change the arrival time of the pulses

SKA (Square Kilometer Array) 2020-International project for radio telescope

Many ground-based and space project

LiteBIRD 2022-　GWs induece polarizations in the Cosmic Microwave background

Indirect detection of GWs

GWs from inflation

smalllarge detector size

Generation of GWs in the early Universe

= GravityMatterCurvature of the space-time

Equation for GWs in the expanding Universe

Gµ� = 8�GTµ�

Einstein equation

Flat Universe ＋ tensor perturbations (=GWs)

Gµ� = 8�GTµ�

hij + 3Hhij �1a2�2hij = 16�G�ij

Tµ�transverse-traceless part of anisotropic stress :

Equation for GWs in the expanding UniverseEinstein equation

a(t) : scale factor

Geometry

H affects GW evolutionH � a

a

Friedmann equation:

→ sum of energy densities

radiation

matter

�r � a�4

�m � a�3

H � a

a: Hubble parameter

⇢ = ⇢r + ⇢m + · · ·

H2 =8⇡G

3⇢� K

a2

density

scale factor : a

∝a-4

∝a-3

radiation

matter

dark energy?

� � H2

constant∝

Hubble expansion rate

H � a

a: Hubble horizon

～ region of causality

Meaning of H

dH ⌘ cH�1

speed of expansion

x

v = Hx

v > cv < cwe have information of the object no information

To be precise… LH =

Z t

0

cdt

a(t)∝ dH

for radiation- and matter-dominated Universe

observer

radiation- dominated

matter- dominated dark energy?

380,000 years 13.8 billion yearslog(time)

(relativistic particles) (non-relativistic particles)

What happened in the early Universe?From Cosmological observations…

What happened in the early Universe?

observer

inflation reheating

accelerated expansion


mechanism to heat the Universe

dense and hotcold


observer

inflation cosmic phase

transitions

reheating


The grand unification theory predicts separation of forces


observer

inflation



cosmic strings

cosmic superstrings

GUT scale string: 1018kg/cm

~1000 × Mt.Fuji

reheating

GW generation


Equation for GWs

2. Sourced by matter component of the Universe

• Preheating

• Phase transition

• Cosmic strings

1. Non-negligible initial condition • Inflation→ quantum fluctuations

→ rapid particle productions

→ bubble collisions

→ heavy string objects generated in phase transition

GW generation


Equation for GWs

2. Sourced by matter component of the Universe

• Preheating

• Phase transition

• Cosmic strings

→ rapid particle productions

→ bubble collisions

→ heavy string objects generated in phase transition

Hubble horizon= region of causality

wavelength of GWs at generation< Hubble horizon size

f/a < H→

H / ⇢12rad / T 2

a / T

f / T→


GWs from inflation

Reheating T~107GeV ~1010GeV

Reheating change the expansion rate

GWs from inflation


Reheating

T~104GeV ~107GeV

exotic model of the expansion can enhance the amplitude

GWs from inflation


pastpresent

~1015GeVPreheating T~109GeV

frequency at the generation ~ (Hubble horizon)-1

GWs from rapid particle productions

f / T→

pastpresent

Electroweak phase transition

T~100GeV

GWs from bubble collisions

frequency at the generation ~ (Hubble horizon)-1 f / T→

pastpresent

cosmic string

Gμ~10-12

tensionGμ~10-10

heavy string objects originating from phase transition or superstring theory

frequency at the generation ~ (Hubble horizon)-1 f / T→

Inflation nowCurrent observation

log(time)380,000 years


reheating

observer

13.8 billion years

→ more details on inflation and cosmic strings in part 2

Observations

SummaryGWs can become a powerful probe of

the very early Universe!

Gravitational waves from the early...

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