COSMOLOGYWITH THE GRAVITATIONAL WAVE
INTERFEROMETER LISA
Chiara Caprini
APC Paris

LISA
space-based interferometer
performing direct GW detection
LISA Pathfinder

launch Dec 2015, operations March 2016 -> now

one LISA arm
reduced in one
spaceship
test the ability to
put two masses
in free fall:measure thedifferential
acceleration
among them
Armano et al, PRL 116, 231101 (2016)

LISA chronology• 1980s - 2011: joint NASA/ESA proposal• 2011: NASA withdraws, ESA continues with descoped mission NGO(two arms)• 2012: ESA selects JUICE for L1• 2013: ESA selects LISA scientific theme for L3: “the gravitationaluniverse”• 2013 - 2016: studies of different configurations and refinement of
the scientific case• 25/10/2016: ESA call for mission• 13/01/2017: LISA Consortium submits the LISA proposal (3 arms),approved!
• 3/2017 - fall 2017: ESA Phase 0 study• fall 2017 - 2019: ESA Phase A study• 2019 - 2020: preparation of industrial implementation• 2020 - 2021: ESA mission adoption• 8.5 years: mission construction• around 2030: launch (Ariane 6)• nominal mission duration 4 years, tested extension up to 10 years• cost: 1050 M€

LISA proposal
https://www.elisascience.org/files/publications/LISA_L3_20170120.pdf

LISA configuration
frequency range of detection:

104

Hz < f < 1 Hz

it is a survey instrument: no pointing
continuous sky observation
best angular resolution for high SNR sources: 1deg2

What LISA measures
1. The gravitational wave strain from the inspiral and mergerof compact binaries : it encodes information on the binaryparameters

Lh(t) ⇠ 2L

Mc , dL , tc , ⌘,c,

LISA target : BH binaries, massive (high SNR) and LIGO-likegalactic binaries
Extreme Mass Ratio Inspirals

What LISA measures
2. the stochastic background of gravitational waves
the superposition of sources that cannot be resolved individually• binaries too numerous and with too low SNR to be identified• signals from the early universe with too small correlation scalewith respect to the detector resolution⇥GWhḣij ḣij i==
GW =⇥c
32 G ⇥c

Zdf d GW
f d ln fenergy density
power spectrum

What LISA measures

LISA AND COSMOLOGY:the stochastic GW background fromprimordial sources: test of early universeand high energy phenomenause of GW emission from binaries to probe
the background expansion of the universe :test of acceleration

LISA AND COSMOLOGY:
the stochastic GW background fromprimordial sources: test of early universeand high energy phenomenause of GW emission from binaries to probe
the background expansion of the universe :test of accelerationbecause of the weakness of the gravitational interaction the universe
is transparent to GW

CMB

GW

lightelements

anisotropies

Inflation

Cosmological dark age(reheating, baryogenesis, phasetransitions, dark matter,…)

BBN

hijMP l  1016GeVCMB

910 GeV

EW

QCD

LIGO

LISA

PTA

MeVeV

CMB

Characteristic frequency for causal sources
H(T⇤ )f⇤ =✏⇤Hubble factor at GW production
parameter depending on thedynamics of the source✏⇤  1

Characteristic frequency for causal sources
H(T⇤ )f⇤ =✏⇤Hubble factor at GW production
parameter depending on thedynamics of the source✏⇤  1assuming standard thermal history and radiation era:a⇤2 · 10fc = f⇤=a0✏⇤characteristicfrequency today

5T⇤
Hz
1 TeV

temperature (energy density) of theuniverse at the source time

Characteristic frequency for causal sources
H(T⇤ )f⇤ =✏⇤Hubble factor at GW production
parameter depending on thedynamics of the source✏⇤  1assuming standard thermal history and radiation era:a⇤2 · 10fc = f⇤=a0✏⇤✏⇤ ' 102T⇤ ' 1 TeV

5T⇤
Hz
1 TeV
fc ' mHz
LISA!

Characteristic frequency for causal sources
���(�+�)✏⇤ = 1038123

182328-50510155���(� [��])0LIGO
LISA-5

PTA-10-15

CMB-20-10

LSSBBN���(� [���])Observational bounds/sensitivities for SGWB
10-4
10-6

h2 ΩGW

10-8

BBN

CMB
Henro-Versillé et al1408.5299

aLIGO (O1)
PTA

10-10

aLIGO (Design)

Lentati et al1504.03692

10-12
10-14
10-16
10-18

Abbott et al1612.02029

eLISA
PlanckAmaro-Seoane et al1702.00786

Ade et al
1502.00612

10-16

10-11

10-6f (Hz)

10-1

104

amplification of vacuum
fluctuations during inflation2ḧij + 3H ḣij + k hij = 0

signal from a simple slow roll inflation model :beyond the reach of direct detection

10-4

BBN

CMB

10-6

aLIGO (O1)h2 ΩGW

10-8

PTA

10-10

aLIGO (Design)

10-12
10-14

eLISAPlanck

V

10-16
10-18

10-16

10-11

1/4

≃ 10

16

10-6
f (Hz)

GeV

10-1

104

other possible sources of GW in the early universe
more promising for direct detection(with future interferometers or PTA):

mechanisms that produce a non-zero tensor anisotropic stressḧij + 3H ḣij + k2TT
hij = 16⇡G ⇧ijother possible sources of GW in the early universe
more promising for direct detection(with future interferometers or PTA):

mechanisms that produce a non-zero tensor anisotropic stressḧij + 3H ḣij + k2

TT
hij = 16⇡G ⇧ij

but which amplitude is needed for detection ?
considerable amount of energy (in some anisotropic form)
is needed to generate a detectable signal

Possible GW sources in the early universe• “non-standard” • particle production during inflationinflation• fluid stiffer than radiation after inflation• preheating after inflation• phase transitions at the end or during inflation• ...

• first order phase transitions• cosmic strings• other topological defects e.g. domain walls• primordial black holes• scalar field self-ordering• ...

First order phase transitions
universe expands and temperature decreases : PTs, if first order lead to GW
potential barrier separates
true and false vacuaquantum tunneling across the barrier :nucleation of bubbles of true vacuum• collisions of bubble walls
source: ⇧ij tensor
anisotropic stress• sound waves and turbulence in the fluid• primordial magnetic fields (MHD turbulence)Example of signal
10-8

LISA sensitivity

h2 ΩGW (f)

10-10

10-12

10-14

total

wall collisionsound waves
MHD turbulence

10-16
10-5

10-4

0.001

0.010

0.100

f[Hz]

temperature of the PT : 100 GeV
strength of the PT : ⇢vac = ⇢radduration of the PT : 0.01 1/H
CC et al, arXiv:1512.06239

Detection prospects for LISA
• LISA is sensitive to energy scales 10 GeV - 100 TeV• LISA can probe the EWPT in BSM models …
- singlet extensions of MSSM (Huber et al 2015)- direct coupling of Higgs sector with scalars (Kozackuz et al2013)- SM plus dimension six operator (Grojean et al 2004)• … and beyond the EWPT
- Dark Matter sector : provides DM candidate and confining
PT (Schwaller 2015)- Warped extra dimensions : PT from the dilaton/radion
stabilisation in RS-like models (Randall and Servant 2015)• connections with baryon asymmetry, dark matter : LISA as acomplementary probe of BSM physics
CC et al, arXiv:1512.06239

Detection prospects for LISA
• LISA is sensitive to energy scales 10 GeV - 100 TeV• LISA can probe the EWPT in BSM models …
- singlet extensions of MSSM (Huber et al 2015)- direct coupling of Higgs sector with scalars (Kozackuz et al2013)- SM plus dimension six operator (Grojean et al 2004)• … and beyond the EWPT
- Dark Matter sector : provides DM candidate and confining
PT (Schwaller 2015)- Warped extra dimensions : PT from the dilaton/radion
stabilisation in RS-like models (Randall and Servant 2015)• connections with baryon asymmetry, dark matter : LISA as acomplementary probe of BSM physics
CC et al, arXiv:1512.06239

Example of detection prospects for LISA
temperature of the PT

inverse durationof the PT withrespect to Hubble
time(✏⇤)

strength of the PT

“Non-standard inflation”

10-4

BBN

CMB

10-6
PTA

10-10

aLIGO

2h ΩGW

10-8

10-12
10-14

LISA
Planck

10-16
10-18

10-16

10-11

10-6
f (Hz)

10-1

104

“Non-standard inflation”
N. Bartolo et al, 1610.06481-41010-6• gauge fields during inflation• scalar spectator fields

10PTA• stiff equation of state after inflation

aLIGO

2h ΩGW

10-8-10BBN

CMB

10-12
10-14LISA• broken space reparametrisation
symmetry
during inflation
Planck

10-16
10-18

10-16

10-11

10-6
f (Hz)

10-1

104

“Non-standard inflation”
N. Bartolo et al, 1610.06481

GW background from cosmic strings• model dependent GW signal : here Nambu Goto with large loops• spectral shape extended in frequency because of continuous production

p"1

Pulsars10#4
p"10#3old eLISA
ELISA(2012)LIGO
GΜ"10 #12

#8

10#8

G

GΜ"10 #13

10"ΜGΜ"10 #17

aLIGO

10#12
10#12

13

"10#GΜ

"10#

11

10#10

GΜh2 $gw

10#610#9

10#6f !Hz"0.001

11000

Binetruy et al 2012

LISA bounds on Nambu-Goto strings, loop size
S. Sanidas, LISA internal

Current
NanoGRAV

Gµ < 1.3 · 10

10future
CMB B-modes

Gµ < 109

Future SKA

Gµ < 1013

Janssen et al 2015

LISA AND COSMOLOGY:
the stochastic GW background fromprimordial sources: test of early universeand high energy phenomenause of GW emission from binaries to probe
the background expansion of the universe :test of acceleration

Standard sirens
GW emission by massive black hole binaries can beused as SuperNovae Ia (standard candles)
to test the content of the universe

Standard sirens
GW emission by compact binaries + redshift by an EM counterpart
can be used to probe the distance-redshift relation

4h+ (t) =dL (z)4h⇥ (t) =dL (z)

✓✓

GMc
c2
GMc
c2

◆ 53 ✓◆ 53 ✓

⇡fc
⇡fc

◆ 23

◆ 23

1 + cos2 ıcos[ (t)]2cos ı sin[ (t)]Mc = (1 + z)Mc

redshifted chirp massdL (H0 , ⌦⇤ , ⌦M , w0 , wa )

Standard sirens
GW emission by compact binaries + redshift by an EM counterpart
can be used to probe the distance-redshift relation

4h+ (t) =dL (z)

✓✓GMc
c2

◆ 53 ✓◆ 53 ✓⇡fc

◆ 23

1 + cos2 ıcos[ (t)]
2

◆ 23

4GMc
⇡fh⇥ (t) =cos ı sin[ (t)]2dL (z) no cdistancec ladder

Mc = (1 + z)Mc

redshifted chirp massdL (H0 , ⌦⇤ , ⌦M , w0 , wa )

Standard sirens
GW emission by compact binaries + redshift by an EM counterpart
can be used to probe the distance-redshift relation

4h+ (t) =dL (z)✓✓GMcc2◆ 53 ✓◆ 53 ✓⇡fc◆ 23

1 + cos2 ıcos[ (t)]
2

◆ 23

4GMc
⇡fh⇥ (t) =cos ı sin[ (t)]2dL (z) no cdistancec ladder

Mc = (1 + z)Mc

but no redshift either!
redshifted chirp massdL (H0 , ⌦⇤ , ⌦M , w0 , wa )

Standard sirens
GW emission by compact binaries + redshift by an EM counterpart
can be used to probe the distance-redshift relation

4h+ (t) =dL (z)4h⇥ (t) =dL (z)

✓✓GMc
c2
GMcc2

◆ 53 ✓◆ 53 ✓⇡fc
⇡fc

◆ 23

◆ 23

1 + cos2 ıcos[ (t)]2cos ı sin[ (t)]Mc = (1 + z)Mc

redshifted chirp mass
Analogous to SNIa, but :• direct measurement of dL up to large redshift with GW - good• needs an independent (optical) measurement of the redshift - badstandard sirens with LISA: MBHB coalescence
N. Tamanini et al arXiv:1601.07112

example of simulated datawith counterparts(SKA+EELT)
and weak lensing errors

VERY FEW EVENTS AT
LOW REDSHIFT !
• where needed to probe DE (bad)• can test expansion at highredshift (good)standard sirens with LISA: MBHB coalescence⇤CDM
most optimistic scenario for BBH formation gives an
independent measurement of the Hubble parameter to 1%LISA alone :⌦M = 0.3 ± [0.05, 0.03]

h = 0.67 ± [0.02, 0.01]

Planck alone :⌦M = 0.308 ± 0.0012
h = 0.678 ± 0.009

LISA fixing ΩM :h = 0.67 ± [0.006, 0.004]• fully independent constraint• 0.6% in best casestandard sirens with LISA: MBHB coalescence
Dynamical Dark Energy
too few events at low redshift to get a good measurement

w0 =

1 ± [0.3, 0.1]

wa = 0 ± [1.5, 0.8]

Euclid forecast :w0 = 0.02
wa = 0.1

standard sirens with LISA: MBHB coalescence
Dynamical Dark Energy
too few events at low redshift to get a good measurement

w0 =

1 ± [0.3, 0.1]

w0 = 0.02

Euclid forecast :wa = 0.1

wa = 0 ± [1.5, 0.8]

Example of possible LISA cosmological data
100EMRIs
10dL HGpcL

can be improved using othersources at low redshift
besides MBHBStellar mass
BHBs

MBHBs

1DLC

M

0.1

credits: N. Tamanini

0.01

0.11z10

standard sirens with LISA: MBHB coalescence
Dynamical Dark Energy
too few events at low redshift to get a good measurement

w0 =

1 ± [0.3, 0.1]

w0 = 0.02

Euclid forecast :wa = 0.1

wa = 0 ± [1.5, 0.8]

Example of possible LISA cosmological data

low-redshift sources do not EMRIs
need
can be improved using otherem counterpart
10
Stellar mass
sources at low redshift
besides MBHB

dL HGpcL

100

BHBsMBHBs1DLCM

0.1

credits: N. Tamanini

0.01

0.11z10LISA can provide competitive constrains onmodels where dark energy starts to contribute at early times
Early Dark Energy⌦de fraction of dark energy
at early times

zeredshift up to which darkenergy contributes

Planck alone :⌦de = 0.0036

but only if it contributes up todecoupling, otherwise themeasurement quickly degrades

CC and N. Tamanini arXiv:1607.08755

Interacting Dark Energy⇢˙ dm + 3H⇢dm = Q⇢˙ de + 3H(1 + w0 )⇢de =Qtwo models for the interaction

Q = ✏1 H⇢dm and Q = ✏2 H⇢deredshift when the interaction turns on : zi

✏1 = 0.00199+0.000240.00177✏2 = 0.159+0.146
0.154

Costa et al 2016

Murgia et al 2016

Binary at cosmological distance
4h+ (t) =dL (z)4h⇥ (t) =dL (z)

✓✓

GMc
c2
GMc
c2

◆ 53 ✓◆ 53 ✓

⇡fc
⇡fc

◆ 23

◆ 23

1 + cos2 ıcos[ (t)]2cos ı sin[ (t)]Mc = (1 + z)Mcredshifted chirp mass

if the redshift is constant during the timeof observation of the GW signal

Binary at cosmological distancetime variation of the redshift changes the evolutionof the frequency with time as the binary chirps:
1. the background expansion of the universe varies during thetime of observation of the binary
2. the redshift perturbations due to the distribution of matter
between the GW source and the observer vary in time during
the time of observation of the binary

main effect: peculiar acceleration of the binary centre of mass

C Bonvin et al arXiv:1609.08093

Extra term in the waveform phase• Earth based interferometers are not sensitive to this effect: they do notfollow the GW source for enough time

• but this effect is relevant for LISA: binaries which stay in band forenough time, with low chirp-mass, that enter the detector around tenmHz and go to the LIGO band after ~5 years

A Sesana
arXiv:1702.04356

Extra term in the waveform phase• the effect can be measured forbinaries with high enoughacceleratione=3¥104 ; h=0.25; z=0.05; LISA+LIGO
120kmv ⇠ 200
sec

100Mcz @Mü Dr ⇠ 1 pc

8020%

• knowing the acceleration canprovide information on theformation of the binary(nearby a SMBH?)

30%

6050%
100%
40tc =

Inayoshi et al 1702.06529

10ytc =

5y200.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020
fmin @HzD

Conclusions
we have assisted to a historical event, the aLIGO/Virgo detection
which (so far) confirms GRand opens the era of GW astronomy and cosmology

LISA has been fully approved by ESA
and it is on the path to launch in 2030

GW could be a powerful mean to probe the early universe(and consequently high energy physics)
and the late-time cosmology:
detection is difficult but great payoff