What can Cosmology tell us about
Gravity?
Alessandra Silvestri
Instituut Lorentz, Leiden U.
Cosmic Controversies, KICP Chicago

October 6th, 2019

M. Martinelli

C.M.Hidalgo

G. Papadomanolakis

B.Shiralilou

F.Renzi

R.DalalS.Peirone

S.Maleubre

What can Cosmology tell us about
Gravity?
Alessandra Silvestri
Instituut Lorentz, Leiden U.
Cosmic Controversies, KICP Chicago

October 6th, 2019

How special is GR?
Weinberg-Deser theorem: A Lorentz invariant theory of a massless spin-2
particle must be GR at low energies.

Lovelock’s theorem: The only possible second-order, Euler-Lagrange equations(1971)

obtainable in a 4D spacetime from an action containing solely the4D metric and its derivatives are the Einstein field equations

So, to modify GR we can either give mass to the graviton, introduce new DOF or break
Lorentz invarianceextra dynamica DOF(s)Clifton et al., Phys.Rept. 513 (2012)

The Standard Model of Cosmology
The standard model is based on GR :Cosmic acceleration is sourced by the cosmological constant.
Growth of structure is scale-independent!
The growing mode goes like: D1 (a) = 5⌦m H(a)2 H0Z a0hda0
H(a0 )

a 0 H0i3

The Standard Model of Cosmology
The standard model is based on GR :Cosmic acceleration is sourced by the cosmological constant.
Growth of structure is scale-independent!
The growing mode goes like: D1 (a) = 5⌦m H(a)2 H0LCDM:

Z a0hda0
H(a0 )

a 0 H0i3

The Standard Model of Cosmology
The standard
modelLCDM,
is baseddarkon GR:
Beyondenergyis dynamical, clustering and lensing aremodified, and possibly have scale-dependent pattern.
At the level of the background and LSS we can capture this into three
Cosmic acceleration is sourced by the general
cosmologicalconstant.
functions:
Growth of structure is scale-independent!
Z a RH2⌦r⌦5⌦0 DE (a))
M H(a)
3 (1+wdam=++⌦aFriedmann:
Thegrowing mode goes like:
DE
2D(a)
=
4
3
1H0aa 2 H0 0 h H(a0 ) i3
a 0 H0Poisson:

LCDM:

Lensing:Some recent constraints
Planck 2018,arXiv:1807.06209

DES I
PRD (2019)

DES IThe upcoming missions
0.80.0wa...
−0.8

−1.6
Planck 2015−1.2

−1.0

−0.8

w0−0.6

The upcoming missions
0.8

Euclid + Planck
0.0wa...
−0.8−1.6
Planck 2015

−1.2

−1.0

−0.8

w0−0.6

The upcoming missions
0.8

Euclid + Planck
0.0

wa...
−0.8

THEORYTHEORY−1.6
Planck 2015

−1.2

−1.0

−0.8

w0−0.6

How about the tensors?

Modified Gravity after GW170817& GRB170817A

Extended theories of gravity, generally give you:2ḧij + (3 + ↵M ) H ḣij + (1 + ↵T ) k hij = 0

Modified Gravity after GW170817& GRB170817A

Extended theories of gravity, generally give you:2ḧij + (3 + ↵M ) H ḣij + (1 + ↵T ) k hij = 0
conformal coupling
non-trivial kinetic termModified Gravity after GW170817& GRB170817A

Extended theories of gravity, generally give you:2ḧij + (3 + ↵M ) H ḣij + (1 + ↵T ) k hij = 0
conformal coupling
non-trivial kinetic term

2cT = 1

↵T = 0Covariant Galileons, as well as quartic and quintic Horndeski, “are gone”.
This cuts a big chunk of self-accelerating models, but it leaves
space for non-trivial LSS phenomenology.

Creminelli & Vernizzi, PRL 2017
Ezquiaga, Zumalacarregui, PRL 2017
Baker et al., PRL 2017

Modified Gravity after GW170817& GRB170817A

Extended theories of gravity, generally give you:2ḧij + (3 + ↵M ) H ḣij + (1 + ↵T ) k hij = 0
conformal coupling
non-trivial kinetic term

2cT = 1

↵T = 0Covariant Galileons, as well as quartic and quintic Horndeski, “are gone”.
This cuts a big chunk of self-accelerating models, but it leaves
space for non-trivial LSS phenomenology.

Creminelli & Vernizzi, PRL 2017
Ezquiaga, Zumalacarregui, PRL 2017see de Rham& Melville,PRL 2018
Bakeret al., PRL 2017

Modified Gravity after GW170817& GRB170817A

Extended theories of gravity, generally give you:2ḧij + (3 + ↵M ) H ḣij + (1 + ↵T ) k hij = 0
conformal coupling
non-trivial kinetic term

No gravitational slip on
large scales!

µ 0 = ⌃02cT = 1↵T = 0Pogosian & Silvestri PRD 2016

Covariant Galileons, as well as quartic and quintic Horndeski, “are gone”.
This cuts a big chunk of self-accelerating models, but it leaves
space for non-trivial LSS phenomenology.

Creminelli & Vernizzi, PRL 2017
Ezquiaga, Zumalacarregui, PRL 2017see de Rham& Melville,
PRL 2018
Bakeret al., PRL 2017

EFT of DE &Theoretical Priors

A unified action for linear perturbations
Jordan frame

⇢

Z

2pm
04
S= d xg⌦(t)R + ⇤(t) c(t) a2 g 00
243M2 (t) 2 00 2 M̄1 (t) 2 00µ+a ga gKµ222M̄22 (t)aµ 2µ00⌫+KµK⌫ Kµg
R + ...
22+Sm [gµ⌫ ,Gubitosi, Piazza, Vernizzi, JCAP 1302 (2013) 032

Piazza, Vernizzi, Class.Quant.Grav. 30 (2013) 214007

J. Gleyzes et al., Phys.Rev.Lett. 114 (2015)m ],Bloomfield, Flanagan, Park, Watson JCAP 1308 (2013) 010

J. B. Achour et al., JHEP 1612 (2016) 100

R. Kase, S. Tsujikawa, Int.J.Mod.Phys

A unified action for linear perturbations
Jordan frame

⇢Z2pm
04
S= d xg⌦(t)R + ⇤(t) c(t) a2 g 00
243M2 (t) 2 00 2 M̄1 (t) 2 00µ+a ga g
Kµ222M̄22 (t)aµ 2µ00⌫+KµK⌫ Kµg
R + ...
22+Sm [gµ⌫ ,UNITARY GAUGE@µnµ ⌘ p(@µ )2m ],And the action is built out of all geometrical quantities that are invariant under theGubitosi, Piazza, Vernizzi, JCAP 1302 (2013) 032 time-dependent
Piazza, Vernizzi, Class.Quant.Grav.
30 (2013)
214007
Bloomfield, Flanagan, Park, Watson JCAP 1308 (2013) 010
3D spatialdiffeomorphisms.
J. Gleyzes et al., Phys.Rev.Lett. 114 (2015)J. B. Achour et al., JHEP 1612 (2016) 100

R. Kase, S. Tsujikawa, Int.J.Mod.Phys

A unified action for linear perturbations
Jordan frame⇢Z2pm
042 00S = dUnifiedx andg physically⌦(t)R+⇤(t)c(t)
ainformed framework g
24
3M2mapping(t) 2 withM̄
2Exactmodels
1 (t) 2 00
00 manyµ+a g
a gKµ22
2 beyond LCDM
Agnostic
explorationofviableM̄22 (t)aµ 2µ00⌫+KµK⌫ Kµg
R + ...
22Unified treatment of vast range of observables+Sm [gµ⌫ ,UNITARY GAUGE@µnµ ⌘ p(@µ )2m ],And the action is built out of all geometrical quantities that are invariant under theGubitosi, Piazza, Vernizzi, JCAP 1302 (2013) 032 time-dependent
Piazza, Vernizzi, Class.Quant.Grav.
30 (2013)
214007
Bloomfield, Flanagan, Park, Watson JCAP 1308 (2013) 010
3D spatialdiffeomorphisms.
J. Gleyzes et al., Phys.Rev.Lett. 114 (2015)

J. B. Achour et al., JHEP 1612 (2016) 100

R. Kase, S. Tsujikawa, Int.J.Mod.PhysWhat can Cosmology tell us about Gravity?
Is Σ=1?
YESNOIs µ≥1?

Are µ-1 and Σ-1of the same sign?

NOYES

Constrain
GBDparametersm(a) and β(a)

NOYES

GBD
ruled out

Horndeski
disfavoured
Study Horndeski models
with non-canonicalkinetic terms
k-dependencein Σ or µ?

Covariant Galileons
ruled outNO

YESIs Σ = µ ?
What is thetransitionscale?

NOYES

Is µ∞≥ µ0?

Is cT ≠1 allowed?
NOYES
YESNO

Horndeski
ruled out

Evidence of
5th forceIs Σ0= µ0?
NOαT≠0, evidence of
non-trivial G4 and G5
Is cT ≠1 allowed?
YES

Majordiscovery!

NOHorndeski
ruled out

YES

Restrict tomodels withknown αT

αT =0

Probing thek/a >> M
regimeIs Σ∞= µ∞?
YESModels withnon-trivial G4and G5 ruled out

NODetectionof αM

Pogosian & AS, PRD (2016)

What can Cosmology tell us about Gravity?
Is Σ=1?
YESNOIs µ≥1?

Are µ-1 and Σ-1of the same sign?

NOYES

Constrain
GBDparametersm(a) and β(a)

NOYES

GBD
ruled out

Horndeski
disfavoured
Study Horndeski models
with non-canonicalkinetic terms
k-dependencein Σ or µ?

Covariant Galileons
ruled outNOYESIs Σ = µ ?
What is thetransitionscale?

NOYESIs µ∞≥ µ0?

Is cT ≠1 allowed?
NOYESYESNO

Horndeski
ruled out

Evidence of5th force

Is Σ0= µ0?
NOαT≠0, evidence of
non-trivial G4 and G5
Is cT ≠1 allowed?
YES

Major
discovery!

NOHorndeski
ruled out

YES

Restrict tomodels withknown αT

αT =0

Probing thek/a >> M
regimeIs Σ∞= µ∞?
YESModels with
non-trivial G4and G5 ruled out

NODetectionof αM

Pogosian & AS, PRD (2016)

LSS Phenomenology of viable Horndeski

Peirone, Raveri, Pogosian, AS, Koyama, PRD 2018

Theoretical priors

Espejo et al., PRD 2019

Theoretical priors

Espejo et al., PRD 2019

Reconstruction with theoretical priors
w(a)#weak lensing
DES: no cut#Planck 2015 TT, lowTEB, lowl

YR
Aµ(a)

ERP⌃(a)NI
M
I
L#BAO Likelihoods
BAO: 6DF, MGS, eBOSS DR12 (in 9 bins byYTW), eBOSS DR14 (at 4 z_eff by GBZ),eBOSS DR12 Lyman alpha#Others:
Pantheon
H0 = 73.53 +- 1.62
WiggleZ_MPK#Theoretical Prior
Horndeski

Li et al., in preparation

Strong Lensing Time DelayStrong Lensing Time Delay

Time delay btw two light rays:

Dl Ds
tAB = (1 + zl )[ (✓A , )cDls

Cosmology enters in the time delay distance:

Dl Ds
D t = (1 + zl )cDls(✓B , )]

Strong Lensing Time Delay

Time delay btw two light rays:

Dl Ds
tAB = (1 + zl )[ (✓A , )cDls(✓B , )]

HOLiCOW collaboration recently presented a 2.4% bound on
Cosmology enters in the time delay distance:
H0 from 6 lenses.Dl Ds

D t = (1 + zl )cDK.C.
lsWong, arXiv:1907.04869

Strong Lensing Time Delay
LCDM forecast

B. Shiralilou et al., arXiv:1910.XXXX (astro-.ph-CO)

Strong Lensing Time Delay
LCDM forecastin the optimistic case, constraints
on H0 can get up to 0.1%

B. Shiralilou et al., arXiv:1910.XXXX (astro-.ph-CO)

Strong Lensing Time Delay
LCDM forecast

w0 ⇠ 0.05

in the optimistic case, constraints
on H0 can get up to 0.1%

wa ⇠ 0.3
B. Shiralilou et al., arXiv:1910.XXXX (astro-.ph-CO)

Strong Lensing Time Delay
What H0would we get if we were to fit a wCDM universe with a LCDM one?

B. Shiralilou et al., arXiv:1910.XXXX (astro-.ph-CO)

Strong Lensing Time Delay

1000 lenses

100 lenses

Could we build a ‘DE trigger’ binning the lenses and looking for discrepancies in values of H0?
ideal
realisticWrapping up

We are making progress interms of theoreticalframeworks to interpret thiswonderful data, and, inparticular, to ‘nonparametrically reconstruct
physics’ out of it ... bear withus, next years will beexciting!

Wrapping up

We are making progress interms of theoreticalframeworks to interpret thiswonderful data, and, inparticular, to ‘nonparametrically reconstruct
physics’ out of it ... bear withus, next years will be
exciting!

THANK YOU !