Tests of cosmological gravity

Jeremy Sakstein University of Pennsylvania

Astrophysics Seminar UC Irvine

23rd January 2018

Who am I?• Particle-cosmology (baryogenesis, early universe)

• Modified gravity (dark energy, new interactions)

• Astrophysics (tests of gravity, dark matter)

• Strong field (black holes + neutron stars)

• Screening mechanisms (see later)

• Degravitation

TodayWhat can we learn about gravity from:

GW170817 (GWs from merging NSs):

Black holes:

Why modified gravity?

• Dark energy - new d.o.f. can drive acceleration?

• Next gen. surveys will test GR on cosmic scales

• Need alternative theories with different predictions

• CC problem?(degravitation, UV insensitivity, technical naturalness)

(need new IR modifications)

(still have CC problem, want well motivated models)

The problem with MG gravityNewtonian limit of GR:

r2�N = 4⇡G⇢ FN = r�N

Modified gravity — new scalar graviton:

F5 = ↵r�r2� = 8⇡↵G⇢

F5

FN= 2↵2 solar system: 2↵2 < 10�5

(Shapiro time-delay effect, Cassini)

Screening mechanisms

Two options:

non-Poisson kinetic terms Vainshtein screening

galileons

add scalar potential kill off the source no scalar gradient

chameleon/symmetron/f(R)

r2�+ F (@�, @2�, . . .) = 8⇡↵G⇢+ V 0(�)

(= 0)

Vainshtein screening

Change kinetic terms — e.g. cubic galileon:

1

r2d

dr2

r2�0 +

2r2c3

r�02�= 8⇡↵G⇢

Poisson termGalileon term

(crossover scale )rc

Coupling to matter

Vainshtein MechanismWe can integrate this once:

- Vainshtein radius

Vainshtein screening

Vainshtein screening is generic• DGP braneworld gravity

• Galileons

• Massive gravity

• Massive bi-gravity

• Horndeski

• Beyond Horndeski — breaks down inside objects

VERY generic scalar-tensor theories

with three D.O.F

(+ DHOST)

Galileons• Self-acceleration (DE but does not solve CC)

• Nice(ish) UV properties (non-renormlaization)

• Massive (bi)gravity

• Braneworld models

• Hard to test due to Vainshtein screening

(Low cut-off for EFT?)

Hui & Nicolis ‘12

‘gravitational charge’ ‘scalar charge’

r�ext

r�ext

M ~x = �Mr�ext �Qr�ext

Equivalence principle violations

Equivalence principle violations in galileon theories

Baryonic + dark matter: Q = M

Black holes described by mass and spin only!

Hui & Nicolis ‘12

Black holes: Q = 0

Matter falls faster than BHs

Violation of the SEP!

r�ext

r�ext

Hui & Nicolis ‘12

Eötvös experiments with black holes

Galaxy clusters: nature’s leaning towers

BH

Virgo cluster

● Newtonian

● Galileon (rc = 500 Mpc)

● Galileon (rc = 6000 Mpc)

-- RMS Cosmological

0.5 1 5 10

50100

5001000

5000104

(km/s)2/kpc

rVnDGP

self-accelerating

NFW, c=5M = 1015M�

Offset

● ρ = 0.05M☉ pc-3, M200 = 1015M☉

● ρ = 0.1M☉ pc-3, M200 = 1015M☉

-- ρ = 0.1M☉ pc-3, M200 = 2x1014M☉

0.5 1 5 10 Mpc

0.05

0.10

0.50

1

Offsetkpc

M87

M 87

LLR

7.9 5. 3.8

/Mpc

/(1000 km)-1self-acceleration

⇤3 =�6Mp/r

2c

�1/3

JS, Jain, Heyl, Hui APJL ‘17

Future tests

• More galaxies — SDSS, DES, Euclid + X-ray/Radio

• Morphological distortions

• Missing SMBHs!

This is one galaxy!

GW170817GWs and Photons from merging NSs

�t 1.7s

Geometry of GW170817

40 Mpc

) cT � c

c< 10�15

NGC 4993

Gravitational wavesGalileons predict photons move slower than GWs:

c2T � c2

c2=

4c4x2

1� 3c4x2

x =�

HMpl

c4 ⇠ (H0rc)4

Probed by GWs

⌦� = ⌦�(x, c4,↵)

Probed by SMBHs

Galileons are cosmologically irrelevant

SpeedofGravitons

SMBHs

-10 -8 -6 -4 -2 0-10

-8

-6

-4

-2

0

↵ = 1

JS & Jain ‘17 PRL

What else is ‘ruled’ out?JS & Jain ’17, Baker et al. ’17, Ezquiaga & Zumalacárregui ’17, Creminelli & Vernizzi ‘17

Healthy scalar-tensor theories (Horndeski):

Lp�g

= K(�, X) +G3(�, X)⇤�+G4(�, X)R

+G4, X

⇥(⇤�)2 � (rµr⌫�)

2⇤+G5(�, X)Gµ⌫rµr⌫�

�1

6G5, X

⇥(⇤�)3 � 3rµr⌫�rµr⌫⇤�+ 2r⌫rµ�+r↵r⌫�rµr↵�

⇤

• Three (2 tensor + 1 scalar) degrees of freedom • Healthy • Can extend to ‘beyond Horndeski’ cT = c

X = �(@�)2/2 cT 6= c

Other theories that are ‘ruled’ out

• beyond Horndeski (more general)— similar story

• DHOST (even more general) — similar story

• Vector-tensor — similar story

Theories:

Exception: can always fine-tune (Crisostomi & Koyama ‘17)

Important: what is allowed

Cosmological (scalar acts as dark energy):

Conformal rescalings (tuned DHOST, beyond Horndeski)

gµ⌫ = ⌦2(�, X)gµ⌫

quintessence k-essence

cubic galileons

Brans-Dicke f(R)

Lp�g

= K(�, X) +G3(�, X)⇤�+G4(�)R

Important: what is allowed

Non-cosmological (no DE):

Everything!

What else can we do?

• Test dark energy on small scales

• Varying speed of light theories

Effective description of dark energy

Parameterize cosmological perturbations:

↵Hbeyond Horndeski:

↵V �1 �2 �3DHOST:

Horndeski: ↵M ↵B↵K

speed of tensors

↵T = c2T � c2

(@�)n (@�)2⇤�G/HG

} Vainshtein breaking

Bellini & Sawicki `14, Gleyzes et al. ’14, Langlois et al. `17

Screened

Unscreened

(�PPN = 1)

Vainshtein breaking

ds2 = �(1 + 2�) dt2 + (1 + 2 )�ij dxi dxj

Kobayashi et al. ’14, Koyama & JS ’15, Saito et al. ‘15

d�

dr=

GM

r2+

⌥1G

4

d2M

dr2

d

dr=

GM

r2� 5⌥2G

4r

dM

dr+⌥3G

d2M

dr2

stellar structure, rotation curves

Lensing

Example: quartic Horndeski

⌥1 =4↵2

H

c2T(1 + ↵B)� ↵H � 1

⌥2 =4↵H(↵H � ↵B)

5 [c2T(1 + ↵B)� ↵H � 1]

⌥3 = 0

cT ⇡ 1 can measure cosmology on small scales

Brown dwarf (no hydrogen burning)

Red dwarf (hydrogen burning)

Minimum mass for hydrogen burning

(MMHB)

Bounds: low-mass stars

MMHB changes in beyond Horndeski

JS ’17 PRL, JS 17’ PRD

���� ���� ���� �

�����������������������������������

1

Lightest observed red dwarf

⌥1 < 1.6

Galaxy cluster lensing

d�

dr=

GMhydrostatic(⌥1)

r2d

dr=

GMlensing(⌥2,⌥3)

r2

X-ray brightness Weak lensing

JS et al ‘16

⌥1 = �0.11+0.93�0.67

⌥2 = �0.22+1.22�1.19

Constraints

Dwarf Stars

Galaxy Clusters

-1.0 -0.5 0.0 0.5 1.0-2

-1

0

1

2

More general theories (cubic, DHOST)

• Need more bounds (pulsar decay rate etc.)

• Need to impose tuning relations so that cT ⌘ 1

See Crisostomi & Koyama ’17, Langlois et al. ’17, Dima & Vernizzi ‘17

Disformal transformations

Varying speed of light theories

gphotonsµ⌫ = ggravitonsµ⌫ +@µ�@⌫�

M4

c2�c2

= 1� �2

M4

Cosmological time-derivative

LIGO/Fermi

< 6⇥ 10�15(cosmologically irrelevant)

Outlook

‘Is MG dead?’Depends what you care about

• Either need tuning or restricted class of theories • EFT, naturalness, fine-tuning questions • f(R)/chameleon/symmetron fine • (cubic galileon in trouble for other reasons)

Cosmological (DE) theories:

Non-cosmological theories:

• Very few constraints (graviton mass < 10-22 eV)

Summary• Galileons interesting for many reasons

• Predict SEP violations

• Can test this with BH offsets

• New (strongest) constraints on galileons

• GW vs photon speed constrained by LIGO/Fermi

• Severe implications for cosmological gravity