Synergizing Screening Mechanisms on Different Scales

Jeremy Sakstein University of Pennsylvania

Probing the dark sector and general relativity at all scales

CERN 17th August 2017

Or…. What should astrophysical tests of gravity mean to you?

Jeremy Sakstein University of Pennsylvania

Probing the dark sector and general relativity at all scales

CERN 17th August 2017

Two views of MG

• Want UV modifications of gravity

• Higher-order operators

• Typically satisfy SS bounds

• Look for deviations from GR in strong field regime

1) Strong field:

Two views of MG

• Want IR modifications of gravity

• Relevant for cosmology but ruled out by SS bounds

• Use screening mechanisms to hide modifications in SS

• Natural suppression of deviations

• Don’t need to tune parameters

2) Cosmologists:

Screening mechanisms

Non-linear effects decouple cosmological scales from the solar system

solar system astrophysics cosmology

screened partially screened unscreened

Some inconvenient truths about screening mechanisms

• Highly-non-linear field equations

Can’t use PPN Well-posedness? Do we care (EFT)? Two-body/low symmetry systems?

• Need novel tests

Complex modelling for laboratory tests Novel astrophysical probes

Astrophysical probes - mildly screened regime

Cepheid stars Dwarf stars Galaxy clusters

White dwarf stars Neutron starsBlack holes

The problem with MGNewtonian limit of GR:

r2�N = 4⇡G⇢ FN = r�N

Modified gravity — new scalar graviton:

F5 = ↵r�

F5

FN= 2↵2

r2� = 8⇡↵G⇢

solar system: 2↵2 < 10�5

(Shapiro time-delay effect, Cassini)

Screening mechanisms

Two options:

Non-Poisson kinetic terms Vainshtein screening

Kill off the source no scalar gradient

chameleon/symmetron/f(R)

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

Chameleon screening

Add a scalar potential:

r2� = 8⇡↵G⇢+ V (�),�

Get these to cancel out dynamically

r2� = 0

r2� = 8⇡↵G⇢

rs

R

Chameleon/Symmetron/f(R)

Chameleon/Symmetron/f(R)

r2� = 0

r2� = 8⇡↵G⇢

rs

R

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

• Covariant galileons

• Massive gravity

• Massive bi-gravity

• Horndeski

• Beyond Horndeski — breaks down inside objects

VERY generic scalar-tensor theories

with three D.O.F

Screened

Unscreened

(�PPN = 1)

Vainshtein breaking in beyond Horndeski

Fgrav =GM(r)

r2+⌥1G

4

d2M(r)

dr2

Inside objects:

E.g. for the simplest case (one new scalar d.o.f):

T H E A L P H A PA R A M E T E R S

↵B(t) `braiding’ — mixing of scalar + metric kinetic terms.:

kinetic term of scalar field.↵K(t) :

speed of gravitational waves, . ↵T (t) : c2T = 1 + ↵T

running of effective Planck mass.:↵M (t) =1

H

d ln M2(t)

dt

↵H(t) disformal symmetries of the metric.:

VERY important parameter

Credit: Tessa Baker

VERY important parameter

5 functions that control linear cosmology (EFT of DE)

NR probes combinations of three of them:

⌥1 =4↵2

H

c2T (1 + ↵B)� ↵H � 1

Constraining these constrains cosmology!

Outline of this talk

• Chameleon/symmetron/f(R) — Cepheid stars

• Vainshtein/galileons — supermassive black holes

• Beyond Horndeski — dwarf + neutron stars

- strength of fifth-force

- self-screening parameter

object is unscreened if

(fully unscreened)

Chameleon/symmetron/f(R)Two parameters:

(fR0 = 2�0/3)

r2� = 8⇡↵G⇢

rs

Astrophysical screening

main-sequence post-MS dwarf galaxy

Need void dwarfs due to environmental screening

Complication: environmental screening

Can only use unscreened dwarf galaxies in voids!

Screening map of SDSS data: Cabre et al. 2012

Chameleon stars — MESA

A new and powerful tool to compare with observations

2↵2 = 1/3

Testing chameleons using starsParameters probed using distance indicators

Need a formula to relate observational data to distances

Test using distance indicators

Main idea:

• Distances measurements assume theory of gravity

• Different methods should agree

• Compare distances to unscreened galaxies

d2L =L

4⇡FE.g. Luminosity distance:

CepheidsPeriod-luminosity relation

Cares about gravity:

�d

d= �0.3

�G

G

T / G�1/2

Tip of the red giant branch

• Peak luminosity is fixed - standard candle • Set by nuclear physics - independent of gravity

Distance indicators

New constraints

Excluded

Jain, Vikram, JS (2012)

f(R)

The big pictureBurrage, JS ‘16

↵ = � =MPl

M

Astrophysics can’t do better than thisn = 1

Ve↵ =⇤4+n

�n+

↵�⇢

Mpl

Negative n is also a chameleon!

F (R) lives here

⇤ = 2.4⇥ 10�3 eV

Chameleon relevant for cosmology

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Symmetron/Chameleon/f(R)/photon coupling

Astrophysics

AtomInterferometry

Eo..t-Wash

0 5 10 15 20-100

-80

-60

-40

-20

0

Ve↵ = �µ2

2

✓1� ⇢

µ2M2s

◆+

�

4�4

µ = 2.4⇥ 10�3eV

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

• Nice UV properties

• Massive gravity

• Braneworld models

• Hard to test due to Vainshtein screening

No hair theorem

No galileon charge Q so BH does not feel galileon force

Hui & Nicolis ‘12

Black holes described by mass and spin only!

Q = MMatter has

Matter and BH fall at different rates

Violation of the strong equivalence principle

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

M 87

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!

Screened

Unscreened

Tests of beyond Horndeski

Tests of beyond Horndeski

Fgrav =GM(r)

r2+⌥1G

4

d2M(r)

dr2

�2

3< ⌥1 < 1

No stable stellar configurations Saito et al. 2015

Gravity weaker than GR!

Dwarf stars - a new test of gravity

Red dwarf

Dwarf stars - a new test of gravity

Perfect tests:

• Chemically and structurally homogeneous

• Equation of state is well-known

• Lots of interest in low mass objects (KEPLER, GAIA)

Low mass M-R

Brown dwarf

Red dwarf

MMHB

Gravity weaker

Core cooler and less dense at fixed mass

Higher MMHB

Red dwarfs — MMHBHydrogen burning when core is hot and dense enough

Red dwarfs — MMHB

LHB = Le↵

Stable burning when production balances loss

EOS + theory of gravity Proton burning

:

MMMHB = 0.08�(⌥1)

�(⌥1 = 0)M�

New constraintLowest mass star is Gl 886 C

M = 0.0930± 0.0008M�

) ⌥1 < 0.027

JS, PRL (2015)

Neutron stars

Mass — Sun

Radius — few km

Relativistic: v/c ⇠ 1

Mass, spin, charge, quadrupole moment,…, hair!

Testing GR with neutron stars

• No rotation — mass-radius relation

• O( ) — moment of inertia

• O( ) — tidal Love number/quadrupole moment

!Angular velocity

!

!2

Can we test Vainshtein with this?

Most massive NS observed

Larger maximum mass

Larger radii

Devil is in the detail

Babichev, …, JS ‘16

Equation of state is unknown!

Need EOS-independent testsBreu, Rezzolla ‘16

Moment of inertia

We can do this for BH

Modifications are larger than the scatter

This measurement is 10 years away!Need specific systems to decouple spin-orbit coupling

Complication: rotation effects scalar at O( ) but not O( ). Lose integrability.!!2

Credit: Alessandra Bounanno

Summary — novel astrophysical probes

• Chameleons/symmetrons/f(R):

Test using distance indicators Astrophysical region nearly saturated

• Vainshtein:

SMBHs — normal branch in trouble Can push to self-accelerating with future surveys

• Beyond Horndeski:Directly constrains cosmology Dwarf and neutron stars promising probes