Padova 24/01/2013���

Testing General Relativity ���and ���

the equivalence principle ���on���

astrophysical scales���

Jean-Philippe UZAN���

In brief

1.  General relativity in the Solar system���-  Theory (in very short!)���-  How well tested in Solar sytem���-  Parameter space and possible extensions���-  Need to test general relativity on astrophysical scales���

2.  Testing the equivalence principle on astrophysical scales���-  Link between constants an the equivalence principle���-  Physical systems���-  Current observational status���

���3.  Testing General relativity with the large scale structure of the Universe���

-  Idea of the test���-  Weak lensing and large scale structure���

���

General Relativity ���in���

the Solar system���

General Relativity���

Universality of free fall���Local position invariance���Local Lorentz invariance���

General relativity lies on Einstein equivalence principle���which states���

If this principle holds, gravity is the manifestation of the geometry of a spacetime.������Locally, in a free fall reference system, gravity can be “erased”.���

���

The equivalence principle is at the heart of theories of gravity from Galileo, Newton to Einstein.���

Equivalence principle���

The equivalence principle in Newtonian physics���

Inertial mass is the mass that appears in Netwon’s law of motion.���

Passive gravitational mass is the mass that characterizes the response to a ���gravitational field (notion of weight)���

Active gravitational mass characterizes the strength of the gravitational field created���by an object���

Action-reaction law implies that���

And thus is a constant, that can be chosen to be 1.���

Equivalence principle

Dynamics

•  Universality of free fall •  Local lorentz invariance •  Local position invariance

Relativity

General Relativity (with some equations)���

Tests on the universality of free fall

2011 MicroScope

The equivalence principle in Newtonian physics

The deviation from the universality of free fall is characterized by

Second law:

Definition of weight

So that

Consider a pendumum of length L in a gravitational field g,

Then

Lunar laser ranging���

Current contraints���

[Schlamminger, 2008]

Solar system tests���C

ourtesy of G. E

sposito-Farèse

Metric theories are usually tested in the PPN formalism

Perihelion shift of Mercury

Nordtvedt effect

Shapiro time delay

Light deflection

[Will, Liv. Rev. Relat. 2006-3]

Fifth force���The PPN formalism cannot be applied if the modification of General relativity has a range smaller than��� the Solar system scale.������Fifth force experiments���

Adelberger et al., Ann. Rev. Nucl. Part. Sci., 53 77 (2003) Adelberger et al., Prog. Part. Nucl. Phys 62, 102 (2009)

There is a growing need to test general relativity on astrophysical scales���

Testing general relativity on astrophysical scales

dynamics of galaxies ���and dark matter���

acceleration of the universe ���and dark energy���

but also theoretical motivations…���

Can we extend the test of general relativity on astrophysical scales?���

Parameter space

Tests of general relativity on astrophysical scales are needed

- galaxy rotation curves: low acceleration - acceleration: low curvature

Dark energy:

Solar system:

Dark matter:

Cosmology:

-30

-20

-10

0

-10 -15 -5

Black-hole lim

it

BBN

CMB

SNIa Dark energy R<Λ

Dark matter a<a0

Solar system

Sgr A

[Psaltis, 0806.1531]

R

R�

�

Dark sector���

Dark matter appears as a low acceleration problem������Dark energy appears as low curvature problem or low acceleration problem���

The dark energy problem can be attacked by��� - either introducing new physical d.o.f that may or may not be responsible ��� for a long-rande interaction��� - or introducing new geometrical d.o.f, e.g. by going beyond the Copernican��� principle���

���The number of modifications of general relativity are numerous.������We can define universality classes���

Universality classes of extensions

Ordinary matter

Ex : quintessence, ....

Ordinary matter

Ex : scalar-tensor, TeVeS ....

Ordinary matter

Ex : brane induced gravity multigravity,...

Ex : axion-photon mixing

[JPU, Aghanim, Mellier, PRD 05] [JPU, GRG 2007]

Ordinary matter

Always need NEW fields

Variation of constants Poisson equation

Distance duality

Variation of constants Poisson equation

Dark sector���

Dark matter appears as a low acceleration problem������Dark energy appears as low curvature problem or low acceleration problem���

The dark energy problem can be attacked by��� - either introducing new physical d.o.f that may or may not be responsible ��� for a long-rande interaction��� - or introducing new geometrical d.o.f, e.g. by going beyond the Copernican��� principle���

���The number of modifications of general relativity are numerous.������We can define universality classes.������Question:������ How well is GR a good description of gravity on astrophysical scales ?���

Testing the equivalence principle���

Equivalence principle and constants���

In general relativity, any test particle follow a geodesic, which���does not depend on the mass or on the chemical composition���

2- Universality of free fall has also to be violated���

1- Local position invariance is violated.���

In Newtonian terms, a free motion implies��� d�p

dt= m

d�v

dt= �0

Imagine some constants are space-time dependent���

Mass of test body = mass of its constituants + binding energy ���

d⇥p

dt= ⇥0 = m⇥a +

dm

d��̇⇥v

m�aanomalous

But, now���

Equivalence principle and constants

S = ��

mA[�i]c⇥�gµ�vµv�dt vµ = dxµ/dt

uµ = dxµ/d�

Action of a test mass:

with

�S = 0

g00 = �1 + 2�N/c2

(NOT a geodesic)

(Newtonian limit)

Dependence on some constants

aµA = �

⇧

i

⇤⇥ lnmA

⇥�i

⇥�i

⇥x�

⌅ �g�µ + u�uµ

⇥

⇥aA = �c2⇤

i

fA,i

�⇥�i + �̇i

vc2

⇥

fA,i

a = gN + �aA Anomalous force Composition dependent

[Dicke 1964,…]

Atomic clocks

Oklo phenomenon

Meteorite dating Quasar absorption spectra

CMB

BBN

Local obs

QSO obs

CMB obs

Physical systems

JPU, RMP (2003); arXiv:0907.3081, arXiv:1009.5514

Observables and primary constraints A given physical system gives us an observable quantity

External parameters: temperature,...:

Primary physical parameters

From a physical model of our system we can deduce the sensitivities to the primary physical parameters

The primary physical parameters are usually not fundamental constants.

Atomic clocks���Based the comparison of atomic clocks using different transitions and atoms e.g. hfs Cs vs fs Mg : gpµ ;

hfs Cs vs hfs H: (gp/gI)α

Marion (2003) Bize (2003) Fischer (2004) Bize (2005) Fortier (2007)

Peik (2006) Peik (2004)

Blatt (2008) Cingöz (2008)

Blatt (2008)

Examples

High precision / redshift 0 (local)

Quasar absorption spectra���

Observed spectrum

Reference spectrum

Cloud

Earth

Quasar emission spectrum

Absorption spectrum

QSO absorption spectra���3 main methods:

Alkali doublet (AD)

Single Ion Differential α Measurement (SIDAM)

Many multiplet (MM)

Fine structure doublet,

Si IV alkali doublet

Single atom Rather weak limit

Savedoff 1956

Webb et al. 1999

Levshakov et al. 1999

VLT/UVES: Si IV in 15 systems, 1.6<z<3

Chand et al. 2004

Compares transitions from multiplet and/or atoms s-p vs d-p transitions in heavy elements Better sensitivity

Analog to MM but with a single atom / FeII

HIRES/Keck: Si IV in 21 systems, 2<z<3

Murphy et al. 2001

�⇥/⇥ � �2

QSO: many multiplets���

The many-multiplet method is based on the corrrelation of the shifts of different lines of different atoms. Dzuba et al. 1999-2005

Relativistic N-body with varying α:

HIRES-Keck, 143 systems, 0.2<z<4.2

Murphy et al. 2004 5σ detection !

First implemented on 30 systems with MgII and FeII

Webb et al. 1999

R=45000, S/N per pixels between 4 & 240, with average 30 Wavelength calibrated with Thorium-Argon lamp

QSO: VLT/UVES analysis���

Selection of the absorption spectra: - lines with similar ionization potentials most likely to originate from similar regions in the cloud - avoid lines contaminated by atmospheric lines - at least one anchor line is not saturated redshift measurement is robust - reject strongly saturated systems

Only 23 systems lower statistics / better controlled systematics R>44000, S/N per pixel between 50 & 80

VLT/UVES

DOES NOT CONFIRM HIRES/Keck DETECTION

Srianand et al. 2007

To vary or not to vary���

[Webb et al., 2010]

Claim: Dipole in the fine structure constant [« Australian dipole »] Indeed, this is a logical possibility to reconcile VLT constraints and Keck claims of a variation.

Keck VLT Keck&VLT

X

Atomic clocks

Oklo phenomenon

Meteorite dating Quasar absorption spectra

Pop III stars

21 cm

CMB

BBN

Physical systems: new and future

[Coc, Nunes, Olive, JPU, Vangioni]

[Ekström, Coc, Descouvemont, Meynet, Olive, JPU, Vangioni, 2009]

JPU, Liv. Rev. Relat., arXiv:1009.5514

Varying constants

The constant has to be replaced by a dynamical field or by a function of a dynamical field

This has 2 consequences: 1- the equations derived with this parameter constant will be modified one cannot just make it vary in the equations

2- the theory will provide an equation of evolution for this new parameter

The field responsible for the time variation of the « constant » is also responsible for a long-range (composition-dependent) interaction

i.e. at the origin of the deviation from General Relativity. In most extensions of GR (e.g. string theory), one has varying constants.

The new fields can make the constants become dynamical.

Famous example: Scalar-tensor theories

spin 2 spin 0

Maxwell electromagnetism is conformally invariant in d=4

Light deflection is given as in GR

What is the difference?

The difference with GR comes from the fact that massive matter feels the scalar field

Motion of massive bodies determines GcavM not GM.

Thus, in terms of observable quantities, light deflection is given by

which means

graviton scalar

[Strified theory, AQUAL,…, TeVeS,… (See J. Bekenstein, C. Skordis talks]

Example of varying fine structure constant

It is a priori « easy » to design a theory with varying fundamental constants

But that may have dramatic implications.

Consider

Requires to be close to the minimum

Violation of UFF is quantified by

�12 = 2|⇥a1 � ⇥a2||⇥a1 + ⇥a2|

It is of the order of

=fext|f1 � f2|

1 + fext(f1 + f2)/2

Testing general relativity���with���

large scale structures���

Light deflection in the Solar system���

(c) L. Haddad & G. Duprat

Light deflection���Planteray orbits (Kepler law)���

Agreement���

Extending the idea���

We need two independent observables���

Large scale structures���

Matter distribution��� Weak lensing���

Uzan, Bernardeau (2001)���

Original idea of 2001 On sub-Hubble scales, in weak field (typical regime for the large scale structure)

Weak lensing Galaxy catalogues

Distribution of the gravitational potential

Distribution of the matter

Compatible? [JPU, Bernardeau (2001)]

Can we construct a post-ΛCDM formalism for the interpretation the large scale structure data?

Post-ΛCDM Restricting to low-z and sub-Hubble regime

Background

Sub-Hubble perturbations

[JPU, astro-ph/0605313; arXiv:0908.2243] [Schimdt, JPU, Riazuelo, astro-ph/0412120]

Testing ΛCDM

w

η,R,… Q

Interacting DE

Numbers? Functions?

Data and tests

Weak lensing Galaxy map

Integrated Sachs-Wolfe

Velocity field

DATA OBSERVABLE

Various combinations of these variables have been considered

Pδ

PΔΦ

JPU and Bernardeau, Phys. Rev. D 64 (2001)

What to expect with Euclid���

(i) Visible imaging (ii) NIR photometry (iii) NIR spectroscopy. 15,000 square degrees 100 million redshifts, 2 billion images Median z~1 I will provide: - P(k,z) on 15,000 square degrees, 70,000,000 galaxy redshift with 0.5<z<2. - weak lensing on 15,000 square degrees, 40 galaxy images per square arcmin with 0.5<z<3.

The error bars on the B-modes should be divided by (10-40) compared to CFHTLS. Linear regime typically for scales larger than 1 deg. And Euclid will probe scales up to ~40 deg. It will allow to test general relativity on this scales, with the use of the linear regime.

Conclusions���

1.  General relativity in the Solar system���-  Very well tested in the Solar sytem���-  Need to test general relativity on astrophysical scales (dark sector)���-  Huge number of extensions (massive gravity etc..)���

2.  Testing the equivalence principle on astrophysical scales���-  Link between constants an the equivalence principle���-  Number of physical systems is increasing���-  Stronger constraints & soon results from Planck���

3.  Testing General relativity with the large scale structure of the Universe���-  Idea of the test���-  Weak lensing and large scale structure���-  Euclid���-  Possibility to use CMB data depending on what we get for non-Gaussianity���

���

Advertisement���A popular science book explaining the importance of fundamental constants and the whole history arounf their possible variation (from Dirac & Eddington to string theory) has been translated in Italian.���