Universality of free fall
versus ephemeris (INPOP)
Olivier Minazzoli
Chargé de recherche au Centre Scientifique de Monaco
Chercheur associé à ARTEMIS, Observatoire de la Côte d’Azur
Collaboration: Aurélien Hees, Agnès Fienga, Vishnu Viswanathan,
Leo Bernus, Jacques Laskar
INPOP
Intégrateur Numérique Planétaire de
l’Observatoire de Paris
Planetary numerical integrator of the Paris
Observatory
though, also developed a the
Observatoire de la Côte d’Azur
with A. Fienga
[Fienga et al., A&A 2008]
[Fienga et al., Celest. Mech. & Dyn. Astron. 2011]
[Fienga et al., Celest. Mech. & Dyn. Astron. 2015]
...
2
Theory: massless dilaton
[
1
2
S =∫ d x √ −g
R−2(∂
φ
)
(
) + L m ( gμ ν , φ ; Ψ i)
2κ
4
]
3
Theory: massless dilaton
[
1
2
S =∫ d x √ −g
R−2(∂
φ
)
(
) + L m ( gμ ν , φ ; Ψ i)
2κ
4
]
S point particles =∑ A ∫ m A (φ )d τ
Implies a violation of the universality of free fall
(UFF)
d ln m A ⃗
Roughly: δ a⃗A =−
∇ φ depends on composition of A
dφ
4
Linear coupling model:
[Damour & Donoghue, Phys. Rev. D 2010]
Lint =φ
(
de
4e
F −∑i d m mi ψ̄i ψi−d g T g
2
2
anom
i
)
Coefficients parameterizing the coupling to different sectors
T
anom
g
β3 2
=
G + ∑i γ m mi ψ̄i ψi
2 g3
i
An anomaly is said to occur when a symmetry of the classical action
is not a true symmetry of the full quantum theory
5
Linear coupling model:
[Damour & Donoghue, Phys. Rev. D 2010]
Lint =φ
(
de
4e
F −∑i d m mi ψ̄i ψi−d g T
2
2
i
anom
g
)
d ln m A ⃗
δ a⃗A =−
∇φ
dφ
d ln m A
*
=d g + ᾱ A
dφ
Dilatonic charges computed from atomic
physics
(depends on atomic numbers A and Z)
ᾱ A =[ (d m^ −d g)Q ' m^ +(d δ m−d g )Q ' δ m +(d m −d g)Q ' m + d e Q ' e ] A
e
e
6
Linear coupling model:
[Damour & Donoghue, Phys. Rev. D 2010]
At the end of the day:
m
GM A
⃗
a⃗T =∇ ∑ A
(1+δT )
r AT
*
g
δT ∼d ᾱ T
m
G
A
I
A
=1+ δ A
Parametrizes UFF violation
ᾱ T =[ (d m^ −d g )Q ' m^ +(d δ m−d g )Q ' δ m +(d m −d g)Q ' m + d e Q ' e ]T
e
e
7
Non-linear generalization:
[Minazzoli & Hees, Phys. Rev. D 2016]
Lint =
(
D e (φ )
4e
2
F −∑i Dm (φ )m i ψ̄i ψi− Dg (φ )T
2
i
anom
g
)
As well as generalization of gravity sector
[
(
ω(φ )
1
2
S G =∫ d x √ −g
f (φ ) R− φ (∂ φ )
2κ
4
)]
8
In general:
[Minazzoli & Hees, Phys. Rev. D 2016]
New!
At the end of the day:
GM A
⃗
a⃗T =∇ ∑ A
(1+δT )
r AT
*
g
δT ∼d ᾱ T
GM A
⃗
a⃗T =∇ ∑ A
(1+δT +δ AT )
r AT
[
]
f'
δT ∝ d −
ᾱT
2f
*
g
δ AT ∝ ᾱ A ᾱ T
9
GM A
⃗
a⃗T =∇ ∑ A
( 1+δT +δ AT )
r AT
Most of the time:
[
]
f'
δT ∝ d −
ᾱT
2f
*
g
δT ≫δ AT
δ AT ∝ ᾱ A ᾱ T
But sometimes:
δT <~ δ AT
In particular, for a universal coupling of the following form:
1 2
anom
Lint = √ f (φ )
F −∑i mi ψ̄i ψi−T g
2
4e
(
)
10
In general:
[Minazzoli & Hees, Phys. Rev. D 2016]
GM A
⃗
(1+δT +δ AT )
One truly has to consider: a⃗T =∇ ∑ A
r AT
1/ Because it can happen from a theoretical point of view
2/ Most importantly: when it happens, the theory is closer to
satisfying UFF constraints
Or in other words
When it happens, the theory describes something closer to what we
observe
11
What equation of motion goes in
INPOP?
12
What goes in INPOP
Post-Newtonian EIH
equation of motion
Nordtvedt effect
Usual PN param.
~
γ ∝1−α 20
~
2
β ∝1+β0 α 0
η≈α20 (1+ 4 β0 )
In total, 6 parameters to be determined: α 0 ,β0 , d m^ , d δ m , d m , d e
e
13
What about clocks?
νI
δWA
δ ln ν J =( δ^ I −δ^ J + δ^ IA −δ^ JA ) 2
c
(
)
Atomic spectroscopy
Coefficients given in [Minazzoli & Hees, Phys. Rev. D, 2016]
G mE
G
m
E
Δ
ν
^
^
Gravitational redshift ν
=
1+
δ
+
δ
−
1+ δ^ s + δ^ s E )
(
)
(
g
g
E
grav
r
r
e.g. ACES
g
s
g stands for “ground”, and s for “satellite”
14
All the theory is given in
[Hees & Minazzoli, arXiv:1512.05233]
Currently being re-written, new version should appear soon
Results with INPOP are on their way
Expectations:
From Will, Living Reviews
INPOP (planets)
Fienga et al.
δ
INPOP (Moon)
Viswanathan, Fienga
et al.
MICROSCOPE
(launched 2016)
Co-PI G. Metris
15
supplements
16
Linear coupling model:
[Damour & Donoghue, Phys. Rev. D 2010]
Remark:
d ln m A ⃗
δ a⃗A =−
∇φ
dφ
d ln m A
=d *g + ᾱ A
dφ
ᾱ A =[ (d m^ −d g)Q ' m^ +(d δ m−d g )Q ' δ m +(d m −d g)Q ' m + d e Q ' e ] A
e
d g=d m =d m =d m , d e =0
u
d
e
UFF → ✔
e
Lint =−d g φ ( ∑i mi ψ̄i ψi +T g
anom
)
17
The Earth-Moon system
Calern station
Observatoire de la Côte
d’Azur
Lunar and satellite laser
ranging
~50% of LLR data!!
18