Constraints on Lorentz symmetry violations using lunar ...moriond.in2p3.fr/2019/Gravitation/transparencies/4... · CONSTRAINTS ONLORENTZ SYMMETRY VIOLATIONS USING LUNAR LASER RANGING

Rencontres de Moriond, La Thuile, Italy

CONSTRAINTS ON LORENTZ SYMMETRY VIOLATIONS

USING LUNAR LASER RANGING OBSERVATIONS

A. Bourgoin1,2, A. Hees1, C. Le Poncin-Lafitte1,S. Bouquillon1, G. Francou1, M.-C. Angonin1,

C. Courde3, J.-M. Torre3 and J. Chaibe3

1SYRTE, Observatoire de Paris, 2University of Bologna, 3Universite Cote d’Azur, CNRS,Observatoire de la Cote d’Azur, IRD, Geoazur

March 27th, 2019

Outline

1 IntroductionTests of GRPostfit analysisLunar laser rangingDynamical modelingResults in pure GR

2 SME minimally coupledPresentationModelingSME coefficientsRealistic errors

3 SME gravity-matter couplingsPresentationModelingSME coefficientsRealistic error

Outline




Alternative theories of gravity

Solar system scale frameworks

The fifth force formalisma (cf. Fig.) :

V(r) = �Gm

r(1 + ↵e

�r/�).

The PPN formalismb :

10 parameters(�, �, ⇠,↵{1,2,3}, . . .),�� 1 = (+2.1± 2.3)⇥ 10�5 c,��1 = (+0.2±2.5)⇥10�5 d.

a. Fischback et. al, 1986b. Nordtvedt, 1968 & Will, 1971c. Bertotti et. al, 2003d. Verma et. al, 2014

Konopliv et. al, 2011

Standard-model extension (SME)

Colladay and Kostelecky 1997, 1998 ; Bailey and Kostelecky 2006 ; Kostelecky andTasson 2011

Parametrizes Lorentz symmetry violations in all physics,

Contains both the standard model of particles physics and GR,

Derived from an action principle,=) not covered by PPN, fifth force, . . .

4 / 24

Alternative theories of gravity

Solar system scale frameworks

The fifth force formalisma (cf. Fig.) :

V(r) = �Gm

r(1 + ↵e

�r/�).

The PPN formalismb :

10 parameters(�, �, ⇠,↵{1,2,3}, . . .),�� 1 = (+2.1± 2.3)⇥ 10�5 c,��1 = (+0.2±2.5)⇥10�5 d.

a. Fischback et. al, 1986b. Nordtvedt, 1968 & Will, 1971c. Bertotti et. al, 2003d. Verma et. al, 2014

Konopliv et. al, 2011

Standard-model extension (SME)

Colladay and Kostelecky 1997, 1998 ; Bailey and Kostelecky 2006 ; Kostelecky andTasson 2011

Parametrizes Lorentz symmetry violations in all physics,

Contains both the standard model of particles physics and GR,

Derived from an action principle,=) not covered by PPN, fifth force, . . .

4 / 24

Data analysis

Postfit analysisLook for oscillating signatures in residuals,

1 Oscillating signatures are derived analytically,2 Oscillating signatures are fitted in residuals,

Major problems

Oscillating signatures only for short period,

Estimate only SME coefficients=) No correlations with other global parameters,=) Formal errors are over optimistic a.

a. Le Poncin-Lafitte et. al, 2016

Constraints on Lorentz symmetry violations=) Global LLR data analysis : confrontation between observations and predictions.

Simulate the LLR observable in SME framework :=) Effects on orbital motions,=) Effects on light propagation.

Short and long periodic oscillations :=) Numerical integration.

Fit and correlations with global parameters :=) Clean partial derivatives.

5 / 24

Data analysis



Major problems








5 / 24

Data analysis



Major problems








5 / 24

Lunar laser ranging

5 LLR stations :McDonald 2.7m, MLRS1, MLRS2 (Texas)Grasse Yag, Rubis, MeO (France)Haleakala (Hawaii)Matera (Italie)Apache-point (Texas)

•••••

5 retroreflectors :Apollo XIApollo XIVApollo XVLunokhod 1Lunokhod 2

•••••1 pulse contains

1018 photons

Only 1 photonover 109 is reflected

Only0.01 photonsper pulse are

detected

1 pulse ' 0.2ns

pulse separation ' 2.9ns

10 pulsesper second

6 / 24

Ephemeride Lunaire Parisienne Numerique (ELPN)

Modeling

ICRF (cT, X, Y, Z), with T the TDB,

Earth, the Moon, the Sun, planets, Pluto and the 70 most massive asteroids,

Physical effects1 Newtonian point-mass interactions.

2 Figure potential of bodies :=) J2 for the Sun,=) Jn, with n = 5 for the Earth,=) Degree 2, 3, 4 and 5 for the Moon.

3 Earth orientation :=) Precession UAI 1976,=) Nutation UAI 1980 (terms in 18.6 yr).

4 Tidal and spin effects :=) Anelastic deformations (Time-lag),

5 Relativistic point-mass interactions :=) Solar system barycentre,=) TT � TDB = f (TDB),=) Geodetic precession effect,=) SME corrections.

6 Lunar librations :=) Momentums,=) Fluid lunar core (dissipation).

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Residuals ELPN in GR

⇢[c

m]

UTC [year]

McDonaldApache point

GrasseHaleakala

Matera

Stations LLR Period �ELPN [cm] �INPOP13b [cm] 1 �DE430 [cm] 1

McDonald 2.7m 1969-1985 35.0 31.9 30.2McDonald MLRS1 1983-1988 35.1 29.4 27.7McDonald MLRS2 1988-2013 9.7 5.4 4.9

Grasse Rubis 1984-1986 17.6 16.0 14.6Grasse Yag 1987-2005 4.5 6.6 5.6Grasse MeO 2009-2013 3.6 6.1 3.5

Haleakala 1984-1990 9.8 8.6 8.3Matera 2003-2013 9.1 7.1 5.8

Apache-point 2006-2013 3.8 4.9 4.21. Fienga et. al 2014 8 / 24

Outline




SME minimally coupled

The pure gravitational sector (Bailey et. al, 2006)

Stot = Sg + Sm + Sf

Field action : Sg =1

2

Zd4

xp�g(R � uR + s

µ⌫R

T

µ⌫ + t↵�µ⌫

C↵�µ⌫),

Matter action : Sm = Sm[ m, gµ⌫ , u, sµ⌫ , t

↵�µ⌫ ],

Point particle action : Sf = �mc

Zds.

Functional derivativesModified field equations, m minimally coupled to gµ⌫ :=) EEP,=) geodesic equations,

Observational implications

Spontaneous Lorentz violation (u, sµ⌫ , t

↵�µ⌫),At post-Newtonian level, u and t

↵�µ⌫ play no role,=) s

µ⌫ .

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SME minimally coupled

The pure gravitational sector (Bailey et. al, 2006)

Stot = Sg + Sm + Sf

Field action : Sg =1

2

Zd4

xp�g(R � uR + s

µ⌫R

T

µ⌫ + t↵�µ⌫

C↵�µ⌫),

Matter action : Sm = Sm[ m, gµ⌫ , u, sµ⌫ , t

↵�µ⌫ ],

Point particle action : Sf = �mc

Zds.

Functional derivativesModified field equations, m minimally coupled to gµ⌫ :=) EEP,=) geodesic equations,


Spontaneous Lorentz violation (u, sµ⌫ , t

↵�µ⌫),At post-Newtonian level, u and t

↵�µ⌫ play no role,=) s

µ⌫ .

10 / 24

Orbital and time delay effects

Orbital motion

Equations of motion (cT, X, Y, Z) :

aJ =

GNM

r3

s

JK

tr

K �32

sKL

tr

Kr

Lr

J + 3sTK

VK

rJ � s

TJV

Kr

K � sTK

VJr

K

+ 3sTL

VK

rK

rLr

J + 2�m

M

⇣s

TKv

Kr

J � sTJ

vK

rK

⌘�.

Rescaled Newtonian constant : GN = G(1 + 53 s

TT).

3D Traceless tensor sJKt = s

JK � 13 s

TT�JK .

Gravitational light time delay

Time delay (cT, X, Y, Z) :

�⌧g =X

b=S,T

(2GNmb

c3

1 �

23

sTT � s

TJd

J

�ln

"rbO + rbR + d

rbO + rbR � d

#

�GNmb

c3

23

sTT � s

TJd

J � sJK

th

J

bh

K

b

�⇣r

K

bRd

K � rK

bOd

K

⌘

�GNmb

c3

13

sTT

dK

hK

b� s

TJh

J

b+ s

JK

td

Jh

K

b

�hb

�rbR � rbO

�

rbOrbR

),

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Correlations

Data analysis

sµ⌫ =) 10 parameters : (sTT , s

TX , sTY , s

TZ , sXXt

, sXYt

, sXZt

, sYYt

, sYZt

, sZZt

),

Brutal fit of sµ⌫ with 46 other global physical parameters,

=) Some high correlations,=) SME coefficient correlations (cf. Tab.).

sTT

sTX

sTY

sTZ

sXX

ts

XY

ts

XZ

ts

YY

ts

YZ

ts

ZZ

t

sTT

1.00

sTX -0.11 1.00

sTY -0.03 -0.01 1.00

sTZ 0.03 0.02 -0.99 1.00

sXX

t-0.01 0.08 -0.02 0.02 1.00

sXY

t0.01 -0.03 -0.09 0.09 -0.14 1.00

sXZ

t-0.04 -0.01 -0.05 0.05 -0.16 0.30 1.00

sYY

t0.02 -0.11 -0.02 0.01 0.95 -0.12 -0.12 1.00

sYZ

t-0.08 0.73 -0.05 0.07 0.14 -0.07 -0.09 -0.12 1.00

sZZ

t0.07 -0.62 0.03 -0.05 0.40 -0.02 -0.01 0.64 -0.84 1.00

TABLE – Table of correlations between SME coefficients of the minimal SME.

12 / 24

LLR data sensitivity

SME coefficients

4 SME coefficients : (sTT , sTX , s

XYt

, sXZt

),

3 linear combinations : (sA, sC , s

D) where

sA = s

XX

t� s

YY

t,

sC = s

TY + 0.37sTZ ,

sD = s

XX

t+ s

YY

t� 2s

ZZ

t� 1.89s

YZ

t.

sTT

sTX

sXYt

sXZt

sA

sC

sD

sTT

1.00

sTX -0.07 1.00

sXYt

0.00 0.04 1.00

sXZt

-0.04 0.09 0.28 1.00

sA 0.00 -0.01 -0.02 -0.07 1.00

sC 0.03 -0.04 0.03 -0.05 0.04 1.00

sD -0.02 0.04 -0.08 -0.12 -0.31 0.00 1.00


Maximum sensitivity

With LLR : |sTT | < 10�4,

With VLBI : |sTT | < 10�5 (Le Poncin-Lafitte et. al, 2016).

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SME coefficients

4 SME coefficients : (sTT , sTX , s

XYt

, sXZt

),

3 linear combinations : (sA, sC , s

D) where

sA = s

XX

t� s

YY

t,

sC = s

TY + 0.37sTZ ,

sD = s

XX

t+ s

YY

t� 2s

ZZ

t� 1.89s

YZ

t.

sTT

sTX

sXYt

sXZt

sA

sC

sD

sTT

1.00

sTX -0.07 1.00

sXYt

0.00 0.04 1.00

sXZt

-0.04 0.09 0.28 1.00

sA 0.00 -0.01 -0.02 -0.07 1.00

sC 0.03 -0.04 0.03 -0.05 0.04 1.00

sD -0.02 0.04 -0.08 -0.12 -0.31 0.00 1.00


Maximum sensitivity

With LLR : |sTT | < 10�4,

With VLBI : |sTT | < 10�5 (Le Poncin-Lafitte et. al, 2016).

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Systematic errors

Constraints

Realistic error,

Chi-square fit may underestimates formal errors,=) Look for neglected systematics.

Indice (l) N{l} Station Instrument Period0 - - - -1 1590 McDonald 2.7m 1969-19752 1739 McDonald 2.7m 1975-19833 187 McDonald 2.7m 1983-19874 573 McDonald MLRS1 1983-19895 469 McDonald MLRS2 1988-19946 2048 McDonald MLRS2 1994-20007 767 McDonald MLRS2 2000-20158 1182 Grasse Rubis 1984-19879 1494 Grasse Yag 1987-1991

10 1942 Grasse Yag 1991-199511 3479 Grasse Yag 1995-200112 1398 Grasse Yag 2001-200613 1661 Grasse MeO 2009-201514 757 Haleakala - 1984-199115 2378 Apache-point - 2006-201516 107 Matera - 2003-2015

TABLE – Table of definition of LLR data subsamples by LLR stations.14 / 24

Systematic errors

Constraints

Realistic error,

Chi-square fit may underestimates formal errors,=) Look for neglected systematics.

Indice (l) N{l} Station Instrument Period0 - - - -1 1590 McDonald 2.7m 1969-19752 1739 McDonald 2.7m 1975-19833 187 McDonald 2.7m 1983-19874 573 McDonald MLRS1 1983-19895 469 McDonald MLRS2 1988-19946 2048 McDonald MLRS2 1994-20007 767 McDonald MLRS2 2000-20158 1182 Grasse Rubis 1984-19879 1494 Grasse Yag 1987-1991

10 1942 Grasse Yag 1991-199511 3479 Grasse Yag 1995-200112 1398 Grasse Yag 2001-200613 1661 Grasse MeO 2009-201514 757 Haleakala - 1984-199115 2378 Apache-point - 2006-201516 107 Matera - 2003-2015

TABLE – Table of definition of LLR data subsamples by LLR stations.14 / 24

Data subsamples by LLR station

FIGURE – Evolution of formal error of with subsamples by LLR stations.

15 / 24

Data subsamples by LLR retroreflectors

FIGURE – Evolution of formal error with subsamples by LLR retroreflectors.

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Jackknife resampling methode

Jackknife recipe

Let �j

n(D) be an estimator of the jth SME coefficient, defined for sample D = (D1, · · · ,Dn).

We construct n independent estimation of the jth SME coefficient with mean �j

n(D), labeled asps

j

i(D) and called pseudovalues

psj

i(D) = �j

n(D) + (n�1)

h�j

n(D)� �j

n�1(D[i])i

.

Where D[i] means the sample D with the ith value Di deleted from the sample.

We compute the mean and the sample variance of pseudo-values with the central limit theorem

psj = 1

n

nX

i=1

psj

i(D) and Vps(D) = 1

n�1

nX

i=1

hps

j

i(D)� ps

j

i2,

The Jackknife estimator is given by, psj(D)± �jackknife with �jackknife =

q1n

Vps(D).

Application to LLR

Jackknife applied to LLR stations (�sta),

Jackknife applied to LLR retroreflectors (�ref),

Realistic final error : �r =q

�2 + �2sta + �2

ref .

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Constraints on SME coefficients

Analysis Postfit Global

SMETechnique LLR & Atom.

Int. Binary pulsars LLR & Plan.Eph. LLR

sTX [10�9 ] +50 ± 620 �5.2 ± 5.3 +4.3 ± 2.5 �5.5 ± 7.9

sXYt

[10�12] �600 ± 1500 �35 ± 36 +65 ± 32 �3.4 ± 5.7s

XZt

[10�12] �2700 ± 1400 �20 ± 20 +20 ± 10 +0.2 ± 8.6s

A [10�12] �1200 ± 1600 �100 ± 100 +96 ± 56 +1.6 ± 9.3s

C [10�9 ] �100 ± 2900 �10 ± 9 �5 ± 24 +6.3 ± 7.3s

D [10�11] +200 ± 3800 �12 ± 12 +16 ± 8 +1.0 ± 2.3

TABLE – Table of pseudo-constraints (postfit analysis) and constraints (global analysis) on SMEcoefficients of the minimal SME. Results from LLR & Atom. Int. are taken from Battat et. al,2007 and Chung et. al, 2009. Results from binary pulsars are taken from Shao 2014 and resultsLLR & Plan. Eph. are taken from Hees et. al, 2015. Results determined by the global analysisare taken from Bourgoin et. al, 2016 and are given at 1�r .

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Outline




SME gravity matter couplings

General presentation (Kostelecky et. al, 2011)

Stot = Sg + Sm + Sf

Field action : gravitational minimal SME,Matter action : Sm = Sm[ m, gµ⌫ , u, s

µ⌫ , t↵�µ⌫ , cµ⌫ , (aeff)µ],

Point particle action : Sf = �Z

cd�hm

p(gµ⌫ + cµ⌫)uµu⌫ + (aeff)µu

µi

Functional derivativesModified field equations, m is not minimally coupled to gµ⌫ :=) violation EEP,=) 6= geodesic equations.


Spontaneous Lorentz violation (cµ⌫ , (aeff)µ),cµ⌫ = 0,=) (aeff)µ.

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Orbital and time delay effect

Orbital motion

Equations of motion (cT, X, Y, Z) :

aJ =

GN M

r3

(s

JK

tr

K �32

sKL

tr

Kr

Lr

J � sTJ

VK

rK � s

TKV

Jr

K + 3sTL

VK

rK

rLr

J

+ 3

sTK �

23

X

w

nw

3

M↵(a

w

eff)K

�V

Kr

J + 2�m

M

s

TK +X

w

nw

2

�m↵(a

w

eff)K

�v

Kr

J

� 2�m

M

s

TJ +X

w

nw

2

�m↵(a

w

eff)J

�v

Kr

K

).

Depends on composition w = {e, p, n},

Gravitational light time delay

Time delay (cT, X, Y, Z) :

�⌧g =X

b=S,T

(2GN mb

c3

1 �

23

sTT +

X

w

Nw

b

mb

↵(aw

eff)T

�

sTJ �

X

w

Nw

b

mb

↵(aw

eff)J

�d

J � 2X

w

nw

3

M↵(a

w

eff)T

!ln

"rbO + rbR + d

rbO + rbR � d

#

�GN mb

c3

23

sTT +

X

w

Nw

b

mb

↵(aw

eff)T �

s

TJ �X

w

Nw

b

mb

↵(aw

eff)J

�d

J � sJK

th

J

bh

K

b

!⇣r

K

bRd

K � rK

bOd

K

⌘

�GN mb

c3

13

sTT

dK

hK

b�

sTJ �

X

w

Nw

b

mb

↵(aw

eff)J

�h

J

b+ s

JK

td

Jh

K

b

!hb

�rbR � rbO

�

rbOrbR

).

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Analysis

12 parameters ↵(aw

eff)µ [GeV/c2] for w = {e, p, n}.

Neutral macroscopic bodies : Ne

b = Np

b,

=) ↵(ae+p

eff )µ = ↵(ae

eff)µ + ↵(ap

eff)µ=) 8 parameters,With LLR : |↵(ae+p

eff )T | ' |↵(an

eff)T | < 10�4,With free fall (WEP) a : |↵(ae+p

eff )T | ' |↵(an

eff)T | < 10�10

=) 6 parameters.

a. Kostelecky and Tasson, 2010

SME coefficients

2 SME coefficients : (sXY , sXZ),

4 linear combinations : (sA, sD, s

E, sF) where

sA = s

XX

t� s

YY

t,

sD = s

XX

t+ s

YY

t� 2s

ZZ

t� 1.89s

YZ

t,

sE = s

TX � 1.22↵(ae+p

eff )X � 1.23↵(an

eff)X ,

sF = s

TY + 0.37sTZ � 0.12↵(ae+p

eff )Y � 0.12↵(an

eff)Y

� 0.052↵(ae+p

eff )Z � 0.052↵(an

eff)Z .

22 / 24


Analysis

12 parameters ↵(aw

eff)µ [GeV/c2] for w = {e, p, n}.

Neutral macroscopic bodies : Ne

b = Np

b,

=) ↵(ae+p

eff )µ = ↵(ae

eff)µ + ↵(ap

eff)µ=) 8 parameters,With LLR : |↵(ae+p

eff )T | ' |↵(an

eff)T | < 10�4,With free fall (WEP) a : |↵(ae+p

eff )T | ' |↵(an

eff)T | < 10�10

=) 6 parameters.

a. Kostelecky and Tasson, 2010

SME coefficients

2 SME coefficients : (sXY , sXZ),

4 linear combinations : (sA, sD, s

E, sF) where

sA = s

XX

t� s

YY

t,

sD = s

XX

t+ s

YY

t� 2s

ZZ

t� 1.89s

YZ

t,

sE = s

TX � 1.22↵(ae+p

eff )X � 1.23↵(an

eff)X ,

sF = s

TY + 0.37sTZ � 0.12↵(ae+p

eff )Y � 0.12↵(an

eff)Y

� 0.052↵(ae+p

eff )Z � 0.052↵(an

eff)Z .

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Constraints on SME coefficients

Linear combinations

sA = s

XX

t � sYY

t ,

sD = s

XX

t + sYY

t � 2sZZ

t � 1.89sYZ

t ,

sE = s

TX � 1.22↵(ae+p

eff )X � 1.23↵(an

eff)X ,

sF = s

TY + 0.37sTZ � 0.12↵(ae+p

eff )Y � 0.12↵(an

eff)Y

� 0.052↵(ae+p

eff )Z � 0.052↵(an

eff)Z .

SME Valuess

A (+0.4 ± 1.7)⇥ 10�11

sXY

t (�3.9 ± 5.5)⇥ 10�12

sXZ

t (+0.7 ± 7.8)⇥ 10�12

sD (+3.9 ± 6.6)⇥ 10�12

sE (�1.1 ± 1.7)⇥ 10�8

sF (+6.1 ± 7.4)⇥ 10�9

TABLE – Constraints on minimal SME and gravity matter couplings with LLR. Results aredetermined from a global analysis and are given at 1�r . Bourgoin et. al 2017.

23 / 24

Conclusion

Work realizedNew numerical lunar ephemeris in the SME framework,Found independent linear combinations of SME coefficients,=) Some fundamental SME coefficients.Estimate realistic errors with a resampling method,=) First real constraints on SME coefficients from LLR observations,=) No evidence for Lorentz symmetry violations.

Other results : correlationSME coefficients and the rotational motion of the Moon,SME coefficients and the Earth potential.

Perspectives

Coupled analysis with LLR and GRAIL space mission or SLR.

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Conclusion



Perspectives


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Conclusion



Perspectives


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Documents

Constraints on Lorentz symmetry violations using lunar ...moriond.in2p3.fr/2019/Gravitation/transparencies/4... · CONSTRAINTS ONLORENTZ SYMMETRY VIOLATIONS USING LUNAR LASER RANGING