Modifications of General relativity and the equivalence principle. Jean-Philippe Uzan

Transcription

1 Modifications of General relativity and the equivalence principle Jean-Philippe Uzan

2 Modifications of General Relativity, (Constants) and the Equivalence Principle For technical details/references, see JPU, Liv. Rev. Relat. 14 (2011) 2 [arxiv/ ]

3 General Relativity (in 1 slide) Equivalence principle Universality of free fall Local lorentz invariance Local position invariance Dynamics Relativity

4 Equivalence principle and test particles Action of a test mass: with (geodesic) (Newtonian limit)

5 Solar system Direct test of Universality of free fall [Will, Liv. Rev. Relat ] [Schlamminger, 2008]

6 Solar system Metric theories are usually tested in the PPN formalism Light deflection Perihelion shift of Mercury Nordtvedt effect Shapiro time delay Courtesy of G. Esposito-Farèse [Will, Liv. Rev. Relat ]

7 Parameter space Tests of general relativity on astrophysical scales are needed - galaxy rotation curves: low acceleration - acceleration: low curvature 0 Solar system Sgr A Solar system: -10 BBN Cosmology: Dark energy: -20 CMB Black-hole limit Dark matter: -30 Dark matter a<a 0 Dark energy R<Λ SNIa [Psaltis, ]

8 Universality classes of extensions Variation of constants Poisson equation Ordinary matter Ex : quintessence,... Ordinary matter Ex : scalar-tensor, TeVeS... Ordinary matter Ordinary matter Variation of constants Poisson equation Distance duality Ex : axion-photon mixing Always need NEW fields Ex : brane induced gravity multigravity,... [JPU, Aghanim, Mellier, PRD 05] [JPU, GRG 2007]

9 Famous example: Scalar-tensor theories spin 0 spin 2 graviton scalar Motion of massive bodies determines G cav M not GM. G cav is a priori space-time dependent

10 Varying constants The new fields can make the constants become dynamical. In models with varying constant, 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.

11 Equivalence principle and constants Action of a test mass: with Dependence on some constants (NOT a geodesic) (Newtonian limit) Anomalous force Composition dependent [Dicke 1964, ]

12 Example of varying fine structure constant It is a priori «easy» to design a theory with varying fundamental constants Consider But that may have dramatic implications. Violation of UFF is quantified by It is of the order of Generically: variation of fund. Cst. gives a too large violation of UFF

13 Screening & decoupling mechanisms To avoid large effects, one has various options: - Least coupling principle: all coupling functions have the same minimum and the theory can be attracted toward GR [Damour, Nordtvedt & Damour, Polyakov]

14 Screening & decoupling mechanisms To avoid large effects, one has various options: - Least coupling principle: all coupling functions have the same minimum and the theory can be attracted toward GR [Damour, Nordtvedt & Damour, Polyakov] - Chameleon mechanism: Potential and coupling functions have different minima. The field can become massive enough to evade existing constraints. [Khoury, Weltmann, 2004]

15 Screening & decoupling mechanisms To avoid large effects, one has various options: - Least coupling principle: all coupling functions have the same minimum and the theory can be attracted toward GR [Damour, Nordtvedt & Damour, Polyakov] - Chameleon mechanism: Potential and coupling functions have different minima. [Khoury, Weltmann, 2004] - Symmetron mechanism: similar to chameleon but VEV depends on the local density. [Pietroni 2005; Hinterbichler,Khoury, 2010] Symmetry is restored at high density. Environmental dependence

16 Constraints on the variation of fundamental constants For technical details/references, see JPU, Liv. Rev. Relat. 14 (2011) 2 [arxiv/ ]

17 Physical systems Atomic clocks Oklo phenomenon Quasar absorption spectra Meteorite dating CMB BBN JPU, RMP (2003); arxiv: , arxiv: Local obs QSO obs CMB obs

18 Physical systems * * System Observable Primary constraint Other hypothesis Atomic clocks Clock rates α, µ, g i - Quasar spectra Atomic spectra α, µ, g p Cloud physical properties Oklo Isotopic ratio E r Geophysical model Meteorite dating Isotopic ratio λ Solar system formation CMB BBN Temperature anisotropies Light element abundances α, µ Cosmological model Q, τ n, m e, m N, Cosmological model α, B d

19 Atomic clocks Based the comparison of atomic clocks using different transitions and atoms e.g. hfs Cs vs fs Mg : g p µ ; hfs Cs vs hfs H: (g p /g I )α Examples High precision / redshift 0 (local) Marion (2003) Bize (2003) Fischer (2004) Bize (2005) Fortier (2007) Peik (2004) Peik (2006) Blatt (2008) Cingöz (2008) Blatt (2008)

20 Atomic clocks Using a shell model, the gyromagnetic factors can be expressed in terms of g p and g n. All atomic clock constraints take the form Using Al-Hg to constrain α, the combination of other clocks allows to constraint {µ,g p }. [Luo, Olive, JPU, 2011]

21 Importance of unification Unification Variation of α is accompanied by variation of other coupling constants QCD scale Variation of Λ QCD from α S and from Yukawa coupling and Higgs VEV Theories in which EW scale is derived by dimensional transmutation Variation of Yukawa and Higgs VEV are coupled String theory All dimensionless constants are dynamical their variations are all correlated. These effects cannot be ignored in realistic models.

22 Atomic clocks Using QCD, one can express m p and g p in terms of the quark masses and Λ QCD as m i = h i v Assuming unification. ν AB α = C AB ν AB α C AB coefficients range from 70 to 0.6 typically. Model-dependence remains quite large. [Luo, Olive, JPU, 2011]

23 Quasar absorption spectra Quasar emission spectrum Cloud Absorption spectrum Observed spectrum Reference spectrum Earth

24 Generalities The method was introduced by Savedoff in 1956, using Alkali doublet Most studies are based on optical techniques due to the profusion of strong UV transitions that are redshifted into the optical band e.g. z>1.3, z>1 Radio observations are also very important e.g. hyperfine splitting (HI21cm), molecular rotation, lambda doubling, - offer high spectral resolution (<1km/s) - higher sensitivity to variation of constants - isotopic lines observed separately (while blending in optical observations) Shift to be detected are small e.g. a change of α of 10-5 corresponds to - a shift of 20 må (i.e. of 0.5 km/s) at z~2 - ⅓ of a pixel at R=40000 (Keck/HIRES, VLT/UVES) Many sources of uncertainty - absorption lines have complex profiles (inhomogeneous cloud) - fitted by Voigt profile (usually not unique: require lines not to be saturated) - each component depends on z, column density, width

25 QSO absorption spectra 3 main methods: Alkali doublet (AD) Savedoff 1956 Si IV alkali doublet Fine structure doublet, Single atom Rather weak limit VLT/UVES: Si IV in 15 systems, 1.6<z<3 HIRES/Keck: Si IV in 21 systems, 2<z<3 Chand et al Murphy et al Many multiplet (MM) Webb et al Compares transitions from multiplet and/or atoms s-p vs d-p transitions in heavy elements Better sensitivity Single Ion Differential α Measurement (SIDAM) Analog to MM but with a single atom / FeII Levshakov et al. 1999

26 QSO: many multiplets The many-multiplet method is based on the corrrelation of the shifts of different lines of different atoms. Dzuba et al Relativistic N-body with varying α: First implemented on 30 systems with MgII and FeII Webb et al R=45000, S/N per pixels between 4 & 240, with average 30 Wavelength calibrated with Thorium-Argon lamp HIRES-Keck, 143 systems, 0.2<z<4.2 Murphy et al σ detection!

27 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 Srianand et al DOES NOT CONFIRM HIRES/Keck DETECTION

28 Spatial variation? [Webb et al., 2010] X Keck&VLT VLT Keck 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.

29 Can it make sense? - Dipole is not aligned with the CMB dipole - With such a dipole, CMB fluctuations must be modulated [Moss et al., 2010] [Prunet, JPU, Bernardeau, Brunier, 2005] - Theoretically: in all existing models, time variation is larger than spatial variation Is it possible to design a model compatible with such a claim?

30 Wall of fundamental constant [Olive, Peloso, JPU, 2010] Idea: Spatial discontinuity in the fundamental constant due to a domain wall crossing our Hubble volume.

31 Wall of fundamental constants -Parameters - We assume only ξ F is non vanishing BUT the scalar field couples radiatively to nucleons Loop correction Finite temperature

32 Constraints - Constraints from atomic clocks / Oklo / Meteorite dating are trivially satisfied - To reproduce the «observations» - The contribution of the walls to the background energy is Assume - CMB constraints - Valid field theory up to an energy scale - Astrophysical constraints - Tunelling to the true vacuum - Walls form at a redshift of order 8x10 9

33 Physical systems: new and future Atomic clocks Oklo phenomenon Meteorite dating Quasar absorption spectra Pop III stars [Ekström, Coc, Descouvemont, Meynet, Olive, JPU, Vangioni, 2009] 21 cm CMB BBN [Coc, Nunes, Olive, JPU, Vangioni] JPU, Liv. Rev. Relat., arxiv:

34 Conclusions The constancy of fundamental constants is a test of the equivalence principle. The variation of the constants, violation of the universality of free fall and other deviations from GR are of the same order. «Dynamical constants» are generic in most extenstions of GR (extra-dimensions, string inspired model. Need for a stabilisation mechanism (least coupling principle/chameleon) Why are the constants so constant? Variations are expected to be larger in the past (cosmology) All constants are expected to vary (unification) Observational developments allow to set strong constraints on their variation New systems [Stellar physics] / new observations Spatial variations: possible but very unlikely. More important: these constraints are of important for ANY physicist (even if he/she does not care about cosmology or this kind of speculations)

35 SI

36 New SI

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38 Fi#h 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., (2003) Adelberger et al., Prog. Part. Nucl. Phys 62, 102 (2009)

39 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.

40 Constants Physical theories involve constants These parameters cannot be determined by the theory that introduces them. These arbitrary parameters have to be assumed constant: - experimental validation - no evolution equation By testing their constancy, we thus test the laws of physics in which they appear. A physical measurement is always a comparison of two quantities, one can be thought as a unit - it only gives access to dimensionless numbers - we consider variation of dimensionless combinations of constants JPU, Rev. Mod. Phys. 75, 403 (2003); Liv. Rev. Relat. 4, 2 (2011) JPU, [astro-ph/ , arxiv: ] R. Lehoucq, JPU, Les constantes fondamentales (Belin, 2005) G.F.R. Ellis and JPU, Am. J. Phys. 73 (2005) 240 JPU, B. Leclercq, De l importance d être une constante (Dunod, 2005) translated as The natural laws of the universe (Praxis, 2008).

41 Stellar carbon production Triple α coincidence (Hoyle) 1. Equillibrium between 4 He and the short lived (~10-16 s) 8 Be : αα 8 Be 2. Resonant capture to the (l=0, J π =0 + ) Hoyle state: 8 Be+α 12 C*( 12 C+γ) Simple formula used in previous studies 1. Saha equation (thermal equilibrium) 2. Sharp resonance analytic expression: N 2 A σv ααα = 3 3 / 2 2 2π 6N A M α k B T 3 5 γ exp Q ααα k B T with Q ααα = E R ( 8 Be) + E R ( 12 C) and γ Γ γ E R = resonance energy of 8 Be g.s. or 12 C Hoyle level (w.r.t. 2α or 8 Be+α) [Ekström, Coc, Descouvemont, Meynet, Olive, JPU, Vangioni,2009] Nucleus 8 Be 12 C E R (kev) 91.84± ±0.2 Γ α (ev) 5.57± ±1.0 Γ γ (mev) - 3.7±0.5

42 Microscopic calculation Hamiltonian: A H = T( r i ) + V Coul. r ij i=1 i< j=1 ( ( ) + V Nucl. ( r ij )) Where V Nucl. (r ij ) is an effective Nucleon-Nucleon interaction A Minnesota N-N force [Thompson et al. 1977] optimized to reproduce low energy N-N scattering data. α-cluster approximation for 8 Be g.s. (2α) and the Hoyle state (3α) [Kamimura 1981] Scaling of the N-N interaction V Nucl. (r ij ) (1+δ NN ) V Nucl. (r ij ) to obtain B D, E R ( 8 Be), E R ( 12 C) as a function of δ NN : Link to fundamental couplings through B D or δ NN

43 Composition at the end of core He burning Stellar evolution of massive Pop. III stars We choose typical masses of 15 and 60 M stars/ Z=0 Very specific stellar evolution 60 M Z = 0 The standard region: Both 12 C and 16 O are produced. The 16 O region: The 3α is slower than 12 C(α,γ) 16 O resulting in a higher T C and a conversion of most 12 C into 16 O The 24 Mg region: With an even weaker 3α, a higher T C is achieved and 12 C(α,γ) 16 O(α,γ) 20 Ne(α,γ) 24 Mg transforms 12 C into 24 Mg The 12 C region: The 3α is faster than 12 C(α,γ) 16 O and 12 C is not transformed into 16 O Constraint 12 C/ 16 O ~ < δ NN < or < ΔB D /B D < 0.009

44 Comparison: need for cosmology η=10-12 (blue) & η=10-13 (red) Light field not responsible for late time acceleration (dotted) Compatible meteorite/oklo/atomic clocks η=10-12 Light field not responsible for late time acceleration (dotted) Different unification hypothesis Huge sensitivity to the hypothesis of the models (coupling, unification, )