Theoretical Aspects of the Equivalence Principle

Theoretical Aspects of the Equivalence Principle Thibault Damour Institut des Hautes Études Scientifiques Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 1 / 22

(Einstein) Equivalence Principle (EP) Not a basic principle of physics A heuristic generalization of an experimental fact: hypothesis of equivalence (Einstein) very successful in building General Relativity (GR) GR is based on two basic postulates: (1) EP: Universal coupling of matter to gravity (η µν g µν (x)) plus usual coupling constants of special relativistic physics (2) Dynamics of the gravitational field g µν (x) S = S matter [ψ, A, φ; g µν ; g a, Y, λ, µ] + d 4 x g R(g µν) 16πG Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 2 / 22

Special Relativistic Physics (SM, MSSM,...) S SM [ψ, A, φ; η µν ; g a, Y, λ, µ] based on two types of absolute structures Space-time structure: η µν Coupling constants: gauge couplings g 1, g 2, g 3 scalar boson (BEH) parameters µ, λ Yukawa couplings UV cut-off about 20 parameters in SM and 100 in MSSM Y ij Λ UV Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 3 / 22

What determines the coupling constants? (I) Very unsatisfactory to put them by hand: this is against the principle of reason nihil est sine ratione (Leibniz) The history of physics suggests that there are no absolute structures in physics Einstein s GR: η µν g µν (x) absolute, rigid spacetime elastic spacetime, dynamically influenced by matter Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 4 / 22

What determines the coupling constants? (II) Kaluza-Klein s idea: g 1 or α em 3 8 g 2 1 4π hc 1 137 g 55 (x) higher-dimensional elastic spacetime Dynamical symmetry breaking: the vacuum state minimizes the energy V (φ) which dynamically determines φ µ λ m e Y e φ Y e µ λ Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 5 / 22

Origin of the mass scales in the SM? A striking property of the SM: its near conformal invariance. Classical conformal invariance is only broken by µ in BEH sector. Then m quarks and m leptons α µ. On the other hand, m hadrons Λ QCD Λ UV e c g UV 2 (Coleman, Weinberg 73). dimensional transmutation Quantum breaking of classical conformal invariance as possible origin of mass scale of quarks and leptons (Meissner, Nicolai 07): extended scalar sector V scalar (Φ, ϕ) = λ 1 4 (Φ Φ) 2 + λ 2 2 ϕ2 (Φ Φ) + λ 3 4 ϕ4 quantum corrections modify V scalar (Φ, ϕ) and introduce a scale coming from Λ UV, λ UV i : m leptons and m quarks Λ UV f (λ UV i ) Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 6 / 22

In both cases external dynamical effects determine the structure of local vacuum η µν = g µν (x) α em g 55 (x) (if KK) m A Y A µ λ Then if any of the coupling constants of local physics (e.g., α em, m e /m p, m q /m p,...) is x-dependent = violation of (weak) equivalence principle (Dicke 1962) Notably violation of universality of free fall = m A [α(x),...] g µν (x) dx µ dx ν S ma Composition-dependent acceleration a A = g ln m A [α(x),...] = g ln m A α α... Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 7 / 22

General dilaton-like model of EP violations Assume general dependence of coupling constants on some dilaton field ϕ: α EM (ϕ), (m q/λ QCD )(ϕ), (m e/λ QCD )(ϕ),. Then the dependence of m A upon fundamental coupling constants: m A = Λ QCD ^m A (α EM, m u Λ QCD, m d Λ QCD, m e Λ QCD ) a ϕ dependence of m A and a corresponding dilaton coupling to m A α A = ln m A(ϕ) ϕ Composition-dependent modification of Newtonian interaction V (r) = G m A m B r (1 + α A α B e mϕr ) WEP analog of the SEP scalar coupling α A discussed in G. Esposito-Farèse s talk. In the following: inverse range of ϕ: m ϕ = 0. Weak EP violation ( ) a η AB = (α A α B )α E a AB Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 8 / 22

Composition-dependence of weak EP violations General possible (dilaton-like) phenomenology (Damour-Polyakov 94, Dent 08, Damour-Donoghue 10): A N + Z ( ) [ a c1 = a AB A + c Z 2 1/3 2 A + c A 2Z 4/3 3 A (A 2Z ) 2 ] + c 4 A 2 AB Plausible simplified (dilaton-like) phenomenology (Damour-Donoghue 2010) ( ) [ a c1 a AB A + c Z 2 ] 1/3 2 A 4/3 AB Two dominant EP signals, linked to nuclear physics (variation of m q /Λ QCD ) and Coulomb effects (variation of α EM = e 2 / hc) Two material pairs suffice to constrain the two dominant EP parameters c 1, c 2 Dilaton-like models allow to a priori compare the sensitivity of various EP tests: e.g. the dilaton charge vector of the pair Rb 85, Rb 87 can be compared to that of Pt, Ti and is found to be 10 2 smaller. Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 9 / 22

String-inspired motivation for EP violation String theory: magically unites Relativistic Quantum Theory with GR {η µν + string + h} dynamical g µν (x) naturally unifies gauge-theories (A µ ) with gravity (g µν ), and more generally matter, interactions and space-time at face value, string theory contains no arbitrary coupling constants, and is a vast generalization of the Kaluza-Klein idea g D= 4 a = f ( φ 1 (x), φ 2 (x),..., φ n (x),...) many scalar (moduli) fields of dynamical origin: brane positions,... compactified dimensions, Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 10 / 22

The dynamical nature of all coupling constants (and mass ratios) in string theory a priori suggests the presence of EP violations. However, it seems (in the weak coupling domain) that if the moduli fields stay massless, the level of EP violation would be phenomenologically too large (and would also jeopardize inflation) Majority view: try to find string vacua which stabilize all moduli fields at the minimum of some effective potential V (φ 1, φ 2,...) = all moduli acquire a mass m 2 a 2 V / φ 2 a (see Denef2008) EP tests are important because they test an assumption commonly made in string theory, and could refute it. Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 11 / 22

String-inspired cosmological attractor mechanism A different scenario for trying to reconcile the existence of (massless) moduli with phenomenology (Damour-Polyakov, Damour-Piazza-Veneziano). Modulo some assumption about the (strong-field) behaviour of the coupling functions g a (φ) of moduli, φ might be cosmologically attracted towards a value φ where φ decouples from matter; i.e. α A (φ) α A (φ ) = 0 during cosmological expansion This mechanism naturally generates a/a 1 without using small parameters. It gives an existence proof of an EP violation which is naturally below the currently tested level a/a 10 13 Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 12 / 22

Dilaton run-away scenario (DPV) dilaton Φ: L eff = B R (Φ) R(g) + B Φ (Φ)( Φ) 2 + B F (Φ) F 2 µν +... where B i (Φ) = various dilaton coupling functions. Assume B i (Φ) = C i + O(e 2Φ ) as Φ + (strong coupling domain). Then, during cosmological expansion, because of the B(Φ)-induced Φ- dependence of the matter density, the dilaton Φ is attracted towards large positive values (Φ = + ). = coupling of Φ to matter B i Φ values. = O(e 2Φ ) is naturally driven to small Observational consequences today. Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 13 / 22

Observational consequences today of dilaton-runaway scenario Weak EP violation (assuming inflationary potential V (χ) = λ(φ) χ n with n = 2) ( ) 2 ( ) 2 ( ) 2 a a 5 bf δρ bf 10 4 10 12 b λ c ρ b λ c where b F, b λ, c are dimensionless parameters and δρ/ρ 5 10 5 the observed level of primordial density fluctuation: Link EP / cosmology. Variation of constants: α EM = e 2 / hc,... d ln α EM dt ±10 16 1 + q 0 3 2 Ω m Link α EM /α EM and EP violation level a 1012 1 yr a Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 14 / 22

In dilaton models: also link EP and tests of (PN) gravity a a 10 2 d q d g 1 γ PPN 2 where d q ln(m q /Λ QCD )/ ϕ, d g ln(λ QCD /m Planck )/ ϕ and either d q d g or d q d g /40. In the worst case 1 γ PPN 10 4 a/a so that a/a 10 15 1 γ PPN 10 11. also link between WEP and clock tests of EEP (e.g. grav. redshift) (see, e.g., TD gr-qc/9904032). When comparing frequencies of atomic transitions A A at two different locations r 1, r 2 : where ν A A (r 1) ν A A (r 2) 1 + (1 + αaa α E)(U E (r 1 ) U E (r 2 )) α A A = ln E A A ϕ computable from coupling-constant dependence of E A A transition E A A m ee 4 g I m e m p e 4 F rel (Ze 2 ).. E.g. fro hyperfine Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 15 / 22

Motivation from the observed dark energy The observation of dark energy ρ vac 10 123 mplanck 4 0 poses a challenge. May be it is an indication of a V (φ) relaxing towards zero ( quintessence, Wetterich,..., Steinhardt,...), which suggests the existence of EP violations linked to the nearly massless φ. May be the solution of the challenge involves some type of spontaneous breaking of scale invariance (Wetterich,..., Rabinovici2008). Then, under some assumptions (Wetterich08) such a scenario might realize the runaway version of the cosmological attractor scenario, with associated small EP violation. Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 16 / 22

Motivation from dark matter? If dark matter is some light (sub ev ) particle, it might have EP-violating coherent couplings to ordinary matter. Recent example leading to EP violations: sub-ev scalar dark matter with Higgs portal coupling (Piazza, Pospelov 2010) L AφH H super-renormalizable coupling: avoid the unnaturalness of a very light φ in presence of quantum corrections (only logarithmically divergent corrections to m ϕ ). V scalar = m2 n 2 H H + λ(h H) 2 + A(H H)φ + m2 ϕ need A 2 < 2λ mϕ 2 for stable minimum. after symmetry breaking φ = A v H 2 2 mϕ 2 + ϕ 2 φ2 Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 17 / 22

ϕ mediates a fifth force of range m 1 ϕ : V (r) = G m A m B r (1 + α A α B e mϕ r ) α A = 2 M ln m A (ϕ) P ϕ m A (N + Z ) m nuc (ϕ) + N Z np m(ϕ) +... 2 ratio between (N Z ) EP-violating coupling and (N + Z ) approximately composition-independent one predicted by H-coupling A α N+Z 10 5 ev if A m ϕ 10 12 ev (m 1 ϕ 100 km) and α N+Z 10 14 a a 10 17 Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 18 / 22

Anthropic-type argument for EP violation (Damour-Donoghue2010) Independently of any specific theoretical model one might argue (along the anthropic approach to the vast multiverse of cosmological and/or string backgrounds) that: (i) the EP is not a fundamental symmetry principle of Nature (ii) the level η a/a of EP violation can be expected to vary, quasi-randomly, within some range of order unity over the full multiverse (iii) as there is probably a maximal level of EP-violation, say η 0, which is compatible with the development of life (and physicists), one should a priori expect to observe, in our local environment, an EP violation η of order η. Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 19 / 22

Awaiting surprising for tests of gravity in space? Chameleon mechanism (Khoury, Weltman 04,..., Brax,...) combining the attractor mechanism (which uses ϕ-dependence of Lagrangian couplings e.g. B(φ) = e βφ/mp ) with a quintessence-like potential V (φ) = M 4+n φ n V eff (φ) = V (φ) + ρ B(φ) environment-dependent m φ = m φ (ρ) m φ in the near vacuum of space could be much smaller than m φ in Earthbound experiments. Existence proof that space experiments could measure larger deviations from usual gravity than extrapolated from ground experiments: e.g. for value of G, or EP-violation η AB. Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 20 / 22

Conclusions (I) EP is intimately connected with some of the basic aspects of modern physics, and of the unification of gravity with particle physics. The historical tendency of physics to discard any absolute structures, as well as the generalized Kaluza-Klein aspects (moduli) of string theory a priori suggests there could exist EP violations. The recent observation of ρ vac 10 123 mplanck 4 poses a challenge to physics which suggests that we are missing some key understanding of IR gravity. This might provide additional motivation for EP violation (either via some Nambu- Goldstone mode, or via anthropic arguments). Even within the majority view of the moduli stabilization issue, EP experiments are testing a key assumption of current string models. Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 21 / 22

Conclusions (II) no firm prediction for level of EP violation, but some phenomenological models show that the violation could naturally be just below the currently tested level. In dilaton-like models, the composition-dependence of EP signals is (probably) dominated by two signals, depending on A 1/3 and Z 2 A 4/3. In such dilaton-like models, there exist correlated modifications of gravity ( a/a, γ PPN 1 0, α a 0, dα a /du 0,...) but EP tests stand out as our deepest probe of new physics, when compared to, e.g., solar-system (γ PPN ) or clock tests ( α a or dα a /du). Indeed, a a 10 2 d q d g 1 γ PPN 2 where d q ln(m q /Λ QCD )/ ϕ, d g ln(λ QCD /m Planck )/ ϕ and either d q d g or d q d g /40. In the worst case 1 γ PPN 10 4 a/a so that a/a 10 15 1 γ PPN 10 11. Thibault Damour (IHES) Theoretical Aspects of the EP Q2C5 Cologne 9 12 October 2012 22 / 22