Stefano Liberati SISSAISAS Trieste 2004 Quantum Gravity Phenomenology

Stefano Liberati SISSA/ISAS, Trieste 2004 Quantum Gravity Phenomenology and Lorentz violation T. Jacobson, SL, D. Mattingly: PRD 66, 081302 (2002); PRD 67, 124011 -12 (2003) T. Jacobson, SL, D. Mattingly: Nature 424, 1019 (2003) T. Jacobson, SL, D. Mattingly, F. Stecker: astro-ph/0309681 Collaborators: D. Mattingly, T. Jacobson, F. Stecker

The Quantum Gravity problem… n n Why we need it? n Philosophy of unification QM-GR (reductionism in physics) n Lack of predictions by current theories (e. g. GR singularities) To eventually understand QG, we will need to n observe phenomena that depend on QG n extract reliable predictions from candidate theories & compare with observations Old “dogma” we cannot access any quantum gravity effect…

Possible QG Phenomena? Motivated by tentative theories, partial calculations, potential symmetry violation, hunches, philosophy… n Primordial gravitons from the vacuum n Loss of quantum coherence or state collapse n QG imprint on initial cosmological perturbations n Scalar moduli or other new field(s) n Extra dimensions and low-scale QG : Mp 2=Rn Mp(4+n)n+2 n dev. from Newton’s law n collider black holes n Violation of global internal symmetries n Violation of spacetime symmetries

Lorentz violation as the first evidence of QG? LI linked to scale-free spacetime: unbounded boosts expose ultra-short distances… Suggestions for Lorentz violation come from: n need to cut off UV divergences of QFT & BH entropy n tentative calculations in various QG scenarios, e. g. semiclassical spin-network calculations in Loop QG (caveat: not solutions of the Hamiltonian constraints) n n n string theory tensor VEVs n spacetime foam n non-commutative geometry n some brane-world backgrounds possibly missing GZK cutoff on UHE cosmic rays

Milestones in LV investigations… n Is there an Aether? (Dirac 1951) n Dispersion & LV (Pavlopoulos, 1967) n Emergent LI in gauge theory? (Nielsen & Picek, 1983) n LV modification of general relativity (Gasperini, 1987, Jacobson and coll. ) n Spontaneous LV in string theory (Kostelecky & Samuel, 1988) n LV Dispersion & Hawking radiation (Unruh-Jacobson, 1994 -1995) n Possibilities of LV phenomenology (Gonzalez-Mestres, 1995 -…)

The turning LV tide “Standard model extension” & lab. experimental limits (Colladay & Kostelecky, 1997, & many experimenters) High energy threshold phenomena: photon decay, vacuum Cerenkov, GZK cutoff (Coleman & Glashow, 1997 -8) GRB photon dispersion limits (Amelino-Camelia et al, 1997) Trans-GZK events? (AGASA collab. 1998)

GZK cut-off Since the sixties it is well-known that the universe is opaque to protons (and other nuclei) on cosmological distances via the interactions In this way, the initial proton energy is degraded with an attenuation length of about 50 Mpc. Since plausible astrophysical sources for UHE particles (like AGNs) are located at distances larger than 50 -100 Mpc, one expects the so-called Greisen-Zatsepin-Kuzmin (GZK) cutoff in the cosmic ray flux at the energy given by • The data collected show about twenty cosmic ray events with energies just above the GZK energy. • Yet, the whole observational status in the UHE regime is controversial. • Hi. Res collaboration claim that they see the expected event reduction • A recent reevaluation of AGASA data seems to confirm the violation of the GZK cutoff.

A GZK cutoff puzzle? The observational status is not settled, but it is clear that if the GZK violation is confirmed, the origin of the super-GZK particles constitutes one of the most pressing puzzles in modern high-energy astrophysics. We need better statistic: Future crucial role of the Auger observatory. Approximately 100 times higher event rate, better systematics Some proposed explanations to super-GZK events o Bottom-Up scenarios UHECR accelerated in objects (AGN, GRBs, SNR…) within the GZK range o Top-Down scenarios decay of ultra-heavy particles: cosmic strings, topological defects, Wimpzillas! (109 -1019 Ge. V) o. Particles without GZK cut-off § Z-bursts: true UHECR are neutrinos that finally hit relic DM neutrinos and produce hadrons via a Z-resonance p Z p (problem: needs very large initial energy for p) • Lorentz violating dispersion relations: threshold shift due to modified dispersion relations

Theoretical Framework for LV? EFT? Renormalizable, or higher dimension operators? Stochastic spacetime foam? Rotational invariant? Lorentz Violation or Doubly Special Relativity? (i. e. preferred frame or possibly a relativity with two invariant scales? , c and lp) Universal, or species dependent?

EFT, all dimension ops, rotation inv. , non-universal Not because it *must* be true, but because: • EFT ü well-defined & simple ü implies energy-momentum conservation (below the cutoff scale) ü covers standard model, GR, condensed matter systems, string theory. . . • All dimension ops: who knows? • Rot. invariance ü simpler ü cutoff idea only implies boosts are broken, rotations maybe not ü boost violation constraints likely also boost + rotation violation constraints • Non-universal ü EFT implies it for different polarizations & spins ü different particle interactions suggest different spacetime interactions ü "equivalence principle" anyway not valid in presence of LV

QG phenomenology via modified dispersion relations Missing a definite prediction from QG one approach can be to consider dispersion relations of the kind We presume that any Lorentz violation is associated with quantum gravity and suppressed by at least one inverse power of the Planck scale M and we violate only boost symmetry

Constraints at lowest orders In a such a framework the n=1, 2 terms will dominate at low energies p «. o At high energies, p» , the p 3 term, if present, will dominate. o If p 3 is absent then the p 4 term will dominate if p 2» M and so on… o A large amount of both theoretical and experimental work has been carried out in the case n≤ 2 which includes the “standard model extension proposal” and models like those proposed in VSL and by Coleman. Glashow Compared to “Planck-suppressed” expectation (with =relevant mass scale for observation/experiment) Laboratory ~ 1 -2 orders weaker ¨ High energy astrophysics ~ 1 -2 orders weaker ¨ GZK (if confirmed) ~ comparable ¨ Vacuum birefringence ~ few orders stronger ¨ So is it n=3 the next relevant order?

An open problem: un- naturalness of small LV. Renormalization group arguments might suggest that lower powers of momentum in will be suppressed by lower powers of M so that n≥ 3 terms will be further suppressed w. r. t. n≤ 2 ones. I. e. one could have that This need not be the case if a symmetry or other mechanism protects the lower dimensions operators from violations of Lorentz symmetry Of course we do not know at the moment if this is indeed the case!

Observability of O(E/MP) Lorentz violations Lab experiments: o Time-dependence of spin resonance frequencies Astrophysical observations: Accumulation over long travel times: dispersion & birefringence Purely kinematical effects (presume only modified dispersion relation and standard definition of group velocity). o Anomalous threshold reactions or threshold shift in standard ones Need assumptions on energy/momentum conservation and dynamics. o Reactions affected by “speeds limits” (e. g. synchrotron radiation) Need assumption of effective quantum field theory o

Constraining n=3 Lorentz violations in the QED sector Times of flight First idea: Just constrain the photon LIV coefficient by using the fact that different colors will travel at different speeds. On long distances one expects different time of flight corresponding to different speed of propagations. Then Best constraint up to date is Schaefer (1999) using GRB 930131, a gamma ray burst at a distance of 260 Mpc that emitted gamma rays from 50 ke. V to 80 Me. V on a time scale of milliseconds. The constraint is | |<122. Very recently (Oct. 2003) Corburn et al. using GRB 021206 obtained | |<77 However, probably GRB are not “good” objects (different enrgies emission at different times), then best constraint is Biller (1998, Markarian 421) <252.

Threshold reactions Key point: the effect of the non LI dispersion relations can be important at energies well below the fundamental scale Corrections start to be relevant when the last term is of the same order as the second. If is order unity, then For n=3 n pcrit for e- pcrit for p+ 2 p ≈ m ~1 e. V p≈me=0. 5 Me. V p≈me=0. 938 Ge. V 3 ~1 Ge. V ~10 Te. V ~1 Pe. V 4 ~100 Te. V ~100 Pe. V ~3 Ee. V

Threshold reactions: new phenomena o New threshold reactions o Vacuum Cherenkov: e- e-+ § Moreover now possible Cherenkov with emission of an hard photon o Gamma decay: e++e- These reactions are almost instantaneous (interaction with zero point modes) If allowed the particle won’t propagate. o Anomalous thresholds (modification of standard threshold reactions) Shift of lower thresholds (Coleman-Glashow, …) o Emergence of upper thresholds (Klusniak, JLM) o Asymmetric pair production (JLM) o So far constraints from o Photon pair creation using AGN: + CMB, FIRB e++e. Best limit so far from Mkr 501 o For proton-pions GZK reaction: p++ CMB p++ -

Novelties in threshold reactions: why v Asymmetric configurations: Pair production can happen with asymmetric distribution of the final momenta v. Upper thresholds: The range of available energies of the incoming particles for which the reactions happens is changed. Lower threshold can be shifted and upper thresholds can be introduced

Nature 424, 1019 (2003) The synchrotron radiation LI synchrotron critical frequency: e - electron charge, m - electron mass B - magnetic field Naively, corrections important when : If synchrotron source electrons have E>10 Te. V, sensitive to LV! To get a real constraint one needs a detailed re-derivation of the synchrotron effect with LIV. One needs to presume that EQFT holds. This leads to a modified formula for the peak frequency: The key point is that for negative , is now a bounded function of E! There is now a maximum achievable synchrotron frequency max for ALL electrons! So one gets a constraints from asking max≥ Stronger constraint for smaller B/ observed ( max)observed Best case is Crab nebula. . .

The Crab nebula: a key object for QG phenomenology The Crab Nebula A supernova remnant SNR at about 2 Kpc. Appeared on 4 July 1054 A. D. Optica l Radio X-ray

The EM spectrum of the Crab nebula From Aharonian and Atoyan, astro-ph/9803091 Crab alone provides three of the best constraints. We use: synchrotron Inverse Compton Crab nebula (and other SNR) well explained by self-synchrotron Compton model. SSC Model: 1. Electrons are accelerated to very high energies at pulsar 2. High energy electrons emit synchrotron radiation 3. High energy electrons undergo inverse Compton with ambient photons We shall assume SSC correct and use Crab observation to constrain LV.

Observations from Crab Gamma rays up to 50 Te. V reach us from Crab: no photon annihilation up to 50 Te. V. o By energy conservation during the IC process we can infer that electrons of at least 50 Te. V propagate in the nebula: no vacuum Cherenkov up to 50 Te. V o The synchrotron emission extends up to 100 Me. V (corresponding to ~1500 te. V electrons if LI is preserved): LIV for electrons (with negative ) should allow an Emax 100 Me. V. B at most 0. 6 m. G o

Constraints from Crab No photon annihilation up to 50 Te. V No vacuum Cherenkov up to 50 Te. V Synchrotron photons up to 100 Me. V

Photon absorption of gamma rays from Markarian 501 Gamma r ays FIRB Blazar- Mkn 501~ 147 Mpc Earth Te. V photons are expected to loose energy by pairproduction due to scattering with the far infrared background (FIRB) photons + FIRB e++e-

Observational evidence It was recently shown by Konopelko et al. (2003) that the observation is fully consistent with a synchrotron-Self-Compton origin of emission and the best available model for the FIRB spectrum at least up to 20 Te. V. Requirements: A. B. We do not want to lower the standard threshold at 10 Te. V We assume incompatible with observation to shift the threshold of 20 Te. V to the region were the 10 Te. V are normally absorbed. We shall assume that observations are in fair agreement with standard expectations at least up to 20 Te. V. Stecker-de Jagger 2001, Stecker 2002

Dispersion relations from EFT The constraints just shown were obtained by making use of simple dispersion relations considered on a purely phenomenological basis. Are this the more general obtainable within a EFT framework? No Let’s consider all the Lorentz-violating dimension 5 terms (n=3 LIV in dispersion relation) that are quadratic in fields, gauge & rotation invariant, not reducible to lower order terms (Myers-Pospelov, 2003). For E» m All violate CPT photon helicities have opposite LIV coefficients Moreover electron and positron have inverted and opposite positive and negatives helicities LIV coefficients. Electron spin resonance in a Penning trap yields electron helicities have independent LIV coefficients Positive Helicity Negative helicity Electron R L Positron - L - R

Consequences of helicity dependence on previous constraints o Photon time of flight: the opposite coefficients for photon helicities imply larger dispersion 2| |p/M rather than (p 2 -p 1)/M. Now best limits (using Biller. 1998) | |<63 (or, using Boggs et al. 2003, | |<34). o Photon decay and photon absorption (i. e. pair creation processes): one needs new analysis but order of magnitude of the constraint remains the same. o Synchrotron: we can constraint at most only one of the electron parameters R, L since we cannot exclude that all the synchrotron is produced by electrons of one helicity. o Vacuum Cherenkov: neither photon helicities can be emitted so | | is bounded but we cannot exclude that one electron helicity is “cherenking” and the other produces the spectrum IC. So we can say that at least one electron helicity is bounded.

New constraints using EFT: New Cherenkov-Synchrotron constraint The logic: Consider larger and larger values of the one such that >-7 10 -8. Let’s call it s 1. For any s calculate the electron energy required to get 100 Me. V synchrotron. This is VERY INSENSITIVE TO . 2. Calculate the value of for which vacuum Cerenkov starts to happen 3. s, must lie on the line segment between , - since electron cannot Cerenkov with either helicity photon. Joining the Synch: Cerenkov with IC Cerenkov (why s is the same that satisfies the Cherenkov constraint) 1. As s becomes more and more positive, the required electron energy for 0. 1 Gev synch. radiation becomes lower and lower. 2. Beyond the IC Cerenkov line it is below 50 Te. V. Producing the observed amount of radiated energy with lower energy electrons requires many more electrons (in LI case electron energy is 1500 Te. V). 3. Different electron populations would be producing IC radiation and synch. radiation. Problems with population ‘tuning’, i. e. 30 times IC producing electrons would be too numerous to match observed spectrum. Future work?

New constraints using EFT: New Birefringence constraint Opposite for the photon helicities imply different phase velocities: birefringence of vacuum 1) There is a rotation of linear polarization direction through an angle. For a plane wave of wave-vector k: 2) Observation of polarized radiation from distant sources can hence be used to constraint The difference in rotation angle for two different energies is The constraint araises from the fact that if the difference is too large over the range of the observed polarized flux, then the instantaneous polarization at the detector would fluctuate enough to suppress the net polarization well below the observed value. 3) 4)

Birefringence constraint from GRB 021206 Recently polarized gamma rays in the energy range 0. 15 --2 Me. V were observed (Coburn-Boggs, 2003) in the prompt emission from the -ray burst GRB 021206 using the RHESSI detector. A linear polarization of 80% 20% was measured by analyzing the net asymmetry of their Compton scattering from a fixed target into different directions. The Reuven Ramaty High Energy Solar Spectroscopy Imag Major portion of flux from 0. 1 -0. 5 Me. V, require < 3 /2 in this range, take conservatively z 0. 1 (0. 5 Gpc) This then yields the constraint where d 0. 5 is the distance to the burst in units of 0. 5 Gpc. N. B. This constraint could be improved with detailed analysis. N. B. II Recently Boggs and Coburn was criticized by Ritledge and Fox. Boggs-Coburn defended their analysis. If this observation not correct best limit so far from Birefringence is obtained by Gleiser and Kozameh using observed 10% polarization from distant, z=1. 82, radio galaxy 3 C 256

Combined constraints The vast improvement in the birefringence constraint overwhelms the new synchrotron. Cherenkov constraint, while the latter improves the previous birefringence constraint (Gleiser-Kozameh, 2001) by a factor 102. The allowed region is defined above and below by the birefringence bound O(10 -14), on the left by the synchrotron bound O(10 -7), and on the right by the IC Cherenkov bound O(10 -2). For negative parameters minus the logarithm of the absolute value is plotted, and a region of width 10 -18 is excised around each axis. The synchrotron and Cherenkov constraints are known to apply only for at least one R, L. The IC and synchrotron Cherenkov lines are truncated where they cross. Prior photon decay and absorption constraints are shown in dashed lines since they do not account for the EFT relations between the LV parameters.

The future? The combined constraints severely limit first order Planck suppressed LV, making any theory that predicts this type of LV very unlikely. Constraints of n=4 LIV If GZK confirmed (Auger observatory) ¨ Proton Cerenkov: < O(10 -5) ¨ GZK threshold: > - O(10 -2) n Neutrino vacuum Cerenkov *IF* 1020 e. V detected *AND* rate high enough: < O(10 -21) (Amanda, Ice. Cube) n Neutrino/photon/GW time delay? n Better measures of energy, timing, polarization from distant -ray sources (GLAST? , SWIFT? , VERITAS? ) n What’s next? n n Definitively rule out n=3 LV, O(E/M), including chirality effects ¨ Strengthen the positive and | R- L| bounds: e. g. via helicity decay. ¨ (a) Rule out or (b) see LV at O(E 2/M 2), n=4 A true messenger of QG phenomenology will arrive? We’ll be there!

A possible new constraint: helicity decay If R and L are unequal, say R> L then a positive helicity electron can decay into a negative helicity electron and a photon, e-R e-L+ even when the LV parameters do not permit the vacuum Cherenkov effect. o o Such ``helicity decay" has no threshold energy, so whether this process can be used to set constraints on R, L is solely a matter of the decay rate which depends on | R- L| With the current constraints on | R- L| the transition energy is approximately 10 Te. V and the lifetime for electrons below this energy is greater than 104 seconds. This is long enough to preclude any terrestrial experiments from seeing the effect. o The lifetime above the transition energy is instead of about 10 -11 seconds for energies just above 10 Te. V. The lifetime might therefore be short enough to provide new constraints. From Crab might get o

Standard Model Extension (Colladay & Kostelecky, 1997) Add to the Standard Model Lagrangian all possible Lorentz-violating terms that preserve field content, gauge symmetry, and renormalizability. E. g. , leading order terms in the QED sector: If rotationally invariant:

Why now QG phenomenology? Observational improvements By increasing detector size, or going into space, or using technological improvement, or technique improvement, observations are probing… n n n n Higher energies Weaker interactions Lower fluxes Lower temperatures Shorter time resolution Longer distances Gravitational waves

Phenomenology of Lorentz Violation Time-dependence of spin or hyperfine resonance, or energy levels as lab moves w. r. t. preferred frame or directions … n Long baseline dispersion (GRB’s, AGN’s, pulsars) and vacuum birefringence (e. g. spectropolarimetry of galaxies) n n New thresholds (photon decay, vacuum Cerenkov) n Shifted thresholds (photon annihilation from blazars, GZK, …) n Maximum velocity (synchrotron peak from SNR) n Gravitational effects (static fields, waves)