Quantum Gravity Phenomenology and Lorentz violation

1
Quantum Gravity Phenomenology and Lorentz
violation

• Stefano Liberati
• SISSA/ISAS, Trieste 2004

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
2
The Quantum Gravity problem

• Why we need it?
• Philosophy of unification QM-GR (reductionism in
  physics)
• Lack of predictions by current theories (e.g. GR
  singularities)

• To eventually understand QG, we will need to
• observe phenomena that depend on QG
• extract reliable predictions from candidate
  theories compare with observations

Old dogma we cannot access any quantum gravity
effect
3
Possible QG Phenomena?
Motivated by tentative theories, partial
calculations, potential symmetry violation,
hunches, philosophy

• Primordial gravitons from the vacuum
• Loss of quantum coherence or state collapse
• QG imprint on initial cosmological perturbations
• Scalar moduli or other new field(s)
• Extra dimensions and low-scale QG Mp2Rn
  Mp(4n)n2
• dev. from Newtons law
• collider black holes
• Violation of global internal symmetries
• Violation of spacetime symmetries

4
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

• need to cut off UV divergences of QFT BH
  entropy
• tentative calculations in various QG scenarios,
  e.g.
• semiclassical spin-network calculations in Loop
  QG (caveat not solutions of the Hamiltonian
  constraints)
• string theory tensor VEVs
• spacetime foam
• non-commutative geometry
• some brane-world backgrounds
• possibly missing GZK cutoff on UHE cosmic rays

5
Milestones in LV investigations

• Is there an Aether? (Dirac 1951)
• Dispersion LV (Pavlopoulos, 1967)

• Emergent LI in gauge theory? (Nielsen Picek,
  1983)
• LV modification of general relativity
  (Gasperini, 1987, Jacobson and coll.)
• Spontaneous LV in string theory (Kostelecky
  Samuel, 1988)
• LV Dispersion Hawking radiation
  (Unruh-Jacobson, 1994-1995)
• Possibilities of LV phenomenology
  (Gonzalez-Mestres, 1995-)

6
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)
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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.
• HiRes collaboration claim that they see the
  expected event reduction
• A recent reevaluation of AGASA data seems to
  confirm the violation of the GZK cutoff.

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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

• Bottom-Up scenarios
• UHECR accelerated in objects (AGN, GRBs, SNR)
  within the GZK range
• Top-Down scenarios
• decay of ultra-heavy particles cosmic strings,
  topological defects,
• Wimpzillas! (109-1019 GeV)

• 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

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The years of the boom

• GRB photon dispersion limits (Amelino-Camelia et
  al, 1997)
• LV dispersion from Loop QG (Gambini Pullin,
  1998)
• Are we at the dawn of quantum gravity
  phenomenology? (Amelino-Camelia, 1999)
• Photon pair creation threshold shift (Kifune,
  Kluzniak, 1999)
• Infrared-TeV gamma ray crisis? (Protheroe
  Meyer, 2000)
• Probably not!
• Thresholds limits (Aloisio et Al. 2000
  Amelino-Camelia, Piran 2001, Jacobson, SL
  Mattingly 2002)
• Birefringence limits (Gleiser Kozameh, 2001)
• Primordial fluctuation imprints? (Martin
  Brandenberger, Niemeyer, 2001)
• At most H/M, perhaps even (H/M)3
• Synchrotron constraint (Gonzalez-Mestres 2001
  Jacobson, SL Mattingly 2002)

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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?
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EFT, all dimension ops, rotation inv.,
non-universal

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

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QG phenomenologyvia 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
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Constraints at lowest orders

• In a such a framework the n1,2 terms will
  dominate at low energies p?.
• At high energies, p?, the p3 term, if present,
  will dominate.
• If p3 is absent then the p4 term will dominate
  if p2?M and so on

A large amount of both theoretical and
experimental work has been carried out in the
case n2 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 n3 the next relevant order?
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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 n3 terms
will be further suppressed w.r.t. n2 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!
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Observability of O(E/MP)Lorentz violations
Lab experiments

• 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).
• Anomalous threshold reactions or threshold shift
  in standard ones
• Need assumptions on energy/momentum conservation
  and dynamics.
• Reactions affected by speeds limits (e.g.
  synchrotron radiation)
• Need assumption of effective quantum field theory

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Constraining n3 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 GRB930131, a gamma ray burst at a distance
of 260 Mpc that emitted gamma rays from 50 keV to
80 MeV on a time scale of milliseconds. The
constraint is ?lt122. Very recently (Oct. 2003)
Corburn et al. using GRB021206 obtained
?lt77 However, probably GRB are not good
objects (different enrgies emission at different
times), then best constraint is Biller (1998,
Markarian 421) ?lt252.
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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 n3
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Threshold reactions new phenomena

• New threshold reactions
• Vacuum Cherenkov e-?e-?
• Moreover now possible Cherenkov with emission of
  an hard photon
• Gamma decay ??ee-
• These reactions are almost instantaneous
  (interaction with zero point modes)
• If allowed the particle wont propagate.
• Anomalous thresholds (modification of standard
  threshold reactions)
• Shift of lower thresholds (Coleman-Glashow, )
• Emergence of upper thresholds (Klusniak, JLM)
• Asymmetric pair production (JLM)
• So far constraints from
• Photon pair creation using AGN
  ??CMB,FIRB?ee-
• Best limit so far from Mkr 501
• For proton-pions GZK reaction p?CMB? p?-

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Novelties in threshold reactions why

• Asymmetric configurations
• Pair production can happen with asymmetric
  distribution
• of the final momenta

• 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

20
The synchrotron radiation
Nature 424, 1019 (2003)
e - electron charge, m - electron massB -
magnetic field
LI synchrotron critical frequency
Naively, corrections important when
If synchrotron source electrons have Egt10 TeV,
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 (?max)observed
Stronger constraint for smaller B/?observed Best
case is Crab nebula...
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The Crab nebula a key object for QG
phenomenology
X-ray
The Crab Nebula A supernova remnant SNR at about
2Kpc. Appeared on 4 July 1054 A.D.
Optical
Radio
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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.
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Observations from Crab

• Gamma rays up to 50 TeV reach us from Crab no
  photon annihilation up to 50 TeV.
• By energy conservation during the IC process we
  can infer that electrons of at least 50 TeV
  propagate in the nebula no vacuum Cherenkov up
  to 50 TeV
• The synchrotron emission extends up to 100 MeV
  (corresponding to 1500 teV electrons if LI is
  preserved)
• LIV for electrons (with negative ?) should allow
  an Emax?100 MeV.
• B at most 0.6 mG

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Constraints from Crab
No photon annihilation up to 50 TeV
No vacuum Cherenkov up to 50 TeV
Synchrotron photons up to 100 MeV
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Photon absorption of gamma rays from Markarian 501
FIRB
Gamma rays
Blazar- Mkn 501 147 Mpc
Earth
TeV photons are expected to loose energy by
pair-production due to scattering with the far
infrared background (FIRB) photons ? ?FIRB ?ee-
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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 TeV.
?

• Requirements
• We do not want to lower the standard threshold
  at 10 TeV
• We assume incompatible with observation to shift
  the threshold of 20 TeV to the region were the 10
  TeV are normally absorbed.

We shall assume that observations are in fair
agreement with standard expectations at least up
to 20 TeV.
?
Stecker-de Jagger 2001, Stecker 2002
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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
Lets consider all the Lorentz-violating
dimension 5 terms (n3 LIV in dispersion
relation) that are quadratic in fields, gauge
rotation invariant, not reducible to lower order
terms (Myers-Pospelov, 2003). For Em
All violate CPT
photon helicities have opposite LIV coefficients
electron helicities have independent LIV
coefficients
Moreover electron and positron have inverted and
opposite positive and negatives helicities LIV
coefficients.
Electron spin resonance in a Penning trap yields
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Consequences of helicity dependence on previous
constraints

• Photon time of flight the opposite coefficients
  for photon helicities imply larger dispersion
  2?p/M rather than ?(p2-p1)/M. Now best limits
  (using Biller. 1998) ?lt63
• (or, using Boggs et al. 2003, ?lt34).
• Photon decay and photon absorption (i.e. pair
  creation processes) one needs new analysis but
  order of magnitude of the constraint remains the
  same.
• 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.
• 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.

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New constraints using EFT New
Cherenkov-Synchrotron constraint

• The logic Consider larger and larger values of
  the one ? such that ? gt-7?10-8. Lets call it ?s
• For any ?s calculate the electron energy required
  to get 100 MeV synchrotron.
  This is VERY INSENSITIVE TO ?.
• Calculate the value of ? for which vacuum
  Cerenkov starts to happen
• ?s, ? must lie on the line segment between ?,-?
  since electroncannot Cerenkov with either
  helicity photon.

• Joining the Synch Cerenkov with IC Cerenkov (why
  ?s is the same that satisfies the Cherenkov
  constraint)
• As ?s becomes more and more positive, the
  required electron energyfor 0.1 Gev synch.
  radiation becomes lower and lower.
• Beyond the IC Cerenkov line it is below 50 TeV.
  Producing the observed amount of radiated energy
  with lower energy electrons requires many more
  electrons(in LI case electron energy is 1500
  TeV).
• 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?

30
New constraints using EFT New Birefringence
constraint

• Opposite ? for the photon helicities imply
  different phase velocities birefringence of
  vacuum
• There is a rotation of linear polarization
  direction through an angle. For a plane wave of
  wave-vector k
• 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.

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Birefringence constraint from GRB021206
Recently polarized gamma rays in the energy range
0.15--2 MeV were observed (Coburn-Boggs, 2003) in
the prompt emission from the ?-ray burst
GRB021206 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
Imager
Major portion of flux from 0.1-0.5 MeV, require
??lt 3?/2 in this range, take conservatively z
?0.1 (0.5 Gpc)
This then yields the constraint
where d0.5 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,
z1.82, radio galaxy 3C 256
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Combined constraints
The vast improvement in the birefringence
constraint overwhelms the new synchrotron-Cherenko
v 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.
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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 n4 LIV

• If GZK confirmed (Auger observatory)
• Proton Cerenkov h lt O(10-5)
• GZK threshold h gt - O(10-2)
• Neutrino vacuum Cerenkov IF 1020 eV detected
  AND rate high enough h lt O(10-21)
• (Amanda, IceCube)
• Neutrino/photon/GW time delay?
• Better measures of energy, timing, polarization
  from distant ?-ray sources
• (GLAST?, SWIFT?, VERITAS?)

Whats next?

• Definitively rule out n3 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(E2/M2), n4
• A true messenger of QG phenomenology will arrive?

Well be there!
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A possible new constraint helicity decay

• If ?R and ?L are unequal, say ?Rgt?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.
• 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 TeV 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.
• The lifetime above the transition energy is
  instead of about 10-11 seconds for energies just
  above 10 TeV. The lifetime might therefore be
  short enough to provide new constraints. From
  Crab might get

35
Constraint on electron helicities

• Electron spin resonance in a Penning trap yields
  (Myers-Pospelov, 2003)

• Nuclear spins give stronger constraints, but
  involves more parameters
• Constraints can be improved using RG analysis

36
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
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Why now QG phenomenology?Observational
improvements
By increasing detector size, or going into
space, or using technological improvement, or
technique improvement, observations are probing

• Higher energies
• Weaker interactions
• Lower fluxes
• Lower temperatures
• Shorter time resolution
• Longer distances
• Gravitational waves

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Phenomenology of Lorentz Violation

• Time-dependence of spin or hyperfine resonance,
  or energy levels as lab moves w.r.t. preferred
  frame or directions
• Long baseline dispersion (GRBs, AGNs, pulsars)
  and vacuum birefringence (e.g. spectropolarimetry
  of galaxies)
• New thresholds (photon decay, vacuum Cerenkov)
• Shifted thresholds (photon annihilation from
  blazars, GZK, )
• Maximum velocity (synchrotron peak from SNR)
• Gravitational effects (static fields, waves)