Quantum Gravity Phenomenology

RCM and Maxim Pospelov,hep-ph/0301124

10th Conference on General Relativity and Relativistic Astrophysics

Planck scale physics has captured the imaginationof theorists in the quest for a consistent frameworkunifying general relativity and quantum field theory

? superstrings, loop quantum gravity, causalsets, noncommutative geometry, . . . .

GeV 10195

Planck ≈=Gc

Eη

Must this search be a purely theoretical exercise,devoid of any contact with experiment?

Amelino-Camelia, Ellis, Mavromatos,Nanopoulos & Sarkar, Nature 1998

“Quantum Gravity Phenomenology”

violations of local Lorentz invariance may bemanifest in modified dispersion relations:

++= 222 mpE ααη +2

Pl

pM

1

and are phenomenological parametersη α

. . . . +

NO!

“Sacred Symmetries”:CPT, spin-statistics, Lorentz symmetry, …..

Why think of violations of local Lorentz invariance (LLI)?

• certain scenarios of quantum gravity suggest LLIbroken or modified at Planck scale

e.g., loop quantum gravity – spacetime replacedwith discrete structure at ?

noncommutative geometry emerges at ?

braneworld scenarios?

• Lorentz group has infinite volume

Planckλ

Planckλ

Amelino-Camelia et al, Nature 1998

“Quantum Gravity Phenomenology”

violations of local Lorentz invariance may bemanifest in modified dispersion relations:

++= 222 mpE ααη +2

Pl

pM

1

and are phenomenological parametersη α

. . . . +

Look for energy/time-of-arrivalcorrelations for high energy

photons from gamma-ray bursters

3

Pl

22 pM

pE :1ξ

α +==

CGRO, 1998:

GLAST, 2006:

310≤ξ( )1O≤ξ

cL

tPlM

Eξ≈∆

pM

1pE

vPl

gξ

+=∂∂

=

Other ideas:? Examining UltraHigh Energy Cosmic Rays

(GZK cutoff: 5 × 1010 GeV)

? Detecting spacetime foam with gravity wave interferometers

? Induced phase incoherence of light overcosmological distance scales

? Imprints in the cosmic microwave background

? Birefringence effects

? Threshold tests

(Jacobson et al; Konopka & Major)

Constraints on p3 parameters: electron η; photon ξ

γ+→ −− eeCerenkov:

Photon decay:+− +→ eeγ

Crab synchrotron radiation: 910−−≥η

vacuum Cerenkov effect:modify only electron dispersion relation

if >0, high-E electrons can emit (null) photons

3

Pl

222 pM

mpE η

++=

p

E222 mpE +=

0>η

η

(Jacobson et al; Konopka & Major)

Constraints on p3 parameters: electron η; photon ξ

γ+→ −− eeCerenkov:

Photon decay:+− +→ eeγ

Crab synchrotron radiation: 910−−≥η

Effective field theory and Lorentz violations:

Standard Model and General Relativity provide anexcellent description of physics for E << MPl = 1019 GeV

Dimension 3,4 operators are extensively studiedand tremendously constrained!!

(Kostelecky; Coleman; Glashow; Carroll; ...)

( ) cdababcd

abab FFk

41

FF41

F−−e.g.,

31F 10k −≤

(Kostelecky & Mewes)

Effective field theory and Lorentz violations:

Standard Model and General Relativity provide anexcellent description of physics for E << MPl = 1019 GeV

Dimension 3,4 operators are extensively studiedand tremendously constrained!!

(Kostelecky; Coleman; Glashow; Carroll; ...)

Dimension 5 operators may generate p3 terms in dispersion relations.

Strategy: Ignore dim–3,4 operators (however, we use these results later)

Define preferred frame withfixed timelike vector na (n·n=+1)

Dim–5 Operators:

1. Quadratic in the same field2. One extra derivative beyond kinetic term3. Gauge invariant4. Lorentz invariant except for na

5. Not reducible to lower dimension operatorby equations of motion

6. Not reducible to a total derivative

Also, assume the operators are suppressed by 1/MPl

(Only appearance of “gravity” in the following )

Complex Scalar:

Dispersion relation:

with na=(1,0,0,0) and pE ≅

• no such term for real scalar (e.g., Higgs)• odd under CPT and C• don’t consider: ( ) ( )φφφφ ∂⋅−≅∂⋅∂ nn 22 m

( ) φφκ

φφ 3

Pl

222n

M∂⋅+−∂ im

3

Pl

222 pM

pEκ

++≅ m

( ) 0pM

pE yx3

Pl

22 =±

±− εε

ξi

( ) ( )bdbad

a

Pl

2 F~

nnFnM

F41

∂⋅+−ξVector:

Dispersion relation:

with ka=(E,0,0,p) , na=(1,0,0,0) and pE ≅

• chiral dispersion relation → birefringence• CPT odd; C even• nonabelian extension straightforward

( ) 0M

p2pE 521

Pl

3222 =

+−−− ψγηηm

Spinor:

( ) ( ) ( ) ψγγηηψψγψ 2521

Pl

nnM

1∂⋅⋅++−∂⋅ mi

Dispersion relation:

with na=(1,0,0,0) and pE ≅

• two independent parameters• chiral basis: (as required by SM)• both CPT odd; C(η1) odd, C(η2) even

21LR, ηηη ±=

Dispersion relations incompatible with field theory!!

Constraints revisited: electron η; photon ξ

γ+→ −− eeCerenkov:

Photon decay:+− +→ eeγ

Crab synchrotron radiation: 910−−≥η

Constraints revisited: electron η1 (η2=0) ; photon ξ

γ+→ −− eeCerenkov:Photon decay:

+− +→ eeγ

Crab synchrotron radiation: 91 10−−≥η

.2-.2-.2

.2

ξ

η1

Polarization constraint: 410−≤ξ (Gleiser & Kozameh)

Loops and all that:

x2η

ψγγψη 5Pl

2UV

2 nM

⋅Λ

≈

even if cutoff is SUSY scale (TeV), all parameters are bounded smaller than 10 –10 !!

as a result of quantum fluctuations,dim–5 operators naturally feed down to dim–3,4:

Loops with a twist:

x

ψγγψψηγγψ

cba5UV

bca52UV

pplogΛ+Λ≈

ψγγψ cba5 ∂∂

Replace vector–triple by traceless combination:

( )abccabbcacbaabccba nnn61

nnnCnnn ηηη ++−=→

• log divergences → RG flow• high energy dispersion relations unchanged

Laboratory tests:

Precision terrestial experiments can competewith limits from astrophysical tests!

na defines preferred frame but does notcoincide with earth-bound laboratory frame

v),1(na ≅

e.g., if preferred frame is that of CMB: 3i 10vn −≅≅

Motion establishes preferred spatial direction, which can be searched for in spin interactions

Lepton couplings:

“Chiral” electron coupling is boundedby torsion balance tests

GeV10b 28i

−≤e

4n

M GeV10i2

Pl28

2 ≅≤−

e

e

mη

( ) ψγγψηψγγψη i

5iPl

2

22

5Pl

2 nM

nnM

eee m

≈∂⋅⋅

(Heckel; Adelberger; …..)

Quark and photon couplings:

• can be bounded by “clock comparison” experiments,which search for spatial anisotropies from frequencyvariation of Zeeman hyperfine transition

• estimate induced neutron coupling from dim–5Lagrangian for quarks and photon with QCD sum rule

(Berglund et al, 1995)

( ) Ψ∂⋅⋅Ψ≈ 25

Pl

25 nn

MNLN γγ

η

( ) ( ) ξπ

αηηηηη

413.005.01.0 QuQd2 +−−−≅

( ) ψγγψηψγγψη i

5iPl

2N

22

5Pl

2 nM

nnM

m≈∂⋅⋅

GeV10b 31i

−≤

9i2

N

Pl31

2 10n

M GeV10 −−

≅≤m

η

As before:

( ) ( ) 83QuQd 10105.0 −− ≤+−−− ξηηηη

Loop Quantum Gravity Results:

Heuristic calculations suggest for:

Dirac fermion:

Vector: )1(O≈ξ

,01 =η 1MM

Pl

coh2 <<

≈ Oη

Challenge now is to provide rigorous predictions.

(Gambini & Pullin; Alfaro et al; Sahlmann & Thiemann)

Breaking versus deforming Lorentz symmetry

• our experimental bounds rely on existence of apreferred frame → LLI broken

• some suggestions are that symmetry is deformedby appearance of a dimensionful parameter MPl

→ “doubly special relativity”na = (1,0,0,0) for all observers

• some bounds still applye.g., polarization constraint |ξ| ≤ 10–4

(Amelino-Camelia; Magueijo & Smolin; ...)

Beyond effective field theory

• using EFT is a “theoretical prejudice”

• can study eom, not derivable from an action

( ) ( ) ( ) ( )aba

2

Pl

aba

2

Plab

a FnnM

~F~nn

MF ∂⋅+∂⋅=∂

ξξ

( ) ( ) 0~

Mp

pE yxPl

322 =±

±+− εεξξ i

Dispersion relation:

Fixed vector versus General Relativity

• for generic curved space, there are no constant vectors!

• may apply for FRW cosmology but not for our “lumpy” universe

• perhaps na corresponds to expectationvalue of Planck mass field

(Mattingly & Jacobson)

Conclusions:• Effective field theory constrains form of higherorder dispersion relations [ at O(p3) ]

• Dim–3,4 operators are not induced throughloops from higher twist dim–5 operators

• Effective field theory provides a frameworkwhere terrestial experiments provide stringentbounds on pheno parameters [ at O(p3) ]

4

1010

21

8Qdu,

5

≤−

≤−≤

−

−

ee ηη

ηηξ

What next?

• use RG flows to bound operators at Planck scale(consider effects of dim–5 interactions? No!

e.g., )

• produce predictions for loop quantum gravity

• dim–6 operators?better ideas for experimental bounds

bab

a nFψγψ

S.D. Biller et al (gr-qc/9810044)rapid flare on May 15, 1996 from Markarian 421

z=.031 L=1.1 × 1016 l-sec

(280 sec. bins)

250<ξ