Constraining Lorentz
Invariance Violation
with Fermi
Vlasios Vasileiou
CRESST NASA Goddard Space Flight Center& University of Maryland, Baltimore County

on behalf of the Fermi LAT & GBM
collaborations
Nature published 28 Oct 2009arXiv:0908.1832

Lorentz-Invariance Violation
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

There is a fundamental scale (Planck scale λPl≈10-35 m) at which quantum
gravity (QG) effects are expected to strongly affect the nature of space-time.
Lorentz symmetry implies a scale-free space-time
QG effects might cause violations of Lorentz Invariance (LIV) → υγ(Eγ)≠c :LIV terms are typically described using a Taylor series:

Model-dependent factor ={0,±1}

QG Mass – energy scale that QG
effects are expected to be significant

Lorentz-Invariance Violation
Eγ≪ΜQGc2 → the sum is dominated by the lowest-order term (n) with sk≠0.

The now energy-dependent speed of light is:
Usually n=1 or 2 (linear andquadratic LIV respectively).

LIV perturbation term we would like to constrain.
sn=+1 or -1 for speed retardation or acceleration with an increasing photon energy.
There are many models that allow such Lorentz-Invariance violations, and someothers that actually predict them (e.g. stringy-foam model J. Ellis et al. 2008).

Lorentz-Invariance Violation


If the speed of light depends on its energy → then two photons ofdifferent energies emitted together will arrive at different times.
Then, for example, in the case sn=+1 (speed retardation), thehigher-energy photon (Eh) will arrive after the lower-energy
photon (El) after a time delay Δt:GRB090510


We have used the joint Fermi LAT (20MeV – 300GeV) and GBM (8keV– 40MeV) observations of GRB090510 to place strong and meaningful
constraints on LIV (on MQG).

Short GRB, duration <2s

Spectroscopically-measured redshift z=0.903±0.003

The detected emission extended up to 31GeV.
– Highest-energy photon ever detected from a short GRB.

The 31GeV Photon

Detected 0.829s after the GBM trigger.
1σ Confidence Interval for its energy is 27.97–36.32GeV
Solid evidence of this event being a photon
associated with this GRB– Did not trigger any ACD tiles. Signal at thetracker and the calorimeter consistent withan EM shower.
– 5.8 arcmin from the Swift-UVOT localization(95% PSF at 30GeV is 16 arcmin for thistype of event)Considerations based on the LAT backgroundrate also support its association with the GRB

First method
We set a lower limit on MQG from an upper limit on the time delay Δt ofthe 31GeV photon.
We don't try to assume the specific emission time of the 31GeV photon.

●●We associate the 31GeV photon with a lower-energy emission episode(of energy El ).

●Max Δt

Min MQG

Method only constrains positive time delays → subluminal propagation● Used conservative values for E and zh●

LAT – E vs T

Method #1
1. Most conservative case: 31GeV photon wasemitted some time after the start of the GRB:
Δt≤859ms↔ MQG,1≥1.19MPl

GBM NaI
8-260keV
GBM BGO
0.26-5MeV

2. Photon was emitted some time after the startof the main <MeV emission:Δt≤299ms↔ MQG,1≥3.42MPl
3. Photon was emitted some time after the start

LAT All events

LAT >100MeVof the >100MeV emission:Δt≤199ms↔ MQG,1≥5.12MPl
4. Photon was emitted some time after the start

LAT >1GeVof the >1GeV emission:Δt≤99ms↔ MQG,1≥10.0MPl

Method #1

Associations with individual spikes constrain
both positive and negative time delays (sn=±1)
Such associations are not as secure → used
as intuition builders (what we could do)
31GeV Photon lies at the center of a 20mswide pulse. We constrain both a positive and anegative time delay:|Δt|<10ms↔ MQ G,1 >102MP l

750MeV photon & precursor. We place one
more limit on a negative time delay:|Δt|<19ms↔ MQ G,1 >1.33MP l

Method #2 – DisCan

We also used an alternative and independent method (DisCan* – DispersionCancellation) to constrain LIV.
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➢

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This method extracted dispersion information from all the detected LAT
photons (detected energy range 35MeV – 31GeV).
Performed multiple trials, in which it moved each photon time according to atrial spectral lag coefficient (in ms/GeV).
The spectral lag coefficient which maximized the sharpness of thelightcurve was our measurement of the effective spectral lag.
The spectral lag coefficient was found to be consistent with zero.

We also performed a bootstrap analysis to gauge the statistical errors of thatmeasurement, which produced our final result:– a symmetric upper limit on the spectral lag coefficient|Δt/ΔΕ|<30ms/GeV ↔ MQ G,1 >1.22MP l(99% CL) on possible linear (n=1) dispersion of either sign (sn=±1).

*

Scargle, J. D., Norris, J. P. & Bonnell J. T. 2008

Conclusion

We constrained small changes in the speed of light caused by linear andquadratic perturbations in (Eγ/MQG).
Using two independent techniques, we have placed strong limits on linear
perturbations for both super- and sub-luminal speeds that were all higher
than the Planck Mass.
Our results➢

support Lorentz invariance and disfavor models in which a quantum
nature of space-time on a very small scale alters the speed of light,
giving it a linear dependence on photon energy.

This is the first time that direct measurements of the propagation speed oflight set limits on MQ G,1 that are higher than the Planck Mass.
Parameter space MQG,1>MPl unnatural → renders constrained models
highly implausible.
Results can be used to guide future development of QG and Planck-scalemodels.

Backup Slides

DisCan Method

Bootstrap error analysis

Finding the onset time of the >100MeV Emission