Deformed Relativistic Symmetries in FRW spacetime Giacomo Rosati Institute for Theoretical Physics, University of Wroc� law Experimental search for quantum gravity Trieste September 4, 2014 G.Amelino-Camelia+A.Marcian´ o+M.Matassa+G.R.,arXiv:1206.5315,Phys.Rev.D86(2012)124035 G.Amelino-Camelia+G.R.,arXiv:XXXX.XXXX,forthcoming
LIV vs. DSR Planck-scale modified dispersion relation E 2 − p 2 + L p Ep 2 = m 2 ( L p ∼ 10 − 19 GeV)
LIV vs. DSR Planck-scale modified dispersion relation E 2 − p 2 + L p Ep 2 = m 2 ( L p ∼ 10 − 19 GeV) LIV (Lorentz Invariance Violation)
LIV vs. DSR Planck-scale modified dispersion relation E 2 − p 2 + L p Ep 2 = m 2 ( L p ∼ 10 − 19 GeV) LIV (Lorentz Invariance Violation) ∼ 2000-2001 Amelino-Camelia, DSR (Deformed Relativistic Symmetries) Kowalski-Glikman,Magueijo,Smolin
LIV vs. DSR Planck-scale modified dispersion relation E 2 − p 2 + L p Ep 2 = m 2 ( L p ∼ 10 − 19 GeV) LIV (Lorentz Invariance Violation) The laws of motion are modified at a scale λ LIV ∼ 2000-2001 Amelino-Camelia, DSR (Deformed Relativistic Symmetries) Kowalski-Glikman,Magueijo,Smolin
LIV vs. DSR Planck-scale modified dispersion relation E 2 − p 2 + L p Ep 2 = m 2 ( L p ∼ 10 − 19 GeV) LIV (Lorentz Invariance Violation) The laws of motion are modified at a scale λ LIV Coordinates of different (inertial) observers are connected by ordinary Poincar´ e transformations ∼ 2000-2001 Amelino-Camelia, DSR (Deformed Relativistic Symmetries) Kowalski-Glikman,Magueijo,Smolin
LIV vs. DSR Planck-scale modified dispersion relation E 2 − p 2 + L p Ep 2 = m 2 ( L p ∼ 10 − 19 GeV) LIV (Lorentz Invariance Violation) The laws of motion are modified at a scale λ LIV Coordinates of different (inertial) observers are connected by ordinary Poincar´ e transformations E 2 − p 2 + λ LIV Ep 2 = m 2 holds only for a preferred observer → Poincar´ e symmetries are broken ∼ 2000-2001 Amelino-Camelia, DSR (Deformed Relativistic Symmetries) Kowalski-Glikman,Magueijo,Smolin
LIV vs. DSR Planck-scale modified dispersion relation E 2 − p 2 + L p Ep 2 = m 2 ( L p ∼ 10 − 19 GeV) LIV (Lorentz Invariance Violation) The laws of motion are modified at a scale λ LIV Coordinates of different (inertial) observers are connected by ordinary Poincar´ e transformations E 2 − p 2 + λ LIV Ep 2 = m 2 holds only for a preferred observer → Poincar´ e symmetries are broken Different (inertial) observers, by the same measuring procedure, obtain different values for λ LIV ∼ 2000-2001 Amelino-Camelia, DSR (Deformed Relativistic Symmetries) Kowalski-Glikman,Magueijo,Smolin
LIV vs. DSR Planck-scale modified dispersion relation E 2 − p 2 + L p Ep 2 = m 2 ( L p ∼ 10 − 19 GeV) LIV (Lorentz Invariance Violation) The laws of motion are modified at a scale λ LIV Coordinates of different (inertial) observers are connected by ordinary Poincar´ e transformations E 2 − p 2 + λ LIV Ep 2 = m 2 holds only for a preferred observer → Poincar´ e symmetries are broken Different (inertial) observers, by the same measuring procedure, obtain different values for λ LIV ∼ 2000-2001 Amelino-Camelia, DSR (Deformed Relativistic Symmetries) Kowalski-Glikman,Magueijo,Smolin The laws of motion are modified at a scale ℓ DSR
LIV vs. DSR Planck-scale modified dispersion relation E 2 − p 2 + L p Ep 2 = m 2 ( L p ∼ 10 − 19 GeV) LIV (Lorentz Invariance Violation) The laws of motion are modified at a scale λ LIV Coordinates of different (inertial) observers are connected by ordinary Poincar´ e transformations E 2 − p 2 + λ LIV Ep 2 = m 2 holds only for a preferred observer → Poincar´ e symmetries are broken Different (inertial) observers, by the same measuring procedure, obtain different values for λ LIV ∼ 2000-2001 Amelino-Camelia, DSR (Deformed Relativistic Symmetries) Kowalski-Glikman,Magueijo,Smolin The laws of motion are modified at a scale ℓ DSR Different (inertial) observers, by the same measuring procedure, obtain the same value for ℓ DSR ( ℓ DSR is a relativistic invariant as c )
LIV vs. DSR Planck-scale modified dispersion relation E 2 − p 2 + L p Ep 2 = m 2 ( L p ∼ 10 − 19 GeV) LIV (Lorentz Invariance Violation) The laws of motion are modified at a scale λ LIV Coordinates of different (inertial) observers are connected by ordinary Poincar´ e transformations E 2 − p 2 + λ LIV Ep 2 = m 2 holds only for a preferred observer → Poincar´ e symmetries are broken Different (inertial) observers, by the same measuring procedure, obtain different values for λ LIV ∼ 2000-2001 Amelino-Camelia, DSR (Deformed Relativistic Symmetries) Kowalski-Glikman,Magueijo,Smolin The laws of motion are modified at a scale ℓ DSR Different (inertial) observers, by the same measuring procedure, obtain the same value for ℓ DSR ( ℓ DSR is a relativistic invariant as c ) E 2 − p 2 + ℓ DSR Ep 2 = m 2 holds for all (inertial) observers
LIV vs. DSR Planck-scale modified dispersion relation E 2 − p 2 + L p Ep 2 = m 2 ( L p ∼ 10 − 19 GeV) LIV (Lorentz Invariance Violation) The laws of motion are modified at a scale λ LIV Coordinates of different (inertial) observers are connected by ordinary Poincar´ e transformations E 2 − p 2 + λ LIV Ep 2 = m 2 holds only for a preferred observer → Poincar´ e symmetries are broken Different (inertial) observers, by the same measuring procedure, obtain different values for λ LIV ∼ 2000-2001 Amelino-Camelia, DSR (Deformed Relativistic Symmetries) Kowalski-Glikman,Magueijo,Smolin The laws of motion are modified at a scale ℓ DSR Different (inertial) observers, by the same measuring procedure, obtain the same value for ℓ DSR ( ℓ DSR is a relativistic invariant as c ) E 2 − p 2 + ℓ DSR Ep 2 = m 2 holds for all (inertial) observers Coordinates of different (inertial) observers are connected by ( ℓ -)deformed Poincar´ e transformations (nonlinear) → Poincar´ e symmetries are deformed
LIV vs. DSR Planck-scale modified dispersion relation E 2 − p 2 + L p Ep 2 = m 2 ( L p ∼ 10 − 19 GeV) LIV (Lorentz Invariance Violation) The laws of motion are modified at a scale λ LIV Coordinates of different (inertial) observers are connected by ordinary Poincar´ e transformations E 2 − p 2 + λ LIV Ep 2 = m 2 holds only for a preferred observer → Poincar´ e symmetries are broken Different (inertial) observers, by the same measuring procedure, obtain different values for λ LIV ∼ 2000-2001 Amelino-Camelia, DSR (Deformed Relativistic Symmetries) Kowalski-Glikman,Magueijo,Smolin The laws of motion are modified at a scale ℓ DSR Different (inertial) observers, by the same measuring procedure, obtain the same value for ℓ DSR ( ℓ DSR is a relativistic invariant as c ) E 2 − p 2 + ℓ DSR Ep 2 = m 2 holds for all (inertial) observers Coordinates of different (inertial) observers are connected by ( ℓ -)deformed Poincar´ e transformations (nonlinear) → Poincar´ e symmetries are deformed It is well known that in the DSR approach the observable effects coming from modification of Poincar´ e symmetries are in general smoother, and some of the processes allowed by LIV are not allowed in DSR
Motivation for DSR-FRW The possibility of testing Planck-scale modified dispersion relation has been a central topic for quantum gravity phenomenology in the last two decades.
Motivation for DSR-FRW The possibility of testing Planck-scale modified dispersion relation has been a central topic for quantum gravity phenomenology in the last two decades. Especially through the observation of highly energetic astrophysical sources, for which the cosmological distance traveled by particles act as amplifier for the small, Planckian, effect.
Motivation for DSR-FRW The possibility of testing Planck-scale modified dispersion relation has been a central topic for quantum gravity phenomenology in the last two decades. Especially through the observation of highly energetic astrophysical sources, for which the cosmological distance traveled by particles act as amplifier for the small, Planckian, effect. ✄ � You cannot neglect the effects of spacetime curvature/expansion → FRW spacetime ✂ ✁
Motivation for DSR-FRW For the LIV scenario, a consensus has been reached for the expected delay in the arrival of hard (high energy) photons respect to simultaneously emitted soft photons: � z 1 + ¯ z Ellis, Jacob, Piran,... � � ∆ t = λ LIV ∆ p z ) d ¯ z Ω m (1 + z ) 3 + Ω Λ � H ( z ) = H 0 H (¯ ∼ 2006 -2008 0
Motivation for DSR-FRW For the LIV scenario, a consensus has been reached for the expected delay in the arrival of hard (high energy) photons respect to simultaneously emitted soft photons: � z 1 + ¯ z Ellis, Jacob, Piran,... � � ∆ t = λ LIV ∆ p z ) d ¯ z Ω m (1 + z ) 3 + Ω Λ � H ( z ) = H 0 H (¯ ∼ 2006 -2008 0 This has allowed to put upper bounds on the scale of Lorentz symmetry breaking through observation of highly energetic transient astrophysical events: ✞ ☎ GRBs, AGN,... Fermi, HESS,... short GRBs: λ LIV ≤ 0 . 82 L p ! GRB090510 ✝ ✆ Granot’s talk
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