cpt violation in the early universe & leptogenesis/baryogenesis

CPT VIOLATION IN THE EARLY UNIVERSE &

LEPTOGENESIS/BARYOGENESISNick E. Mavromatos

King’s College London, Physics & CERN/PH-TH

London Centrefor TerauniverseStudies (LCTS)AdV 267352

DISCRETE 2012, IST, Lisbon, December 3-7 2012

• Matter over Antimatter Dominance : open issues

• CPT Symmetry : can it be violated and how?

• CPT Violation (CPTV) Scenarios in Early Universe: Classical or Quantum Gravity? Background-induced Breaking of CPT Symmetry in Early Universe Geometries; Space-time (stringy) defects and quantum aspects of CPTV

The role of Neutrinos : Leptogenesis implies Baryogenesis (observed Baryon Asymmetry in Universe)

• Can we experimentally test such ideas? • Astrophysics, Cosmology, LAB

Generic Concepts• Leptogenesis: physical out of thermal equilibrium

processes in the (expanding) Early Universe that produce an asymmetry between leptons & antileptons

• Baryogenesis: The corresponding processes that produce an asymmetry between baryons and antibaryons

• Ultimate question: why is the Universe made only of matter?

Generic Concepts• Leptogenesis: physical out of thermal equilibrium

processes in the (expanding) Early Universe that produce an asymmetry between leptons & antileptons

• Baryogenesis: The corresponding processes that produce an asymmetry between baryons and antibaryons

• Ultimate question: why is the Universe made only of matter?

escher

• Matter-Antimatter asymmetry in the Universe Violation of Baryon # (B), C & CP

• Tiny CP violation (O(10-3)) in Labs: e.g.

• But Universe consists only of matter

T > 1 GeV

Sakharov : Non-equilibrium physics of early Universe, B, C, CP violation but not quantitatively in SM, still a mystery

Generic Concepts

WMAP + COBE (2003)

• Matter-Antimatter asymmetry in the Universe Violation of Baryon # (B), C & CP

• Tiny CP violation (O(10-3)) in Labs: e.g.

• But Universe consists only of matter

T > 1 GeV

Sakharov : Non-equilibrium physics of early Universe, B, C, CP violation but not quantitatively in SM, still a mystery

Assume CPT

Generic Concepts

WMAP + COBE (2003)

Within the Standard Model, lowest CP Violating structures

Shaposhnikov

This CP Violation Cannot be the Source of BaryonAsymmetry in The Universe

Kobayashi-Maskawa CP Violating phase

sphaleron decoupling T

Beyond SM sources of CP Violation?

• Several Ideas to go beyond the SM (e.g. GUT models, Supersymmetry, extra dimensional models etc.)

• Massive ν are simplest extension of SM• Right-handed massive ν may provide

extensions of SM with: extra CP Violation and thus Origin of

Universe’s matter-antimatter asymmetry due to neutrino masses, Dark Matter

Mohapatra, Pilaftsistalks

Beyond SM sources of CP Violation?

• Several Ideas to go beyond the SM (e.g. GUT models, Supersymmetry, extra dimensional models etc.)

• Massive ν are simplest extension of SM• Right-handed massive ν may provide

extensions of SM with: extra CP Violation and thus Origin of

Universe’s matter-antimatter asymmetry due to neutrino masses, Dark Matter

…BUT MAY NOT BE NECESSARY IF CPT VIOLATION IN EARLY UNIVERSE

CPT VIOLATION IN THE EARLY UNIVERSE

GENERATE Baryon and/or Lepton ASYMMETRY without Heavy Sterile Neutrinos?

CPT Invariance Theorem :(i) Flat space-times(ii) Lorentz invariance(iii) Locality(iv) Unitarity

(ii)-(iv) Independent reasons for violation

Schwinger, Pauli,Luders, Jost, Bellrevisited by:Greenberg,Chaichian, Dolgov,Novikov…

Kostelecky , Potting, Russell, Lehnert, Mewes, Diaz ….Standard Model Extension (SME)PHENOMENOLOGICAL 3-LV parameter (texture) model for neutrino oscillationsfitting also LSND, MINOS

Barenboim, Borissov, Lykken PHENOMENOLOGICAL models with non-local mass parameters

10-35 mJ.A. Wheeler

e.g. QUANTUM SPACE-TIME FOAM AT PLANCK SCALES

Hawking,Ellis, Hagelin, NanopoulosSrednicki, Banks, Peskin, Strominger,Lopez, NEM, Barenboim…

QUANTUM GRAVITY INDUCED DECOHERENCEEVOLUTION OF PURE QM STATES TO MIXEDAT LOW ENERGIES

LOW ENERGY CPT OPERATOR NOT WELL DEFINED

10-35 m

NB: Decoherence & CPTV

May induce quantum decoherence of propagating matter and intrinsic CPT Violation in the sense that the CPT operator Θ is not well-defined

Decoherence implies that

asymptotic density matrix of

low-energy matter :

If Θ well-defined can show that

exists !INCOMPATIBLE WITH DECOHERENCE !

Wald (79)Hence Θ ill-defined at low-energies inQG foam models

NB: Decoherence & CPTV

May induce quantum decoherence of propagating matter and intrinsic CPT Violation in the sense that the CPT operator Θ is not well-defined

Decoherence implies that

asymptotic density matrix of

low-energy matter :

INCOMPATIBLE WITH DECOHERENCE !Wald (79)Hence Θ ill-defined at low-energies in

QG foam models may affect EPR

May contaminate initially antisymmetric neutral meson M state by symmetric parts (ω-effect)

Bernabeu, NEM, Papavassiliou,…

Assume CPT Violation. e.g. due to Quantum Gravity fluctuations,strong in the Early Universe

physics.indiana.edu

Assume CPT Violation. e.g. due to Quantum Gravity fluctuations,strong in the Early Universe

ONE POSSIBILITY: particle-antiparticle mass differences

physics.indiana.edu

Equilibrium Distributions different between particle-antiparticlesCan these create the observed matter-antimatter asymmetry?

Assume dominant contributions to Baryon asymmetry from quarks-antiquarks

Dolgov, ZeldovichDolgov (2009)

High-T quark mass >> Lepton mass

Equilibrium Distributions different between particle-antiparticlesCan these create the observed matter-antimatter asymmetry?

Assuming dominant contributions to Baryon asymmetry from quarks-antiquarks

Dolgov, ZeldovichDolgov (2009)

photon equilibrium density at temperature T

Dolgov (2009)

Current bound for proton-antiproton mass diff.

Reasonable to take: Too smallβΤ=0

NB: To reproducethe observed

ASACUSA Coll. (2011)

Dolgov (2009)

Reasonable to take: Too smallβΤ=0

NB: To reproducethe observed

CPT Violating quark-antiquark Mass difference alone CANNOT REPRODUCE observed BAU

Current bound for proton-antiproton mass diff.

ASACUSA Coll. (2011)

GRAVITATIONALLY-INDUCED

CPT VIOLATION

OTHER INTERESTING IDEAS FOR GENERATING CPT VIOLATING EFFECTSIN THE EARLY UNIVERSE: PARTICLE-ANTIPARTICLE DIFFERENCES IN DISPERSION RELATIONS Differences in populations freeze out Baryogenesis or Leptogenesis Baryogenesis

B-L conserving GUT or

Sphaleron

OTHER INTERESTING IDEAS FOR GENERATING CPT VIOLATING EFFECTS IN THE EARLY UNIVERSE: PARTICLE-ANTIPARTICLE DIFFERENCES IN DISPERSION RELATIONS Differences in populations freeze out Baryogenesis or Leptogenesis Baryogenesis

REVIEW VARIOUS SCENARIOS

Sphaleron

1. GRAVITATIONAL BARYOGENESIS THROUCH

Space-time-CURVATURE/BARYON-NUMBER-CURRENT COUPLING

Davoudiasl, Kitano, Kribs,Murayama, Steinhardt

Ricciscalar

Gravitational Baryogenesis Davoudiasl, Kitano, Kribs,Murayama, Steinhardt

Quantum Gravity (or something else (e.g. SUGRA)) may lead at low-energies (below Plnack scale or a scale M*) to a term in the effective Lagrangian (in curved back space-time backgrounds):

Gravitational Baryogenesis Davoudiasl, Kitano, Kribs,Murayama, Steinhardt

Current e.g. baryon-number Jμ

current(non-conserved in Standard Model due to anomalies)

Generation (flavour) #

Term Violates CP but is CPT conserving in vacuo

Gravitational Baryogenesis

Term Violates CP but is CPT conserving in vacuoIt Violates CPT in the background space-time of an expanding FRW Universe

Energy differences between particle vs antiparticles Dynamical CPTV

LIKE A CHEMICALPOTENTIAL FOR FERMIONS

Baryon Asymmetry @ T < TD , TD = Decoupling T

Calculate for various w in some scenarios

Baryon Asymmetry for w=1/3 (occuring in radiation era)@ T < TD , TD = Decoupling T

Baryon Asymmetry for w=0 (occuring in dust era)

due to interactions among massless particles

entropy-dilution factor included, TD < TDR = radiation dominance T

Other scenarios: non-thermal component w >1/3 domination etc

Sphaleron

Independent of Initial Conditions

@ T >>Teq

Heavy Right-handed Majorana neutrinos enter equilibrium at T = Teq > Tdecay

Standard Thermal Leptogenesis

Fukugita, Yanagida,

Lepton number Violation

Produce Lepton asymmetry

Observed Baryon Asymmetry In the Universe (BAU)

Equilibrated electroweakB+L violating sphaleron interactions

Kuzmin, Rubakov,Shaposhnikov, Akhmedov, Smirnov,…

Estimate BAU by solving Boltzmann equations for Heavy Neutrino Abundances

Pilafsis,Buchmuller, di Bari et al.

Out of Equilibrium Decays

@ T >>Teq

Heavy Right-handed Majorana neutrinos enter equilibrium at T = Teq > Tdecay

Standard Thermal Leptogenesis

Fukugita, Yanagida,

Lepton number Violation

Kuzmin, Rubakov,Shaposhinkov

Estimate BAU by solving Boltzmann equations for Heavy Neutrino Abundances

Pilafsis,Buchmuller, di Bari et al.

Out of Equilibrium Decays

No Heavy Right-handed Majorana neutrinosCPTV Thermal Leptogenesis

Fukugita, Yanagida,

CPT Violation

Kuzmin, Rubakov,Shaposhinkov

Estimate BAU by fixing CPTV background parametersIn some models this means fine tuning ….

Early UniverseT > 1015 GeV

2. CPTV Effects of different Space-Time-Curvature/Spin couplings between

neutrinos/antineutrinos

B. Mukhopadhyay, U. Debnath, N. Dadhich, M. SinhaLambiase, Mohanty

Curvature Coupling to fermion spin may lead to different dispersion relationsbetween neutrinos and antineutrinos (assumed dominant in the Early eras) in non-spherically symmetric geometries in the Early Universe.

Dirac Lagrangian (for concreteness, it can be extended to Majorana neutrinos)

Gravitational covariant derivativeincluding spin connection

Christoffel Symbolvielbeins (tetrads)

For homogeneous and isotropic Friedman-Robertson-Walker geometries the resulting Bμ vanish

Can be constant in a givenlocal frame in Early Universeaxisymmetric cosmologiesor near rotating Black holes

CPTV Effects of different Space-Time-Curvature/Spin couplings between ν, ν in Bianchi Cosmologies-

B. Mukhopadhyay, U. Debnath, N. Dadhich, M. SinhaLambiase, Mohanty

Assumption: Neutrinos non clustering properties, dominant species in early Universe

B3 = B1 = 0

DISPERSION RELATIONS OF NEUTRINOS ARE DIFFERENT FROM THOSE OF ANTINEUTRINOS IN SUCH GEOMETRIES

± refers to chiral fields (here neutrino/antineutrino)

CPTV Dispersion relations

but (bare) masses are equal between particle/anti-particle sectors

Abundances of neutrinos in Early Universe, then, different from those of antineutrinosif B0 is non-trivial.

NOT the Effective fermion/antifermion masses (p=0)

Abundances of neutrinos in Early Universe different from those of antineutrinosif B0 ≠ 0

BARYOGENESIS VIA LEPTOGENESIS

@ T = Td (decoupling Temp. of Lepton number (L) Violating processes) there is a constant ratio of net neutrino/antineutrino asymmetry (ΔL) to entropy density ( ~T3)

Communicated to Baryon sector, and thus generates BAU either via a B-L conserving symmetry as in GUT models or via B + L conserving sphaleron processe BARYOGENESIS

(Leptogenesis)

Neutrino/antineutrino asymmetry around black holes

Consider the metric of a Kerr (rotating) black hole

B. Mukhopadhyay, astro-ph/0505460

and we have

angular momentum

and we have

Calculate the vector Bμ can show that it is non vanishing,hence there is CPT Violation induced in this case

Consider the neutrino-antineutrino population difference

Consider Kerr black holes for which and show that

Then, if B0 << T

averaged over the spatial volume V

Asymmetry depends on the sign of B0

REMARKS

PRIMORDIAL BLACK HOLES WITH MASSES MBH < 1015 gm have evaporatedtoday, only BH with masses MBH > 1015 gm may survive today

Hawking temperature

To reproduce observed Baryon asymmetry Δn = O(10 -10 ) we need 106 BH with the same sign of B0 fine tuning …..

3. CPTV induced by SPACE-TIME with TORSION

Generic Concepts on Torsionful Geometries

Fermionic Torsion in Einstein-Cartan theory & CPTV

Kalb-Ramond Torsion in String-Inspired Effective theories & CPTV

Einstein theories of gravity postulate that torsion is absent (constraint)

Einstein-Cartan and Kibble (1961) Sciama (1964) theories , this constraintis not used and torsion is considered as a dynamical field.

Fermions in gravitational field, when formulated in the so called first-orderformalism, where spin connection and vierbein are treated as independentthe torsion does not vanish & is proportional to the axial fermion current

3. Gravity with TORSION

If torsion then Γμν ≠ Γνμ antisymmetric part is the contorsion tensor, contributes to

vielbeins (tetrads)independent fromspin connection ωμ

now ….

3. Fermions in Gravity with TORSION

If torsion then Γμν ≠ Γνμ antisymmetric part is the contorsion tensor, contributes to

vielbeins (tetrads)independent fromspin connection ωμ

now ….

3. Fermions in Gravity with TORSION

Gravity with Torsion contains Antisymmetric parts in the spin connection:

Contorsion tensor

Curvature tensor in first order torsionful formalism

Torsion decomposes in vector, Tμ , axial vector Sμ and tensor qμνρ parts

Variation of the combined actions SG + SFERMION w.r.t. T, S and q components of torsion,viewed as independent fields, yields:

These solutions allow for the spin connection with torsion to be written as:

So that torsion is associated with the spinor axial current.

torsion-free

Hehl-Datta equation

Variation with respect to torsion yields connection of torsion to axial currentsthen substitution back to fermion equations yields the higher order equation

Hehl-Datta equation

Variation with respect to torsion yields connection of torsion to axial currentsthen substitution back to fermion equations yields the higher order equation

obtained from effective lagrangian

repulsive four fermion interaction

Complex conjugate equation

Go compare

opposite signs

FERMIONIC-TORSION INDUCED CPTVN. Poplawski, Physical Review DVol. 83, No. 8 (2011) 084033

Using plane wave approximation we obtain differentdispersion relations between particles/antiparticlesAT FINITE DENSITIES ASSUMING CONSTANT BACKGROUND TORSION

fermion antifermion

FERMIONIC-TORSION INDUCED CPTVN. Poplawski, Physical Review DVol. 83, No. 8 (2011) 084033

Assume condensates that preserve spatial rotations but violate Lorentz, i.e. only temporal components

Only for chiral matter e.g.

active neutrinos

fermion antifermion

NB: Lagrangian is C (harge conjugation) symmetric but Hehl-Datta equation is NOT

fermion antifermion

inverse normalizationof Dirac spinor wavefunctionof order of (energy scale)3

for the Universeat temperature T

particle/antiparticle asymmetry can thus be generated from torsion ? Finite T analysis of condensates pending

BARYON-ASYMMETRY FROM TORSIONFUL GEOMETRIES?N. Poplawski, PR D 83 (2011)

fermion antifermion

inverse normalizationof Dirac spinor wavefunctionof order of (energy scale)3

Has the pheno - right value if

not appropriate for neutrinos (TD ≈ 1015 GeV)

N. Poplawski, PR D 83 (2011)

BARYON-ASYMMETRY FROM TORSIONFUL GEOMETRIES?

3b. CPTV induced by SPACE-TIME with (string-inspired) Kalb-Ramond TORSION

NEM & Sarben Sarkar, arXiv:1211.0968

If torsion then Γμν ≠ Γνμ antisymmetric part yields non –zero contributions to Bμ

Massless Gravitational multiplet of (closed) strings: spin 0 scalar (dilaton) spin 2 traceless symemtric rank 2 tensor (graviton) spin 1 asntisymmetric rank 2 tensor

Effective field theories (low energy scale E << Ms) `` gauge’’ invariant

Depend only on field strength :

Bianchi identity :

String Theories with Antisymmetric Tensor Backgrounds

KALB-RAMOND FIELD

ROLE OF H-FIELD AS TORSION

EFFECTIVE GRAVITATIONAL ACTION IN STRING LOW-ENERGY LIMIT CAN BE EXPRESSED IN TERMS OF A GENERALIZED CURVATURE RIEMANN TENSOR WHERE THE CHRISTOFFEL CONNECTION INCLUDES TORSION PROVIDED BY H-FIELD

4-DIM PART

Contorsion

ROLE OF H-FIELD AS TORSION – AXION FIELD

EFFECTIVE GRAVITATIONAL ACTION IN STRING LOW-ENERGY LIMIT CAN BE EXPRESSED IN TERMS OF A GENERALIZED CURVATURE RIEMANN TENSOR WHERE THE CHRISTOFFEL CONNECTION INCLUDES TORSION PROVIDED BY H-FIELD

4-DIM PART

IN 4-DIM DEFINE DUAL OF H AS : b(x) = Pseudoscalar

(Kalb-Ramond (KR) axion)

FERMIONS COUPLE TO H –TORSION VIA GRAVITATIONAL COVARIANT DERIVATIVE

TORSIONFUL CONNECTION, FIRST-ORDER FORMALISM

gauge field contorsion

Non-trivial contributions to Bμ

FERMIONS COUPLE TO H –TORSION VIA GRAVITATIONAL COVARIANT DERIVATIVE

TORSIONFUL CONNECTION, FIRST-ORDER FORMALISM

gauge field contorsion

Non-trivial contributions to Bμ

Exact (conformal Field Theories on World-sheet) Solutions from String theoryAntoniadis, Bachas, Ellis, Nanopoulos

In Einstein frame E (Scalar curvature term in gravitational effective action has canonical normalisation):

Cosmological Solutions, non-trivial time-dependent dilatons, axions

Central charge of uderlying world-sheet conformal field theory

Kac-Moodyalgebra level``internal’’ dims

central charge

Covariant Torsion tensor

Constant

constant B0

Lepton Asymmetry as in previous cases , e.g. for neutrinos

Requires @ Td

+ standard Dirac terms without torsion

Fermions:

Bianchi identity conserved ``torsion ‘’ charge

classical

Postulate conservation at quantum level by adding counterterms

Implement via constraint lagrange multiplier in Path integral

Quantum Fluctuations of Torsion (on top of any background)

NEM, Pilaftsis arXiv: 1209.6387

NB: any H- background ignored here , if there it contributes to the action as discussed above ….

Duncan, Kaloper & Olive Nucl.Phys. B387 (1992)

partial integration

Use chiral anomaly equation (one-loop) in curved space-time:

Hence, effective action of torsion-full QED

partial integration

Hence, effective action of torsion-full QED coupling

Upon Yukawa coupling of a toMajorana fermion radiatively (3-loop) generated fermion mass

a = axionmixing with KR field b

Hence, effective action of torsion-full QED

Can give rise to fermionicconstant torsion CPTV viaLV fermion condensates

4. STRINGY SPACE-TIME D(efect)-FOAM

Our UniverseNO LONGERLorentz Invariant

(Standard Model particles)

(Gravitons)

D-particle defect

Recoil of defect

BRANE-WORLDS with D-PARTICLE (POINT-LIKE BRANE) DEFECTS

J ELLIS, NEM, WESTMUCKETT

Charge conservation:D-foam/neutral particles (eg neutrinos, photons)dominant interactions

Eur.Phys.J. C72 (2012) 1956

Space time Foam situations – Average over both populations of defects & quantum fluctuations

Isotropic & (in)homogeneous foamfor a brane observer:

Lorentz Invarianceon Average

Violated in flcts

Can argue that due to forces exerted from bulk D-particles overclosure of theUniverse can be avoided even forsufficiently dense populations of D-particles

NEM, Mitsou, Vergou, Sarkar

matter momentum transfer

Stochastic Fluctuations of D-foam & CPTV

± B0constant > 0if σ2 ≈ constin an era

Correct Sign for Matter dominance over Antimatterdue to Energetics no Fine Tuning

One can thus generate a Lepton asymmetry and, then through B-L conserving processes in the Early Universe a Baryon asymmetry.

frame dragging

D-foam Induced CPTV for Neutrinos

One can thus generate a Lepton asymmetry and through B+L conserving processes in the Early Universe a Baryon asymmetry. The correct value (observed) for BAU is reproduced for

implying that in these scenarios, for σ2 < 1, one must have Ms/gs > 200 TeV

for D-foam at Td ~ 1015 GeV

PHENOMENOLOGY OF EARLY UNIVERSE NEEDS TO BE CHECKED FOR COMPATIBILITY…. IN PROGRESS

Effective (Anti)Neutrino CPTV D-foam Mass

@ Td ~ 1015 GeV

Bounds from WMAP Cosmology (z < 1000)

to generate BAU

Dust type D-particles

is a safe not strong bound on foam flcts σ2 today (within current exp errors)

No mixing

EXPERIMENTAL TESTS?

Experimental Tests? Stochastic D-foam Models: Non-trivial optical properties of vacuum, refractive index different arrival times of cosmic photons of different energies from localised regions in intense astrophysical sources (GRB, AGN…)

Space-Time Defects interaction with photons would affect CMB spectrum

Primordial Black hole searches through modifications of tensor mode polarization (Planck …)

Kalb-Ramond axion field searches

Direct CPT tests today (if sufficiently large density of defects today decoherence effects of neutral matter could be significant ``smoking-gun evidence’’ modifications of EPR correlations in entangled states of mesons (?) (A Di Domenico’s talk)

…Atomic precision experiments

…Cosmological (high energy, high distance) neutrino oscillations etc

But strength of background-induced CPTV effects may be significant only for Early Universe

Experimental Tests? Stochastic D-foam Models: Non-trivial optical properties of vacuum, refractive index different arrival times of cosmic photons of different energies from localised regions in intense astrophysical sources (GRB, AGN…) : higher-energy photons delayed

Experimental Tests?

Cosmic Photon Polarization angle may rotate (cosmological birefringence)

Stochastic D-foam Models: Non-trivial optical properties of vacuum, refractive index different arrival times of cosmic photons of different energies from localised regions in intense astrophysical sources (GRB, AGN…) : higher-energy photons delayed

Experimental Tests? Stochastic D-foam Models: Non-trivial optical properties of vacuum, refractive index different arrival times of cosmic photons of different energies from localised regions in intense astrophysical sources (GRB, AGN…) : higher-energy photons delayed

If QCD effects, sub-structure in neutral mesons ignored, and D-foam acts as if they were structureless particles, then for MQG ~ 1018 GeV the estimate for ω: | ω | ~ 10-4 |ζ|, for 1 > |ζ| > 10-2 (natural) Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2)

Φ KSKL

KSKS , KLKL

KSKS , KLKLIF CPT ILL-DEFINED (e.g. FV

D-particle Foam)

• If foam, concept of anti-particle may be perturbatively modified, Neutral mesons no longer indistinguishable particles, initial entangled state:

Bernabeu, NEM, Sarkar, Papavassiliou

ω-effect

Φ KSKL

KSKS , KLKL

KSKS , KLKLIF CPT ILL-DEFINED (e.g. FV

D-particle Foam)

• If foam, concept of anti-particle may be perturbatively modified, Neutral mesons no longer indistinguishable particles, initial entangled state:

Amplification due to mass degeneracy

NB: No CPTV mass shifts for Bosons, ω-effect measures directly fluctuations σ2 in foam-distorted geometry,

Experimental Tests? Stochastic D-foam Models: Non-trivial optical properties of vacuum, refractive index arrival times of different energies of photons of different energies from localised regions in intense astrophysical sources (GRB, AGN…): higher-energy photons delayed

CPTV neutrino/antineutrino mixing & oscillations

Assume Majorana neutrino in Weyl rep (Lepton number violation unavoidable)

M Sinha & B. MukhopadhyayarXiv: 0704.2593

Majorana mass termviolates L number

CPTV neutrino/antineutrino mixing & oscillations

Assume Majorana neutrino in Weyl rep (Lepton number violation unavoidable)

Lead to neutrino/antineutrinomixing & oscillations

neutrino/antineutrino mixing

oscillations

NB: neutrino CPTV mass shifts

neutrino/antineutrino mixing

oscillations

oscilaltion length

NB: neutrino CPTV mass shifts

Modifications in Neutrinoless 2Beta decay rate in 2 flavour mixing (due to CPTV modified effective mass)

Majorana neutrino

Amplitude

ignore neutrino/antineutrinomixing here:

CONCLUSIONS & OUTLOOK

CONCLUSIONS & OUTLOOK• Discussed several

scenarios for CPT Violation (CPTV) induced by curved background space-times and/or quantum gravity fluctuations

• Some of them require fine tuning to reproduce the correct Baryon Asymmetry in the Universe (BAU).

• One stringy Model of (brane-theory-inspired) defects in space-time can lead to background induce CPTV & reproduce the observed BAU without fine tuning

• The model also predicts non-trivial optical properties of the vacuum testable in principle

• Leads to consistent Cosmology avoiding overclosure of Universe & incorporating galactic growth

• Leads to consistent Cosmology avoiding overclosure of Universe & incorporating galactic growth.

Several Consistency checks pending when embed such scenarios in realistic cosmologies

• Leads to consistent Cosmology avoiding overclosure of Universe & incorporating galactic growth. NEM, Sakellariadou & Yusaf, arXiv:1211.1726

• Leads to consistent Cosmology avoiding overclosure of Universe & incorporating galactic growth

Several Experimental Tests (Astrophysical,Cosmological & at the LAB) can check the assumptions for the validity of CPT & bound its possible violations even at the Early Universe

IS THIS CPTV ROUTE WORTH FOLLOWING? ….

CPT Violation

Construct Microscopic Quantum Gravity models with strong CPT Violation in Early Universe, but maybe weak today… Fit with all available data…Estimate in this way matter-antimatter asymmetry in Universe.

SPARES

String Splitting & (``momentary’’) Capture by the defects

INTEMEDIATE STRINGCREATION/EXCHANGEPURELY NON-LOCAL EFFECT

Matter/D-foam Interactions

CHARGE CONSERVATIONMUST BE RESPECTED DURING STRING SPLITTING, INTERNEDIATECREATION AND STRETCHING:

ONLY ELECTRICALLYNEUTRAL EXCITATIONS(e.g. Photons, Neutrinos)INTERACT VIA CAPTURE DOMINANTLY WITH FOAM

ELLIS, NEM, SAKHAROV, NANOPOULOS

CHARGE CONSERVATIONMUST BE RESPECTED DURING STRING SPLITTING, INTERNEDIATECREATION AND STRETCHING:

ONLY ELECTRICALLYNEUTRAL EXCITATIONS(e.g. Photons, Neutrinos)INTERACT VIA CAPTURE DOMINANTLY WITH FOAMDEFECT RECOIL OCCURS

Time Delays due to Intermediate String Creation & Oscillations – Subluminal Vacuum Refractive Index

J ELLIS, NEM, NANOPOULOS

Explicit local breaking of SO(3,1) down to SO(2,1) rotation and boosts in transverse directions

Induced metric dependson momenta as well as coordinates(Finsler type) : e.g. u || X1

Local Lorentz Violation due to direction of Defect recoil velocities

``Frame Dragging by recoiling D-particle’’

Galilean River Galilean D-particles

Relativistic fishes Open string (SM excitations)

Analogy with Gullstrand-Painlevè (GP)metric for Schwarzschild BH metric

Hamilton-Lisle (2008)The river Model for BH

ui << 1

``Frame Dragging by recoiling D-particle’’

GP coordinates

Eur.Phys.J. C72 (2012) 1956

Violated in flcts

Can argue that due to forces exerted from bulk D-particles overclosure of theUniverse can be avoided even forsufficiently dense populations of D-particles

NEM, Mitsou, Vergou, Sarkar

leading to light cone fluctuations

Violated in flcts

c.f. Stochastic Foam, through coherent graviton states

Ford (95)

Modified Neutrino dispersion relations due to locally induced metric

Interpret (Dirac hole theory ) negative energies as corresponding to anti-particles Fermions, exclusion principle

Momentum-Energy conservation during ν scattering with D-particles

NEM, Sarkar, Tarantino Phys.Rev. D84 (2011) 044050

cpt violation in the early universe & leptogenesis/baryogenesis

universe violation of

expanding early universe

baryon asymmetry cpt

cpt violation cptv scenarios

matter t

c cp tiny cp violation

cpt violating effectsin

route matter

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