FLAVOUR VACUA BraneFoam Universes Neutrino Dark Energy N
FLAVOUR VACUA: Brane-Foam Universes & Neutrino Dark Energy N. E. Mavromatos King’s College London Physics Department CORFU 2009 2 nd Workshop, Corfu (Greece), 6 – 13 September 2009 23/05/2007 KAON '07 N. MAVROMATOS MRTN-CT 2006 -035863 Universe. Net
OUTLINE (I) FLAVOUR VACUA: Basic definitions & concepts (Blasone, Vitiello, Henning ) (II) COSMOLOGICAL IMPLICATIONS OF FLAVOUR VACUA: Non-perturbative contributions to the Cosmological Constant (Blasone, Vitiello, Capolupo, Capozzielo, Carloni, Barenboim, NM ) (III) SPACE-TIME FOAM IN STRING/BRANE THEORY (D 0 -PARTICLE FOAM), FLAVOUR VACUA & NEUTRINO INDUCED COSMOLOGICAL (CONSTANT? ) VACUUM ENERGY; comments on Lorentz breaking (NM, Sarben Sarkar, W. Tarantino) CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 2
MOTIVATION : Important unresolved issues The flavour Problem Flavour mixing, Neutrino Mass Differences ? Microscopic origin? v v How can we quantise a field theory with mixing ? CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 3
MOTIVATION : Important unresolved issues The flavour Problem Flavour mixing, Neutrino Mass Differences ? Microscopic origin? v v v Cosmological Dark Energy How can we quantise a field theory with mixing ? Sn. Ia, CMB Galaxies, Baryon Osc. CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS Dark Matter(23%) Dark Energy (73%) Ordinary matter (4%) 4
MOTIVATION : Important unresolved issues The flavour Problem Flavour mixing, Neutrino Mass Differences ? Microscopic origin? v v v Cosmological Dark Energy How can we quantise a field theory with mixing ? Is Fock space quantisation Applicable ? (Blasone, Vitiello) CORFU 2 nd Workshop 6 -13 Sept. 2009 Sn. Ia, CMB Galaxies, Baryon Osc. N. E. MAVROMATOS Dark Matter(23%) Dark Energy (73%) Ordinary matter (4%) 5
Are these Problems linked ? The flavour Problem Flavour mixing, Neutrino Mass Differences ? Microscopic origin? v v v Cosmological Dark Energy How can we quantise a field theory with mixing ? Is Fock space quantisation Applicable ? (Blasone, Vitiello) CORFU 2 nd Workshop 6 -13 Sept. 2009 Blasone, Capolupo, Capozzielo, Carloni, Vitiello Sn. Ia, CMB Dark Matter(23%) Galaxies, Dark Energy (73%) Baryon Osc. Ordinary matter (4%) N. E. MAVROMATOS 6
Further Motivation…Lorentz Violation v. A seemingly unrelated issue: v Experimental Evidence of Delayed Arrivals of Energetic Photons from Cosmic Sources (MAGIC, HESS, FERMI/LAT Collaborations) v Most recent Fermi Obsevation on GRB 090510, 30 Ge. V Photons delayed (compared to lower energy ones) up to 0. 5 sec, hence -- if modified dispersion relations of photons due to Quantum Gravity foam– v then CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 7
Further Motivation…Lorentz Violation v. A Mkn 501 (z=0. 03) seemingly unrelated issue: Te. V photons Delayed v Experimental Evidence of Delayed Arrivals ofby O(min) Energetic Photons from Cosmic Sources (MAGIC, HESS, FERMI/LAT Collaborations) v Most recent Fermi Obsevation on GRB 090510, 30 Ge. V Photons delayed (compared to lower energy ones) up to 0. 5 sec, hence -- if modified dispersion relations of photons due to Quantum Gravity foam– v then CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 8
Further Motivation…Lorentz Violation v. A Mkn 501 (z=0. 03) seemingly unrelated issue: Te. V photons GRB 080916 c (z=4. 3) Delayed by O(min) v Experimental Evidence of Delayed Arrivals of 13 Ge. V photons by O(10 sec) Cosmic Sources (MAGIC, Energetic. Delayed Photons from HESS, FERMI/LAT Collaborations) v Most recent Fermi Obsevation on GRB 090510, 30 Ge. V Photons delayed (compared to lower energy ones) up to 0. 5 sec, hence -- if modified dispersion relations of photons due to Quantum Gravity foam– v then CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 9
Further Motivation…Lorentz Violation v. A Mkn 501 (z=0. 03) seemingly unrelated issue: Te. V photons GRB 080916 c (z=4. 3) Delayed by O(min) v Experimental Evidence of Delayed Arrivals of 13 Ge. V photons by O(10 sec) Cosmic Sources (MAGIC, Energetic. Delayed Photons from HESS, FERMI/LAT Collaborations) v Most recent Fermi Obsevation on GRB 090510, 30 Ge. V Photons delayed (compared to lower energy ones) up to 0. 5 sec, Hence – if modified dispersion relations of photons due to Quantum Gravity foam– then CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 10
Quantum-Gravity Induced Modified Dispersion for Photons Modified dispersion due to QG induced space-time (metric) distortions (c=1 units): CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 11
Further Motivation…Lorentz Violation v. A seemingly unrelated issue: v Experimental Evidence of Delayed Arrivals of Energetic Photons from Cosmic Sources (MAGIC, HESS, FERMI/LAT Collaborations) v Most recent Fermi Obsevation on GRB 090510, 30 Ge. V Photons delayed (compared to lower energy ones) up to 0. 5 sec, hence -- if modified dispersion relations of photons due to Quantum Gravity foam– imply quantum gravity scales v For n=1: MQG > (5 - 100) MPlanck CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 12
Are these Problems linked ? The flavour Problem Flavour mixing, Neutrino Mass Differences ? Microscopic origin? v v Cosmological Dark Energy I WILL TRY TO ARGUE YES, IN A RIGOROUS WAY, AT LEAST WITHIN THE CONCEPT OF A PARTICULAR MODEL OF SPACE-TIME v(LORENTZ How can. VIOLATING) we quantise a field FOAM IN STRING THEORY…. ONLY NEUTRINO NON-CLUSTERING CONTRIBUTIONS TO theory with mixing ? VACUUM ENERGY FOR SPECIFICALLY STRINGY REASONS … (NM, Sarkar, Barenboim) USE GAMMA RAY ASTROPHYSICS TO DETERMINE Is HIGH-ENERGY Fock space quantisation DENSITY OF FOAM OF THE UNIVERSE & EVEN Applicable ? IN LATE EPOCHSSn. Ia , CMB Dark Matter(23%) FALSIFY THE MODEL… OR: Galaxies, (Blasone , Vitiello explain the recent FERMI results)on GRB 090510 using. Dark dilute. Energy foam (73%) densities Baryon Osc. Ordinary matter (4%) CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 13
Are these Problems linked ? The flavour Problem Flavour mixing, Neutrino Mass Differences ? Microscopic origin? v v Cosmological Dark Energy I WILL TRY TO ARGUE YES, IN A RIGOROUS WAY, AT LEAST WITHIN THE CONCEPT OF A PARTICULAR MODEL OF SPACE-TIME v(LORENTZ How can. VIOLATING) we quantise a field FOAM IN STRING THEORY…. ONLY NEUTRINO NON-CLUSTERING CONTRIBUTIONS TO theory with mixing ? VACUUM ENERGY FOR SPECIFICALLY STRINGY REASONS … (NM, Sarkar, Barenboim) USE GAMMA RAY ASTROPHYSICS TO DETERMINE Is HIGH-ENERGY Fock space quantisation DENSITY OF FOAM OF THE UNIVERSE & EVEN Applicable ? IN LATE EPOCHSSn. Ia , CMB Dark Matter(23%) FALSIFY THE MODEL… OR: Galaxies, (Blasone , Vitiello explain the recent FERMI results)on GRB 090510 using. Dark dilute. Energy foam (73%) densities Baryon Osc. Ordinary matter (4%) CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 14
Flavour Field Theory Issues Blasone, Vitiello Two flavour neutrino mixing (for simplicity & concreteness): νi =1, 2 = Mass eigenstates, m 1 =/= m 2 νe, μ = flavour eigenstates Fock space Canonical quantization: mass eigenstates (in a box of volume V, flat space-time) Canonical (anti) commutation etc. CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 15
Fock Space quantization-flavour states CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 16
Fock Space quantization-flavour states Flavour Vacuum, Finite Volume ! CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 17
Fock Space quantization-flavour states Flavour Vacuum, Finite Volume ! For t = 0, in frame CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS No sum εij = Antisym symbol 18
Fock Space quantization-Flavour States BUT: In the Infinite Volume (Thermodynamic) Limit V → ∞ Flavour and Mass eigenstate Vacua orthogonal… Unitarily inequivalent vacua … Which is the physical vacuum? Blasone , Henning & Vitiello argued that Flavour is the physical vacuum on account of Conservation of probability, which is not preserved by evolving mass eigenstate Vacuum… CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 19
Fock space quantization-flavour states σ = flavour index (e, μ, …) Non-trivial Flavour Vacuum Condensates (Bogolubov coeff. ) : CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 20
Fock-space quantization-flavour states : …: = Normal ordering w. r. t. energy eigenstates : : …: : = Normal ordering w. e. t. flavour states Energy gap for flavour states cannot turn into energy eigenstates: CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 21
Fock-space quantization-flavour states : …: = Normal ordering w. r. t. energy eigenstates : : …: : = Normal ordering w. e. t. flavour states Energy gap for flavour states cannot turn into energy eigenstates: Vacuum Energy Contribution (Cosmological Constant type): V. E. V. w. r. t. flavour vacuum: Neutrino Stress tensor Minkowski Universe Non-Trivial ! Novel Non-perturbative Contributions to vacuum energy… CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 22
Cosmological Implications K = ultraviolet cut-off Equation of State: pressure CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 23
Cosmological Implications K = ultraviolet cut-off Equation of state depends on choice of UV cut-off K Wmix = ρ/p → 1/3 (radiation-like) K >> m 1, m 2 Equation of State: pressure Wmix → 0 (dust-like) K ≤ √m 1 m 2 CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 24
Cosmological Implications K = ultraviolet cut-off Equation of state depends on choice of UV cut-off K Wmix = ρ/p → 1/3 (radiation-like) K >> m 1, m 2 Equation of State: pressure Wmix → 0 (dust-like) K ≤ √m 1 m 2 Early epochs: neutrino flavour state fluid Behaves like dark matter/radiation… CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 25
Cosmological Implications K = ultraviolet cut-off Equation of state depends on choice of UV cut-off K Capolupo, Capozzielo, Vitiello mix (08. 09. 085 [ hep-th]) W = ρ/p → 1/3 (radiation-like) K >> mflavour 1 , m 2 Present epoch: neutrino state fluid Equation of State: pressure mix → -1 Behaves like dark Energy Wmix → 0 W (dust-like) K ≤ √m 1 m 2 Conjectured…Not proven Must check in specific detailed models… We shall do so in the context of brane-models of space-time Foam, where flavour Fock vacua Will be constructed explicitly (NM, Sarben Sarkar, Tarantino 2008, 2009) CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 26
D-particle Space-Time Foam & Flavour Vacua NM, Sarkar (2008) (i) consider a microscopic model of flavour vacua, with Dynamical determination of cutoff (if possible) (ii) Incorporate the Lorentz symmetry breaking of the Flavour condensate by microscopic arguments in vacuo (iii) Select neutrinos among other mixing modes Dynamically (iv) Connect with High Energy Gamma-Ray Phenomenology to constrain density of foam CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 27
D-particle Space-Time Foam & Flavour Vacua NM, Sarkar (2008) (i) consider a microscopic model of flavour vacua, with Dynamical determination of cutoff (if possible) (ii) Incorporate the Lorentz symmetry breaking of the Atcondensate present only effectivearguments FIELD TEORY Flavour by. TOY microscopic in vacuo models of flavour states constructed in this framework. (iii) Select neutrinos among other mixing modes Dynamically Long way ahead before complete understanding in string theory… (iv) Connect with High Energy Gamma-Ray Phenomenology to constrain density of foam CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 28
A Model for flavour vacua v A THEORETICAL MODEL OF SPACE-TIME FOAM INSPIRED FROM NON-CRITICAL STRING THEORY D-PARTICLE (D 0 -BRANE) FOAM (Ellis, NM, Westmuckett, Nanopoulos, Sarkar, Szabo) CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 29
String Theory Basics MODERN VERSION OF STRING/BRANE THEORY Polchinski, Witten, …. Fundamental (F-) Strings, ending on Solitonic string states/space-time defects/domain walls called D(irichlet)-branes D-branes dimensionalities: D(-1) (D-instantons), D 0 (point-like, D-particles) D 1 (string-like, D-strings -> Cosmic Superstrings) Dp (p > 2)-brane domain walls (D 3 -brane Universes, Universes etc. ) CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 30
STRING/D-BRANE BASICS String theory type p-brane types allowed Heterotic Strings admit no p-branes CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 31
STRING/D-BRANE BASICS String theory type p-brane types allowed Heterotic Strings admit no p-branes CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 32
STRING/D-BRANE BASICS String theory type p-brane types allowed Compactify to 3 + 1 Large Dim Heterotic Strings admit no p-branes CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 33
STRING/D-BRANE BASICS String theory type p-brane types allowed Compactify to 3 + 1 Large Dim Wrap up along Three cycles Heterotic Strings admit no p-branes CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS (``D-particles’’) 34
A Stringy (type IA) Model of Space -Time Foam: Properties Orientifold planes, stacks of D 8 branes Ellis, NM, Westmuckett Open strings on D 3 -brane world represent electrically neutral matter or radiation, interacting via splitting/capture with D-particles (electric charge conservation). D-particle foam medium transparent to (charged) Electrons no modified dispersion for them Photons or electrically neutral probes feel the effects of D-particle foam Modified Dispersion for them…. NON-UNIVERSAL ACTION OF D-PARTICLE FOAM ON MATTER & RADIATION CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 35
D-particle Recoil String World-sheet torn apart non-conformal Process, Liouville string CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 36
A Stringy (type IA) Model of Space -Time Foam: Properties Orientifold planes, stacks of D 8 branes Ellis, NM, Westmuckett Open strings on D 3 -brane world represent electrically neutral matter or radiation, interacting via splitting/capture with D-particles (electric charge conservation). D-particle foam medium transparent to (charged) Electrons no modified dispersion for them Photons or electrically neutral probes feel the effects of D-particle foam Modified Dispersion for them…. NON-UNIVERSAL ACTION OF D-PARTICLE FOAM ON MATTER & RADIATION CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 37
Stringy Uncertainties & the Capture Process Ellis, NM, Nanopoulos ar. Xiv: 0804. 3566 During Capture: intermediate String stretching between D-particle and D 3 -brane is Created. It acquires N internal Oscillator excitations & Grows in size & oscillates from Zero to a maximum length by absorbing incident photon Energy p 0 : Minimise right-hand-size w. r. t. L. End of intermediate string on D 3 -brane Moves with speed of light in vacuo c=1 (Seiberg, Susskind, Toumbas) Hence TIME DELAY (causality) during Capture: DELAY IS INDEPENDENT OF PHOTON POLARIZATION, HENCE NO BIREFRINGENCE…. BIREFRINGENCE CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 38
A Stringy (type IA) Model of Space -Time Foam : Properties Orientifold planes, stacks of D 8 branes Ellis, NM, Westmuckett Open strings on D 3 -brane world represent electrically neutral matter or radiation, interacting via splitting/capture with D-particles (electric charge conservation). D-particle foam medium transparent to (charged) Electrons no modified dispersion for them Photons or electrically neutral probes feel the effects of D-particle foam Modified Dispersion for them…. NON-UNIVERSAL ACTION OF D-PARTICLE FOAM ON MATTER & RADIATION CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 39
A Stringy (type IA) Model of Space -Time Foam: Properties Orientifold planes, stacks of D 8 branes Ellis, NM, Westmuckett Open strings on D 3 -brane world represent electrically neutral matter or radiation, interacting via splitting/capture with D-particles (electric charge conservation). D-particle foam medium transparent to (charged) Electrons no modified dispersion for them Photons or electrically neutral probes feel the effects of D-particle foam Modified Dispersion for them…. NON-UNIVERSAL ACTION OF D-PARTICLE FOAM ON MATTER & RADIATION CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 40
A Stringy (type IA) Model of Space -Time Foam: Properties Orientifold planes, stacks of D 8 branes Ellis, NM, Westmuckett Open strings on D 3 -brane world represent electrically neutral matter or radiation, interacting via splitting/capture with D-particles (electric charge conservation). D-particle foam medium transparent to (charged) Electrons no modified dispersion for them Photons or electrically neutral probes feel the effects of D-particle foam Modified Dispersion for them…. NON-UNIVERSAL ACTION OF D-PARTICLE FOAM ON MATTER & RADIATION CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 41
D-particle Recoil & Induced Metric D-particles defects are point-like with masses Ms/gs Ms = sting mass scale (free, in general Ms ≠ MPlnack) gs = string scale (assumed weak, gs < 1 ) Recoil implies distortion of surrounding space-time, analogy with open strings in Background electric fields : Recoil velocity ui plays role of Electric field Ei Open string metric (isotropic foam) : ux = gs Δkx / Ms = D-particle Recoil velocity, Δkx = momentum transfer For a foam situation we have collection of D-particles. Toy case : Isotropic Gaussian foam << … >> = statistical D-particle collection average FRW TYPE UNIVERSE CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 42
D-particle Recoil & Induced Metric D-particles defects are point-like with masses Ms/gs Ms = sting mass scale (free, in general Ms ≠ MPlnack) gs = string scale (assumed weak, gs < 1 ) Recoil implies distortion of surrounding space-time, analogy with open strings in Background electric fields : Recoil velocity ui plays role of Electric field Ei Open string metric (isotropic foam) : ux = gs Δkx / Ms = D-particle Recoil velocity, Δkx = momentum transfer For a foam situation we have collection of D-particles. Toy case : Isotropic Gaussian foam << … >> = statistical D-particle collection average FRW TYPE UNIVERSE CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 43
D-particle Recoil & Induced Metric D-particles defects are point-like with masses Ms/gs Ms = sting mass scale (free, in general Ms ≠ MPlnack) Recoil-induced Commutativity of D-foam gs = string scale (assumed weak, g. Non s <1) Recoil implies distortion of surrounding space-time, analogy with open strings in Background electric fields : Recoil velocity ui plays role of Electric field Ei Open string metric (isotropic foam) : ux = gs Δkx / Ms = D-particle Recoil velocity, Δkx = momentum transfer For a foam situation we have collection of D-particles. Toy case : Isotropic Gaussian foam << … >> = statistical D-particle collection average FRW TYPE UNIVERSE CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 44
D-particle Recoil & Induced Metric D-particles defects are point-like with masses Ms/gs Ms = sting mass scale (free, in general Ms ≠ MPlnack) gs = string scale (assumed weak, gs < 1 ) Recoil implies distortion of surrounding space-time, analogy with open strings in Background electric fields : Recoil velocity ui plays role of Electric field Ei Open string metric (isotropic foam) : ux = gs Δkx / Ms = D-particle Recoil velocity, Δkx = momentum transfer For a foam situation we have collection of D-particles. Toy case : Isotropic Gaussian foam << … >> = statistical D-particle collection average FRW TYPE UNIVERSE CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 45
Cosmology from D-foam Recoil Fluctuations σ could depend on time σ = σ(t) e. g. non-uniform bulk density of D-particles If σ(t) decreases as (cosmic) time increases, then we have EXPANDING FRW-type 46 Cosmology on the 6 -13 brane interactions of strings with foam… CORFU 2 nd Workshop Sept. world, 2009 as a result N. E. of MAVROMATOS
Cosmology from D-foam Recoil Fluctuations σ could depend on time σ = σ(t) e. g. non-uniform bulk density of D-particles NM & Sarkar, Tarantino (2008/09) If σ(t) decreases as (cosmic) time increases, then we have EXPANDING FRW-type 47 Cosmology on the 6 -13 brane interactions of strings with foam… CORFU 2 nd Workshop Sept. world, 2009 as a result N. E. of MAVROMATOS
D-particles & Flavour Non-Conservation NM & Sarkar 2008 An initially flavoured state ``a’’ is captured by the D-particle and a string is created, stretching between D-particle and D 3 -brane. The re-emitted state, after D-particle recoil may be of different flavour ``b’’ ONLY electrically neutral open string states (e. g. Neutrinos) can be captured, due to electric charge conservation. CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 48
Toy Model for Bosons – effective field theory Full string theory problem complicated. Restrict to effective field theory (low-energy limit) of Bosons. Toy Model , sufficient to qualitatively explain effects of flavour states in this setting. SEVERAL REASONS FOR CONSIDERING FLAVOUR STATES (i) Fock space quantization natural in strings. (ii) Lorentz is violated locally due to D-particle recoil (velocity vectors). (iii) Flavour is not conserved in the capture process. D-particle foam induces FRW-cosmological space times, with non-trivial Particle Creation (actually string creation in the full string theory problem). Consider effects of Flavour States to vacuum energy self consistently in those curved (anisotropic) space-times. Extension to isotropic situation straightforward. CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 49
Toy Model for Bosons – effective field theory Full string theory problem complicated. Restrict to effective field theory (low-energy limit) of Bosons. Toy Model , sufficient to qualitatively explain effects of flavour states in this setting. SEVERAL REASONS FOR CONSIDERING FLAVOUR STATES (i) Fock space quantization natural in strings. (ii) Lorentz is violated locally due to D-particle recoil (velocity vectors). (iii) Flavour is not conserved in the capture process. D-particle foam induces FRW-cosmological space times, with non-trivial Particle Creation (actually string creation in the full string theory problem). Consider effects of Flavour States to vacuum energy self consistently in those curved (anisotropic) space-times. Extension to isotropic situation straightforward. CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 50
D-foam induced Neutrino Mass Flips CONSISTENT WITH STRINGY UNCERTAINTIES Energy conservation on average: D-particle mass. From this one has (ΔΕ neutrino energy difference): Potential between D 3 -brane world and D-particle, due to recoil motion of D-particle, perpendicular to D 3 -brane: Potential flct. due to Mass flip for neutrinos Time scales compatible with uncertainties of capture process CORFU 2 nd Workshop 6 -13 Sept. 2009 Provided q = 0, for length of stretched String between D-particle and D 3 -brane of order q = 3 for much smaller Minimum length N. E. MAVROMATOS 51
Normal Ordering Prescription In D-particle foam situation: Choose such that v. e. v. of stress tensor vanishes in the absence of D-particles (ordinary Minkowski vacuum), i. e. subtract the D-particle-Recoil-Velocity-fluctuations independent terms in the above expressions CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 52
Normal Ordering Prescription In D-particle foam situation: Choose such that v. e. v. of stress tensor vanishes in the absence of D-particles (ordinary Minkowski vacuum), i. e. subtract the D-particle-Recoil-Velocity-fluctuations independent terms in the above expressions Subtraction Procedure Independent of choice of C(η) scaling factor CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 53
Boson (Late epochs) Equation of State Result for Late times equation of state p = wρ for Bosons, Cosmological Constant Type Positive energy, negative pressure CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 54
Fermion Equation of State (Late eras) Positive energy, negative pressure CORFU 2 nd Workshop 6 -13 Sept. 2009 Fermions alone cannot In this scenario lead to Accelerating Universes today. One needs the bosons, (e. g. sneutrinos) which arise naturally in Superstring theories N. E. MAVROMATOS 55
Fermion Equation of State (Late eras) Positive energy, negative pressure CORFU 2 nd Workshop 6 -13 Sept. 2009 Fermions alone cannot In this scenario lead to Accelerating Universes today. One needs the bosons, (e. g. sneutrinos) which arise naturally in Superstring theories N. E. MAVROMATOS 56
Estimates of Flavoured Vacuum Energy Dynamical determination of momentum cut-off for ``flavoured’’Fock space modes In D-particle foam models low-momentum modes have a much greater chance of being captured by the D-particle defects Particle production – particle number at momentum scale k in ``flavoured’’ vacuum Significant fall off for scales higher than (ratio of two different orders for Ξ above): Characteristic neutrino Mass scale CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 57
Estimates of Flavoured Vacuum Energy Dynamical determination of momentum cut-off for ``flavoured’’Fock space modes In D-particle foam models low-momentum modes have a much greater chance of being captured by the D-particle defects Particle production – particle number at momentum scale k in ``flavoured’’ vacuum Significant fall off for scales higher than (ratio of two different orders for Ξ above): Characteristic neutrino Mass scale CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 58
Estimates of Flavoured Vacuum Energy Dynamical determination of momentum cut-off for ``flavoured’’Fock space modes In D-particle foam models low-momentum modes have a much greater chance of being captured by the D-particle defects Particle production – particle number at momentum scale k in ``flavoured’’ vacuum Significant fall off for scales higher than (ratio of two different orders for Ξ above): CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS Fix phenomenologically <<…>> proportional to Density of D-particles: Constrained from Lorentz Violation tests from High-Energy Gamma Ray Characteristic neutrino Astrophysics Mass scale 59
Stringy Uncertainties & the Capture Process Ellis, NM, Nanopoulos ar. Xiv: 0804. 3566 During Capture: intermediate String stretching between D-particle and D 3 -brane is Created. It acquires N internal Oscillator excitations & Grows in size & oscillates from Zero to a maximum length by absorbing incident photon Energy p 0 : Minimise right-hand-size w. r. t. L. End of intermediate string on D 3 -brane Moves with speed of light in vacuo c=1 (Seiberg, Susskind, Toumbas) Hence TIME DELAY (causality) during Capture: DELAY IS INDEPENDENT OF PHOTON POLARIZATION, HENCE NO BIREFRINGENCE…. BIREFRINGENCE CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 60
Total Time (Causal) Delays are Additive v v v D-foam: transparent to (or suppressed effects for) electrons D-foam captures photons & re-emits them Time Delay (Causal) in each Capture: v v Independent of photon polarization (no Birefringence) Total Delay from emission of photons till observation over a distance D (assume n* defects per string length): Effectively modified Dispersion relation for photons due to induced metric distortion G 0 i ~ p 0 CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 61
Stringy Uncertainties & the Capture Process Ellis, NM, Nanopoulos ar. Xiv: 0804. 3566 During Capture: intermediate String stretching between D-particle and D 3 -brane is Created. It acquires N internal Oscillator excitations & COMPATIBLE WITH STRING UNCERTAINTY Grows in size & oscillates from PRINCIPLES: Zero to a maximum length by 2 + … photon absorbing Δ t Δ x ≥ α’ , Δ p Δ x ≥ 1 + α’ (Δp 0 )incident Energy p : (α’ = Regge slope = Square of minimum string length scale) Minimise right-hand-size w. r. t. L. End of intermediate string on D 3 -brane Moves with speed of light in vacuo c=1 (Seiberg, Susskind, Toumbas) Hence TIME DELAY (causality) during Capture: DELAY IS INDEPENDENT OF PHOTON POLARIZATION, HENCE NO BIREFRINGENCE…. BIREFRINGENCE CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 62
Universe Expansion - Role of Cosmology v v v D-foam: transparent to electrons Ellis, NM, Nanopoulos ar. Xiv: 0804. 3566 D-foam captures photons & re-emits them Time Delay (Causal) in each Capture: EFFECTIVE QUANTUM v Independent of photon polarization (no Birefringence) v Total. GRAVITY Delay from emission of. SCALE photons till observation over a distance D (assume n defects per string length): MQG = MS / n(z) * Effectively modified Dispersion relation for photons due to induced metric distortion G 0 i ~ p 0 REPRODUCE 4± 1 MINUTE DELAY OF MAGIC from Mk 501 (redshift z=0. 034) For n* =O(1) & Ms ~ 1018 Ge. V, consistently with Crab Nebula & other Astrophysical constraints on modified dispersion relations…… and 30 Gev Photon Delay of < 0. 5 sec GRB 090510 (z=0. 9) for n=O(0. 01)… 63 CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS
Universe Expansion - Role of Cosmology v v v Ellis, NM, Nanopoulos ar. Xiv: 0804. 3566 D-foam: transparent to electrons D-foam captures photons & re-emits them Time Delay (Causal) in each Capture: EFFECTIVE QUANTUM v Independent of photon polarization (no Birefringence) v Total. GRAVITY Delay from emission of. SCALE photons till observation over a distance D (assume n defects per string length): MQG = MS / n(z) * Effectively modified Dispersion relation for photons due to induced metric distortion G 0 i ~ p 0 REPRODUCE 4± 1 MINUTE DELAY OF MAGIC from Mk 501 (redshift z=0. 034) For n* =O(1) & Ms ~ 1018 Ge. V, consistently with Crab Nebula & other Astrophysical constraints on modified dispersion relations…… and 30 Gev Photon Delay of < 0. 5 sec GRB 090510 (z=0. 9) for n=O(0. 01)… 64 CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS
Universe Expansion - Role of Cosmology v v v D-foam: transparent to electrons D-foam captures photons & re-emits them Time Delay (Causal) in each Capture: EFFECTIVE QUANTUM v Independent of photon polarization (no Birefringence) v Total. GRAVITY Delay from emission of. SCALE photons till observation over a distance D (assume n defects per string length): MQG = MS / n(z) * Effectively modified Dispersion relation for photons due to induced metric distortion G 0 i ~ p 0 REPRODUCE 4± 1 MINUTE DELAY OF MAGIC from Mk 501 (redshift z=0. 034) For n* =O(1) & Ms ~ 1018 Ge. V, consistently with Crab Nebula & other Astrophysical constraints on modified dispersion relations…… and 30 Gev Photon Delay of < 0. 5 sec GRB 090510 (z=0. 9) for n=O(0. 01)… 65 CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS
Two kinds of co-existing vacua in D-particle foam Flavoured electrically neutral States (e. g. Neutrinos ) with momenta up to a given scale, that can be captured by the D-particles Rest of the states, not captured by D-particles No Novel Dark Energy Contributions Non-trivial, Non-perturbative Contributions to the Dark Energy of Accelersting Universe type at late epochs (slow expansion) if consider BOTH Fermions and Bosons in SUSY theories … CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 66
Comments on Supersymmetry Breaking In the string effective theory, target space supersymmetry is initially ensured at String scale. Repeat calculations for fermionic partners of flavoured states. Fermion-Boson contributions of flavour vacuum energy do not cancel out… Kind of spontaneous breaking of supersymmetry by flavour condensate, but … Order of breaking very suppressed, of the order of cosmological vacuum energy. Phenomenologically realistic mass splittings achieved via SUPERSYMMETRY OBSTRUCTION via compactification to ``magnetised’’ manifolds. Fermions coupled differently than bosons to an external magnetic field (Zeeman). Induced SUSY obstructing (at excitation level) mass differences, proportional to Magnetic field intensity. String theory have lots of flux fields, playing the role of ``magnetic ‘’ fields in compactified manifolds of extra dimensions. Bachas, Gravanis & N. E. M. Mass diffferences among flavour states insensitive to ``magnetic’’ field SUSY Obstruction does not affect value of Flavour-vacuum contributions to Dark Energy (proportional to flavour-states mass differences…) CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 67
Conclusions v v Flavoured Fock states of (low-momentum) particles have been considered within a semi-microscopic toy model of Dparticle foam in string/brane theory, involving local breaking of Lorentz symmetry (LV), through fluctuations of recoil velocity of D-particles, during capture process. Dynamical arguments for estimating the upper momentum cutoff of flavoured states have been given, based on particle production. Contributions to the vacuum energy of the Universe have been estimated within that model for late eras (slow expansion), for brevity. They are proportional to the LV fluctuations. The latter are constrained by a plethora of high energy astrophysical observations, since D-particles lead to modified dispersion relations for photons (suppressed for other ptcles). CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 68
Outlook v In future: understand the construction within full-fledged string theory, considering string and not particle production and determining dynamically the momentum cut-off. v Examine fermion & boson states contributions and discuss overall vacuum energy contributions of flavour Fock states in connection with Supersymmetry Breaking in (interacting) supersymmetric theories (effective field or string theories). v Long way ahead before drawing definite conclusions in string/brane models, but very encouraging results so far, regarding these novel non-perturbative contributions to Dark Energy of the Cosmos… But so far results appear challenging and intriguing. . . CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 69
CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 70
Type IIB String Model of D-particle Foam T. Li, NM, Nanopoulos, D. Xie String theory type p-brane types allowed Compactify to 3 + 1 Large Dim Wrap up along Three cycles (``D-particles’’) CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 71
Type IIB String Model of D-particle Foam T. Li, NM, Nanopoulos, D. Xie Consider Four-point Veneziano Amplitude for scattering of two open string states to two open string states in the D-particle/D 3 -branes backgrounds Antoniadis, Benakli, Laugier CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 72
Type IIB String Model of D-particle Foam T. Li, NM, Nanopoulos, D. Xie Couplings of ND strings. Stretched between D 3 and D 7 branes (Capture process) D-Foam: Uniform Distribution of D-particles in space with VA 3 = their average 3 D-volume, R’ = radius of forth space dim transverse to D 3 branes. Avoid tachyon condensation: D 3 branes have widths 1. 55 CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 73
Seiberg, Susskind Toumbas Time delays arise by considering Backward scattering u=0. CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 74
OTHER PARTICLES Backward scattering u=0 implies JUST POLE TERMS… NO TIME DELAY AT LEADING ORDER in η CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 75
At order η, there are time delays… CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 76
At order η, there are time delays… CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 77
At order η, there are time delays… CORFU 2 nd Workshop 6 -13 Sept. 2009 N. E. MAVROMATOS 78
- Slides: 78