Transcript CPT & DECOHERENCE IN QUANTUM GRAVITY

FLAVOUR VACUA:
Brane-Foam Universes &
Neutrino Dark Energy
N. E. Mavromatos
King’s College London
Physics Department
CORFU 2009 2nd Workshop,
Corfu (Greece), 6 – 13 September 2009
MRTN-CT2006-035863
UniverseNet
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
(D0-PARTICLE FOAM), FLAVOUR VACUA &
NEUTRINO INDUCED COSMOLOGICAL (CONSTANT?)
VACUUM ENERGY; comments on Lorentz breaking
(NM, Sarben Sarkar, W. Tarantino)
CORFU 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
2
MOTIVATION : Important unresolved issues

The flavour Problem
Flavour mixing,
Neutrino Mass Differences ?
Microscopic origin?

How can we quantise a field
theory with mixing ?
CORFU 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
3
MOTIVATION : Important unresolved issues

The flavour Problem
Flavour mixing,
Neutrino Mass Differences ?
Microscopic origin?


Cosmological Dark Energy
How can we quantise a field
theory with mixing ?
SnIa, CMB
Galaxies,
Baryon Osc.
CORFU 2nd 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?


Cosmological Dark Energy
How can we quantise a field
theory with mixing ?
Is Fock space quantisation
Applicable ?
(Blasone, Vitiello)
CORFU 2nd Workshop 6-13 Sept. 2009
SnIa, 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?


Cosmological Dark Energy
How can we quantise a field
theory with mixing ?
Is Fock space quantisation
Applicable ?
(Blasone, Vitiello)
CORFU 2nd Workshop 6-13 Sept. 2009
Blasone, Capolupo, Capozzielo, Carloni,
Vitiello
SnIa, CMB
Dark Matter(23%)
Galaxies,
Dark Energy (73%)
Baryon Osc.
Ordinary matter (4%)
N. E. MAVROMATOS
6
Further Motivation…Lorentz Violation

A seemingly unrelated issue:
 Experimental Evidence of Delayed Arrivals of
Energetic Photons from Cosmic Sources (MAGIC,
HESS, FERMI/LAT Collaborations)
 Most recent Fermi Obsevation on GRB 090510, 30
GeV 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 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
7
Further Motivation…Lorentz Violation
Mkn 501 (z=0.03)
A seemingly unrelated issue:
TeV photons
Delayed
 Experimental Evidence of Delayed Arrivals
ofby O(min)
Energetic Photons from Cosmic Sources (MAGIC,
HESS, FERMI/LAT Collaborations)
 Most recent Fermi Obsevation on GRB 090510, 30
GeV 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 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
8
Further Motivation…Lorentz Violation
Mkn 501 (z=0.03)
A seemingly unrelated issue:
TeV photons
GRB 080916c (z=4.3)
Delayed
by O(min)
 Experimental
Evidence
of
Delayed
Arrivals
of
13 GeV photons
by O(10
sec) Cosmic Sources (MAGIC,
EnergeticDelayed
Photons
from
HESS, FERMI/LAT Collaborations)
 Most recent Fermi Obsevation on GRB 090510, 30
GeV 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 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
9
Further Motivation…Lorentz Violation
Mkn 501 (z=0.03)
A seemingly unrelated issue:
TeV photons
GRB 080916c (z=4.3)
Delayed
by O(min)
 Experimental
Evidence
of
Delayed
Arrivals
of
13 GeV photons
by O(10
sec) Cosmic Sources (MAGIC,
EnergeticDelayed
Photons
from
HESS, FERMI/LAT Collaborations)
 Most recent Fermi Obsevation on GRB 090510, 30
GeV 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 2nd 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 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
11
Further Motivation…Lorentz Violation

A seemingly unrelated issue:
 Experimental Evidence of Delayed Arrivals of
Energetic Photons from Cosmic Sources (MAGIC,
HESS, FERMI/LAT Collaborations)
 Most recent Fermi Obsevation on GRB 090510, 30
GeV 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
 For n=1:
MQG > (5- 100) MPlanck
CORFU 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
12
Are these Problems linked ?

The flavour Problem
Flavour mixing,
Neutrino Mass Differences ?
Microscopic origin?

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
(LORENTZ
How canVIOLATING)
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 EPOCHSSnIa,
CMB
Dark Matter(23%)
FALSIFY THE MODEL… OR:
Galaxies,
(Blasone,
Vitiello)
explain the recent
FERMI
results on GRB090510
using Dark
diluteEnergy
foam (73%)
densities
Baryon Osc.
Ordinary matter (4%)
CORFU 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
13
Are these Problems linked ?

The flavour Problem
Flavour mixing,
Neutrino Mass Differences ?
Microscopic origin?

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
(LORENTZ
How canVIOLATING)
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 EPOCHSSnIa,
CMB
Dark Matter(23%)
FALSIFY THE MODEL… OR:
Galaxies,
(Blasone,
Vitiello)
explain the recent
FERMI
results on GRB090510
using Dark
diluteEnergy
foam (73%)
densities
Baryon Osc.
Ordinary matter (4%)
CORFU 2nd 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,
m1 =/= m2
νe,μ = flavour eigenstates
Fock space Canonical quantization: mass eigenstates (in a box of volume V, flat space-time)
Canonical
(anti) commutation etc.
CORFU 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
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Fock Space quantization-flavour states
CORFU 2nd Workshop 6-13 Sept. 2009
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Fock Space quantization-flavour states
Flavour Vacuum,
Finite Volume !
CORFU 2nd Workshop 6-13 Sept. 2009
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Fock Space quantization-flavour states
Flavour Vacuum,
Finite Volume !
For t = 0, in frame
CORFU 2nd 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 2nd 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 2nd 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 2nd 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 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
22
Cosmological Implications
K = ultraviolet cut-off
Equation of State: pressure
CORFU 2nd 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 >> m1, m2
Equation of State: pressure
Wmix → 0 (dust-like)
K ≤ √m1m2
CORFU 2nd 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 >> m1, m2
Equation of State: pressure
Wmix → 0 (dust-like)
K ≤ √m1m2
Early epochs: neutrino flavour state fluid
Behaves like dark matter/radiation…
CORFU 2nd 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 (08.09.085
[ hep-th])
mix
W = ρ/p → 1/3 (radiation-like)
K >> mflavour
1, m2
Present epoch:
neutrino
state fluid
Equation of State: pressure
mix → -1
Behaves like dark Energy
Wmix → 0 W
(dust-like)
K ≤ √m1m2
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 2nd 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 2nd 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
byTOY
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 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
28
A Model for flavour vacua

A THEORETICAL MODEL OF SPACE-TIME
FOAM INSPIRED FROM NON-CRITICAL
STRING THEORY
D-PARTICLE (D0-BRANE)
FOAM
(Ellis, NM, Westmuckett, Nanopoulos, Sarkar, Szabo)
CORFU 2nd 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),
D0 (point-like, D-particles)
D1 (string-like, D-strings ->
Cosmic Superstrings)
Dp (p > 2)-brane domain walls
(D3-brane Universes, etc.)
CORFU 2nd Workshop 6-13 Sept. 2009
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STRING/D-BRANE BASICS
String theory
type
p-brane types allowed
Heterotic Strings admit no p-branes
CORFU 2nd Workshop 6-13 Sept. 2009
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31
STRING/D-BRANE BASICS
String theory
type
p-brane types allowed
Heterotic Strings admit no p-branes
CORFU 2nd 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 2nd 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
(``D-particles’’)
Heterotic Strings admit no p-branes
CORFU 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
34
A Stringy (type IA) Model of Space -Time Foam: Properties
Orientifold planes, stacks of D8 branes
Ellis, NM, Westmuckett
Open strings on D3-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 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
35
D-particle Recoil
String World-sheet torn apart
non-conformal Process, Liouville string
VRe c   ui X  ( X ) X ,
0
0
CORFU 2nd Workshop 6-13 Sept. 2009
n
i
iX 0
d e
 ( X )  i Lim 
 0
  i
0
N. E. MAVROMATOS
36
A Stringy (type IA) Model of Space -Time Foam: Properties
Orientifold planes, stacks of D8 branes
Ellis, NM, Westmuckett
Open strings on D3-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 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
37
Stringy Uncertainties & the Capture Process
Ellis, NM, Nanopoulos arXiv:0804.3566
During Capture: intermediate
String stretching between
D-particle and D3-brane is
Created. It acquires N internal
Oscillator excitations &
Grows in size & oscillates from
Zero to a maximum length by
absorbing incident photon
Energy p0 :
Minimise right-hand-size w.r.t. L.
End of intermediate string on D3-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….
CORFU 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
38
A Stringy (type IA) Model of Space -Time Foam : Properties
Orientifold planes, stacks of D8 branes
Ellis, NM, Westmuckett
Open strings on D3-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 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
39
A Stringy (type IA) Model of Space -Time Foam: Properties
Orientifold planes, stacks of D8 branes
Ellis, NM, Westmuckett
Open strings on D3-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 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
40
A Stringy (type IA) Model of Space -Time Foam: Properties
Orientifold planes, stacks of D8 branes
Ellis, NM, Westmuckett
Open strings on D3-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 2nd 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 2nd 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 2nd 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, gNon
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 2nd 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 2nd 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 the6-13
brane
interactions of strings with foam…
CORFU 2nd 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 the6-13
brane
interactions of strings with foam…
CORFU 2nd 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 D3-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 2nd Workshop 6-13 Sept. 2009
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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 2nd 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 2nd 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 D3-brane world and D-particle,
due to recoil motion of D-particle, perpendicular to D3-brane:
Potential flct. due to
Mass flip for neutrinos
Time scales compatible with uncertainties
of capture process
CORFU 2nd Workshop 6-13 Sept. 2009
q = 0, for length of stretched
String between D-particle and
D3-brane of order
q = 3 for much smaller
Minimum length
N. E. MAVROMATOS
Provided
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
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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
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Boson (Late epochs) Equation of State
Result for Late times
equation of state p = wρ for Bosons,
Cosmological Constant Type
Positive energy, negative pressure
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Fermion Equation of State (Late eras)
Positive energy, negative pressure
CORFU 2nd 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
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Fermion Equation of State (Late eras)
Positive energy, negative pressure
CORFU 2nd 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
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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 2nd Workshop 6-13 Sept. 2009
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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 2nd Workshop 6-13 Sept. 2009
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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 2nd 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 arXiv:0804.3566
During Capture: intermediate
String stretching between
D-particle and D3-brane is
Created. It acquires N internal
Oscillator excitations &
Grows in size & oscillates from
Zero to a maximum length by
absorbing incident photon
Energy p0 :
Minimise right-hand-size w.r.t. L.
End of intermediate string on D3-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….
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Total Time (Causal) Delays are Additive





D-foam: transparent to (or suppressed effects for) electrons
D-foam captures photons & re-emits them
Time Delay (Causal) in each Capture:
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 G0i ~ p0
CORFU 2nd Workshop 6-13 Sept. 2009
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Stringy Uncertainties & the Capture Process
Ellis, NM, Nanopoulos arXiv:0804.3566
During Capture: intermediate
String stretching between
D-particle and D3-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
Δt Δx ≥ α’ , Δp Δx ≥ 1 +absorbing
α’ (Δp0 )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 D3-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….
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Universe Expansion - Role of Cosmology





D-foam: transparent to electrons
Ellis, NM, Nanopoulos arXiv:0804.3566
D-foam captures photons & re-emits them
Time Delay (Causal) in each Capture:
EFFECTIVE QUANTUM
Independent of photon polarization (no Birefringence)
TotalGRAVITY
Delay from emission of
photons
SCALE
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 G0i ~ p0
REPRODUCE 4±1 MINUTE DELAY OF MAGIC from Mk501 (redshift z=0.034)
For n* =O(1) & Ms ~ 1018 GeV, 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 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
Universe Expansion - Role of Cosmology





D-foam: transparent to electrons
Ellis, NM, Nanopoulos arXiv:0804.3566
D-foam captures photons & re-emits them
Time Delay (Causal) in each Capture:
EFFECTIVE QUANTUM
Independent of photon polarization (no Birefringence)
TotalGRAVITY
Delay from emission of
photons
SCALE
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 G0i ~ p0
REPRODUCE 4±1 MINUTE DELAY OF MAGIC from Mk501 (redshift z=0.034)
For n* =O(1) & Ms ~ 1018 GeV, 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 2nd Workshop 6-13 Sept. 2009
N. E. MAVROMATOS
Universe Expansion - Role of Cosmology





D-foam: transparent to electrons
D-foam captures photons & re-emits them
Time Delay (Causal) in each Capture:
EFFECTIVE QUANTUM
Independent of photon polarization (no Birefringence)
TotalGRAVITY
Delay from emission of
photons
SCALE
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 G0i ~ p0
REPRODUCE 4±1 MINUTE DELAY OF MAGIC from Mk501 (redshift z=0.034)
For n* =O(1) & Ms ~ 1018 GeV, 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 2nd Workshop 6-13 Sept. 2009
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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 …
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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…)
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Conclusions

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).
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Outlook

In future: understand the construction within full-fledged
string theory, considering string and not particle production
and determining dynamically the momentum cut-off.

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).

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 2nd Workshop 6-13 Sept. 2009
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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’’)
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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/D3-branes
backgrounds
Antoniadis, Benakli, Laugier
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Type IIB String Model of D-particle Foam
T.Li, NM, Nanopoulos, D. Xie
Couplings of ND stringsStretched
between D3 and D7 branes
(Capture process)
D-Foam: Uniform Distribution
of D-particles in space with
VA3 = their average 3D-volume,
R’ = radius of forth space dim
transverse to D3 branes.
Avoid tachyon condensation:
D3 branes have widths 1.55 
s
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Seiberg,Susskind
Toumbas
Time delays arise by considering
Backward scattering u=0.
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OTHER PARTICLES
Backward scattering u=0 implies
JUST POLE TERMS…
NO TIME DELAY AT LEADING ORDER in η
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At order η, there are time delays…
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At order η, there are time delays…
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At order η, there are time delays…
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