a cosmic journey with bikash sinha. the qcd transition in the early universe sibaji raha bose...
TRANSCRIPT
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A COSMIC JOURNEY WITH BIKASH SINHA
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The QCD Transition in the Early Universe
Sibaji Raha
Bose Institute
Kolkata
February 7, 2005
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• WMAP• (Wilkinson Microwave Anisotropy
Probe) • First Year WMAP Observations
• Universe is 13.7 billion years old (±1%) • First stars ignited 200 million years after the Big
Bang • Content of the Universe: 4% Atoms, 23% Cold
Dark Matter, 73% Dark Energy
• Expansion rate (Hubble constant): H0= 71 km/sec/Mpc (±5%)
• New evidence for Inflation (in polarized signal)
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First order phase transition
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Fate of quark bubbles
• Universe expands: low temp. phase expands and cools
• Equilibrium between two phases• Heat transfer from high to low temp. phase
Evaporation of surface layers
and/or• emission of particles of very long mean free path :
Neutrino
and/or
Boiling
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Boiling and evaporation
• For temp T> 0.1I, I binding energy of neutron in strange matter, hadron gas is thermodynamically favoured
• spontaneous nucleation of hadronic bubble
• bubble grows at the expense of quark phases
• all the SQN would dissolve into hadrons (Alcock & Olinto PRD 1989)
• Not enough time for bubbles to nucleate (Madsen & Olesen PRD 1991, 1993)
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B & E Contd. ………
• For neutron binding energy (in SQN) In ~ 20 MeV and nuggets with A< 1052 would evaporate
(Alcock & Farhi PRD1985)
• In = mn - μu - 2 μd
• evaporation reduces no. of neutron and proton and hence μu and μd
• s-quark enriched surface emission of kaons
• Resultant In ~ 350 MeV
• SQN with A 1046 stable
(Madsen et al. PRD1986)
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Further Progress
• Bhattacharjee et al. (PRD 1993): Chromoelectric flux tube model
Stable SQN for A > 1044
• Alam et al . (ApJ 1999) : SQN may close the Universe
• Bhattacharyya et al. (PRD 2000): abundance and size distribution
• Trapped quark domains are stable against evaporation. Could account for Cold Dark Matter (PRD
2000, MNRAS 2003)Signature : Detection of SQM in cosmic
rays!
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What is Dark Energy ??
• From CMBR : Universe is Flat
Curvature k =0 ;
= c (closure density ~ 5 protons/m3)
OR ~ 1
Gravity is same as expansion
Expansion should slow down
BUT distant supernovae are farther away than
expected from red shift
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Accelerated Expansion Some invisible, unidentified energy is
offsetting gravity
Dark Energy
Dark : as it is invisible, difficult to detect
Energy : as it is not matter which is the only other option available
Features
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• Friedman equation
• is -ve if and p are both +ve
(Deceleration)
if p ~ and –ve is +ve (Acceleration)
)3(3
8p
G
R
R
R
R
R
R
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Dark Energy
CDM : Dust like equation of state Pressure p=0 Energy density > 0
Dark energy : p=w ; w < 0 (Ideally w= -1)
+ve energy -ve pressure
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• Dark Energy
(a) emits no light
(b) it has large –ve pressure
(c) does not show its presence in galaxies
and cluster of galaxies, it must be smoothly
distributed
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c~ 10-47 GeV4 , So for DE ~ 0.7,
DE ~ 10-48 GeV4
Natural Explanation : Vacuum energy density
with correct equation of state
Difficulties : higher energy scales
Planck era : ~ 1077 GeV4
GUT : ~ 1064 GeV4
Electroweak : ~ 108 GeV4
QCD : ~ 10-4 GeV4
Puzzle Why DE is so small ???
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T> Tc : coloured quarks and gluons in thermal equilibrium At Tc : bubbles of hadronic phase
grow in size and form an infinite chain of
connected bubbles
universe turns over to hadronic phase
in hadronic phase quark phase gets trapped in
large bubbles
Trapped domains evolve to SQN
What did we miss ???
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Role of colour Charge
Assumption : Many body system
Colour is averaged
Only statistical degeneracy
Too Simplified ?????
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Quantum Entanglement
• Typical quantum phenomena
Particles which are far apart seem to be influencing each other
Condition : Particles must have interacted with each other earlier
Measurement on one immediately specifies the other
Interacting particles always entangled
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• Experiments :
Nicolas Gisin, Switzerland : measurement of two entangled particles separated by miles
G. Rempe, Germany : Young two slit expt.
Pattern is destroyed even if probe has far too little energy, compared to photons
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• Before P.T. Universe singlet
Wave functions of coloured objects entangled
Universe characterized by perturbative vacuum
During P.T. local colour neutral hadrons
Gradual decoherence of entangled wave functions
Proportionate reduction of vacuum energy
Provides latent heat of the transition
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Is entanglement necessary to consider??
Baryogenesis complete much before the QCD era
Net baryon number carried in the form of net quarks
Debye screening occurs in the QCD plasma
gs(T) T )-1 ~ 1 fm
Total number of colour charges ~ 10 - 100
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• Net quark number within a Debye volume ~
10-8 – 10-9
To ensure integer baryon number, long range correlation, much larger than the Debye length, is thus essential.
Total entanglement in colour space solves the problem naturally!
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In Quantum mechanical sense
completion of quark-hadron P.T.
Complete decoherence of colour wave function
Entire vacuum energy disappear
Perturbative vacuum is replaced by non-perturbative one
Does that really happen ????
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End of cosmic quark-hadron phase transition
few coloured quarks separated in space
Colour wave functions are still entangled
Incomplete decoherence
Residual perturbative vacuum energy
Can we make some estimate ???? [Ref: hep-ph/0307366; Physics Letters B (in press)]
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• Estimate : Bag model
• Bag pressure B difference between two vacuum
Beginning of P.T. vacuum energy B
This decreases with increasing decoherence
What will be Measure of entanglement ?
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Measure :
Volume Fraction of coloured degrees of freedom,
Fq = Vcolour / Vtotal
Initially : Fq is unity
complete entanglement
Finally : Small entanglement
tiny but non-zero Fq
Amount of perturbative vacuum energy at the end of QCD transition
= B X Fq,O where Fq,O is due solely to orphan quarks
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Order of magnitude estimate
On average each TFVD one orphan quark
Number of orphan quarks Nq,O
= Number of TFVD NTFVD
Likely length scale of TFVD ~ few cm (Witten 1984)
No. of TFVD at percolation time (~ 100 s) ~ 1018-20
Effective radius associated with each orphan quark ~ 10-14cm
( qq = (1/9) pp ; pp ~ 20mb )
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Fq,O = Nq,O X (Vq,O / Vtotal )
~ 10-42 - 10-44
Residual energy ~ B X Fq,O ~ 10-46 - 10-48 GeV4
DE ~ 0.7
DE Constant
Matter density decreases as R-3
DE is dominant at late times (z=0.17)
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An alternate treatment
• Confinement effect in dilute many body system of quarks
s ~ 1/log(1+Q4/4)
V(q) = s(q2)/ q2
V(r) ~ [ ( r)3 – 12/ ( r) ] For large r, V(r) ~ ( r)3
Inter quark separation
r = [ ( 3/4 ) nq,O ]1/3
Potential energy density for this inter quark separation is
v = ½ nq,O V(r) ~ ( 3/8 ) 4
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~ length scale corresponding to the smallest TFVD
For stable SQN with baryon density ~ 1038 cm-3 ,
corresponding length scale ~ cm
Baryon density at sec epoch ~ 1030 cm-3 (Tc ~ 100 MeV )
Baryon density of smallest TFVD ~ 1030 cm-3
Appropriate length scale ~ 0.01 cm
~ 10-12 GeV 4 ~ 10-48 GeV4
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Collaborators
1. Shibaji Banerjee (St. Xaviers College, Kolkata)
2. Abhijit Bhattacharyya (Scottish Church College, Kolkata)
3. Sanjay K. Ghosh (Bose Institute, Kolkata)
4. Bikash Sinha (VECC & SINP, Kolkata)
5. Hiroshi Toki (RCNP, Osaka)
6. Ernst-Michael Ilgenfritz (RCNP, Osaka)
7. Eiichi Takasugi (Osaka Univ., Osaka)
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Collaborators (Contd.)
• Bhaskar Datta *• Narayan C. Rana *• David N. Schramm *• Jan-e Alam• Pijushpani Bhattacharjee• Somenath Chakraborty
(*) Deceased.