A COSMIC JOURNEY WITH BIKASH SINHA

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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 Tgt 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 Alt 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 gt 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)

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Dark Energy

• CDM Dust like equation of state
• Pressure ? p0
• Energy density ? gt 0
• Dark energy pw ? w lt 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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• ? Tgt 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
• (z0.17)

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An alternate treatment

• Confinement effect in dilute many body system of
  quarks
• ?s 1/log(1Q4/?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.