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A COSMIC JOURNEY WITH BIKASH SINHA. The QCD Transition in the Early Universe. Sibaji Raha Bose Institute Kolkata February 7, 2005. WMAP ( W ilkinson M icrowave A nisotropy P robe) First Year WMAP Observations Universe is 13.7 billion years old (±1%)

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A COSMIC JOURNEY WITH BIKASH SINHA

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A cosmic journey with bikash sinha

A COSMIC JOURNEY WITH BIKASH SINHA


The qcd transition in the early universe

The QCD Transition in the Early Universe

Sibaji Raha

Bose Institute

Kolkata

February 7, 2005


A cosmic journey with bikash sinha

  • 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)


First order phase transition

First order phase transition


Fate of quark bubbles

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


Boiling and evaporation

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)


B e contd

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)


Further progress

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!


What is dark energy

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


A cosmic journey with bikash sinha

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 


A cosmic journey with bikash sinha

  • Friedman equation

  • is -ve if  and p are both +ve

    (Deceleration)

    if p ~  and –ve is +ve (Acceleration)


Dark energy

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


A cosmic journey with bikash sinha

  • 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


A cosmic journey with bikash sinha

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 ???


A cosmic journey with bikash sinha

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 ???


A cosmic journey with bikash sinha

Role of colour Charge

Assumption : Many body system

Colour is averaged

Only statistical degeneracy

Too Simplified ?????


Quantum entanglement

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


A cosmic journey with bikash sinha

  • 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


A cosmic journey with bikash sinha

  • 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


A cosmic journey with bikash sinha

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


A cosmic journey with bikash sinha

  • 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!


A cosmic journey with bikash sinha

 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 ????


A cosmic journey with bikash sinha

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)]


A cosmic journey with bikash sinha

  • 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 ?


A cosmic journey with bikash sinha

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


A cosmic journey with bikash sinha

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 )


A cosmic journey with bikash sinha

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)


An alternate treatment

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


A cosmic journey with bikash sinha

 ~ length scale corresponding to the smallest TFVD

For stable SQN with baryon density ~ 1038 cm-3 ,

correspondinglength 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


Collaborators

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)


Collaborators contd

Collaborators (Contd.)

  • Bhaskar Datta *

  • Narayan C. Rana *

  • David N. Schramm *

  • Jan-e Alam

  • Pijushpani Bhattacharjee

  • Somenath Chakraborty

    (*) Deceased.


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