A COSMIC JOURNEY WITH BIKASH SINHA

1. A COSMIC JOURNEY WITH BIKASH SINHA

2. The QCD Transition in the Early Universe Sibaji Raha Bose Institute Kolkata February 7, 2005

3. 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)

4. First order phase transition

5. 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

6. 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)

7. 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)

8. 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!

9. 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

10. 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 

11. Friedman equation • is -ve if  and p are both +ve (Deceleration) if p ~  and –ve is +ve (Acceleration)

12. 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

13. 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

14. 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 ???

15. 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 ???

16. Role of colour Charge Assumption : Many body system  Colour is averaged  Only statistical degeneracy Too Simplified ?????

17. 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

18. 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

19. 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

21. 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

22. 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!

23.  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 ????

24. 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)]

25. 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 ?

26. 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

27. 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 )

28. 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)

29. 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

30.  ~ 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

32. 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)

33. Collaborators (Contd.) • Bhaskar Datta * • Narayan C. Rana * • David N. Schramm * • Jan-e Alam • Pijushpani Bhattacharjee • Somenath Chakraborty (*) Deceased.