A COSMIC JOURNEY WITH BIKASH SINHA

The QCD Transition in the Early Universe

Sibaji Raha

Bose Institute

Kolkata

February 7, 2005

• 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

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

• 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. ………

• 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

• 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 ??

• 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

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

• 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

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

• 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

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 ???

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 ???

Role of colour Charge

Assumption : Many body system

Colour is averaged

Only statistical degeneracy

Too Simplified ?????

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

• 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

• 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

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

• 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!

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 ????

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)]

• 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 ?

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

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 )

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

• 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

~ 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

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.)

• Bhaskar Datta *• Narayan C. Rana *• David N. Schramm *• Jan-e Alam• Pijushpani Bhattacharjee• Somenath Chakraborty

(*) Deceased.