Cosmological dark energy from the cosmic QCD phase transition and Colour entanglement

1. Cosmological dark energy from the cosmic QCD phase transition and Colour entanglement Bikash Sinha Saha Institute of Nuclear Physics & Variable Energy Cyclotron Centre 1/AF, Bidhan Nagar, Kolkata, India

2. Recent astrophysical observations indicate that the universe is composed of a large amount of dark energy (DE) responsible for an accelerated expansion of the universe, along with a sizeable amount of cold dark matter (CDM), responsible for structure formation. At present, the explanations for the origin or the nature of both CDM and DE seem to require ideas beyond the standard model of elementary particle interactions. Here, for the first time, we show that CDM and DE can arise entirely from the standard principles of strong interaction physics and quantum entanglement.

3. The past few decades have been momentous in the history of science insofar as several accurate astrophysical measurements have been carried out and cosmology, often considered a fair playground of exotic or fanciful ideas, has had to confront the reality of experiments. Based on the knowledge gleaned so far, the present consensus is that the standard model of cosmology, comprising the Big Bang and a flat universe is correct. The Big Bang nucleosynthesis (BBN), which forms one of the basic tenets of the standard model, shows that baryons can at most contribute ΩB(≡ ρB/ρc, ρc being the present value of closure density ~ 10−47 GeV) ~0.04, whereas structure formation studies require that the total (cold) matter density should be ΩCDM ~ 0.23.

4. Matter contributing to CDM is characterized by a dust-like equation of state, pressure p ≈ 0 and energy density ρ > 0 and is responsible for clustering on galactic or supergalactic scales. Dark energy (DE), on the other hand, is smooth, with no clustering features at any scale. It is required to have an equation of state p = wρ where w < 0 (ideally w = −1), so that for a positive amount of dark energy, the resulting negative pressure would facilitate an accelerated expansion of the universe, evidence for which has recently become available from the redshift studies of type IA supernovae For a flat universe Ω ~ 1, ΩDE ~ 0.73 implies that ρDE today is of the order of 10−48 GeV.

5. WMAP (WilkinsonMicrowaveAnisotropy 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 polarised signal)

9. At T > Tc Coloured quarks and gluons are in a thermally equilibrated state ofperturbative vacuum (QGP) TOTAL COLOUR of the universe is neutral Universe is colour singlet : not necessarily so locally Hadronic phase bubbles appear (percolation) (grey) Grow in size P, n : (small open circles) Remaining high temp quark phase gets trapped in large bubbles (Big Coloured shaded circles) These Trapped False Vacuum Domains (TFVD) Baryon no. Inside TFVD many orders of magnitude higher than normal hadrons (WITTEN 1984) SQN

10. - η b/ ηγ ~ 10 -10 - expansion time scale ~ 10 –5 sec ____ Mini Bang = Big Bang ? Turbulance Inflation Gravitation Horizon

11. Quark Nuggets & Dark Matter : Evolution of the universe, Einstein eqn. Robertson – Walker space time mpl = (1/G) is the Plank mass EOS for QGP

12. -1/2 T α t t i ( on set of the phase transition ) Tc~ (200 – 150 ) Mev : ti ~ few µ sec tc ~ characteristic time scale = (3 M 2pl / 8 π B)½ ~ 40 µ sec

13. 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 ???

14. H L H L L L L H L L Strange quark nuggets (SQN) Isolated expanding bubbles of low temp In high temp phase Expanding bubbles meet H L L L H Isolated shrinking bubbles of High temp phase

15. • • o • • • o o CEFT MODEL Glendenning & matsui -1983 meson evaporation Sumiyoshi et al 1990 Baryon evaporation

16. Chromo electric Flux-tube fission P. Bhattacharya J. Alam S. Raha B.S. (PRD ’93) dNB /dt = [dNB/dt ]ev + [dNB/dt]abs [dNB/dt]abs = -2π2 [ nN υN / mN T2] exp [mN- μNθ / T ] [ dNB / dt ] ev

17. >> ~ H-1(t) = 2t of the universe Q N’s with baryon number NB at time t will stop evaporating (survive) if the time scale of evaporation τev(NB,t) NB dNB / dt

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

20. 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???

21. End of cosmic quark-hadron phase transition Few coloured quarks seperated in space Colour wave function are still entangled Incomplete decoherence Residual perturbative vacuum enrgy Can we make some estimate????

22. Stable nuggets Colour neutral All have integer baryon number At the moment of formation quark number multiples of 3 Statistical system some residual colour For colour neutrality one or two residual quarks

23. 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 only other option available Features

24. Friedman equation Is -ve if  and P are both +ve (Deceleration) If p =  and -ve Is +ve (Acceleration)

25. 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

26. Dark Energy emits no light It has large -ve pressure Does not show its presence in galaxies and cluster of galaxies, it must be smoothly distributed.

27. ρc ~ 10-47 GeV, So for ΩDE ~ 0.7 => ρc~ 10-48 GeV Natural Explanation : Vacuum energy density with correct equation of state Difrficulties: Higher energy scales Planck era : ~ 10-77 GeV GUT : ~ 10-64 GeV Electroweak : ~ 108 GeV QCD : ~ 10-4 GeV Puzzle why ρDE is so small?

28. Polarization energyB (bag parameter) ≈differene between the perturbative and the non perturbative vacuavacuum energy density Bgradually decreases with increasing decoherence* Thermodynamic measure of the entanglement during the phase transitionFg≡ Vcolour / Vtotal

29. On the average, Trapped False vac. Domains (TFVD) each 1 Orphan Quark (Witten) QN (TFVD) ~ few cm Percolation time 100µ sec NQN ~ 1018– 20 ro ~ 10- 14 cm : rp ~ 10- 13 ( σqq ~ 1/9 σpp , σpp ~ 20 mb ) fq,o ~ Nq,o x ( vq,o / Vtotal ) ~ 10- 42 to 10- 44 : vq,o (eff. Vol. of orphan Quark) Residual pQCD vacuum energy ~ 10- 46 to 10- 48 ~ ρDE : Orphan Quarks?

30. Too good to be true ? Not just a coincidence Non perturbative : larg г : qq interaction (Plumer & Raha 1987) (Richardson 1976) V(r)=~((r)3-12/ r) nq,o ≡ Nq,o / VH = ( 3/ 4) Nq,o /RH3 (Uniqueness of orphan quark) r ≡ RH / Nq,o1/3 v = ½ nq,o V(r) ~ Ind. Of density & time, once it is, that is

31. Hard QCD ~ length scale ~ 1 fm TFVD (Quark Nugget) Smallest TFVD ≈ several cm µ sec epoch nb ~ 1030cm-3