Cosmological dark energy from the

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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
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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.
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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 OB ( ?B/?c, ?c 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 OCDM
0.23.
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Matter contributing to CDM is characterized by a
dust-like equation of state, pressure p 0 and
energy density ? gt 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 w?
where w lt 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 O 1, ODE 0.73 implies that ?DE today
is of the order of 10-48 GeV.
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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
polarised signal)
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At T gt Tc
Coloured quarks and gluons are in a thermally
equilibrated state of perturbative 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
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- ? b/ ?? 10 -10
- expansion time scale 10 5 sec
____
Mini Bang Big Bang
?
Turbulance
Inflation
Gravitation
Horizon
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Quark Nuggets Dark Matter
Evolution of the universe, Einstein eqn.
Robertson Walker space time
mpl (1/?G) is the Plank mass
EOS for QGP
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-1/2
T a 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 p B)½ 40 µ sec
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• T gt 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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Strange quark nuggets (SQN)
Isolated expanding bubbles of low temp In high
temp phase
Expanding bubbles meet
L
H
L
L
H
Isolated shrinking bubbles of High temp phase
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CEFT MODEL
Glendenning matsui -1983
meson evaporation
Sumiyoshi et al 1990
Baryon evaporation
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Chromo electric Flux-tube fission
P. Bhattacharya J. Alam S. Raha B.S. (PRD 93)
dNB /dt dNB/dt ev dNB/dtabs
dNB/dtabs -2p2 nN ?N / mN T2 exp mN- µN?
/ T dNB / dt ev
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Q Ns with baryon number NB at time t will stop
evaporating (survive) if the time scale of
evaporation tev(NB,t) NB
dNB / dt
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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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• 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 seperated in space
Colour wave function are
still entangled
Incomplete decoherence
Residual
perturbative vacuum enrgy Can we make some
estimate????
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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
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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 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 wgt0
• (Ideally w-1)
• ve energy -ve pressure

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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.

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?c 10-47 GeV, So for ODE 0.7 gt ?c
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 ?DE is so small?
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Polarization energyB (bag parameter)
differene between the perturbative and the non
perturbative vacuavacuum energy density B
gradually decreases with increasing
decoherence Thermodynamic measure of the
entanglement during the phase transitionFg
Vcolour / Vtotal
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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
( sqq 1/9 spp , spp 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
?DE Orphan Quarks ?
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Too good to be true ? Not just a coincidence
Non perturbative larg ? 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
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Hard QCD length scale 1 fm
TFVD (Quark Nugget)
Smallest TFVD several cm
µ sec epoch
nb 1030 cm-3