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.

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.

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.

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)

At T > Tc

Coloured quarks and gluons are in a thermally equilibrated state of perturbative vacuum (QGP)

TOTAL COLOUR of the universe is neutralUniverse is colour singlet : not necessarily so locally

cT ~ T Hadronic phase bubbles appear (percolation)

Grow in size (grey)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

- η b/ ηγ ~ 10 -10

- expansion time scale ~ 10 –5 sec ____

Mini Bang = Big Bang ?

Turbulance

Inflation

Gravitation

Horizon

Quark Nuggets & Dark Matter :

Evolution of the universe, Einstein eqn.

Robertson – Walker space time

2

2

3

8

plmR

R

EOS for QGP

BaTP

BaT

4

43274.0

t

033 PdRRd

mpl = (1/G)

is the Plank mass

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

-1/2

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 ???

Strange quark nuggets (SQN)Strange quark nuggets (SQN)

L

L

L

H

H

L

H

L L

L

Isolated expanding bubbles of low temp In high temp phase

L

L

L

H

H

Expanding bubbles meet

Isolated shrinking bubbles of High temp phase

• •o

• •oo •

CEFT MODEL

Glendenning & matsui -1983

Sumiyoshi et al 1990

meson evaporation

Baryon evaporation

Chromo electric Flux-tube fission

P. BhattacharyaJ. AlamS. RahaB.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

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

>> H-1(t) = 2t of the universe~

c1

~K BC,

• 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

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 seperated in space

Colour wave function are still entangled Incomplete decoherence Residual perturbative vacuum enrgy

Can we make some estimate????

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

Accelerated Expansion

Some invisible, Unidentified energy is offsetting gravityDark Energy

Dark: as it is invisible, difficult to detect

Energy: as it is not matter which is only other option available

Features

Friedman equation

pG

RR

33

8..

RR..

Is -ve if and P are both +ve (Deceleration)

If p = and -veRR..

Is +ve (Acceleration)

Dark Energy

CDM: Dust like equation of statePressure ≈ p=0Energy density > 0

Dark Energy: p=w; w>0(Ideally w=-1)

+ve energy -ve pressure

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.

ρc ~ 10-47 GeV, So for ΩDE ~ 0.7

=> ρc ~ 10-48 GeVNatural Explanation : Vacuum energy density with correct

equation of state

Difrficulties: Higher energy scales

Planck era : ~ 10-77 GeVGUT : ~ 10-64 GeVElectroweak : ~ 108 GeVQCD : ~ 10-4 GeV

Puzzle why ρDE is so small?

Polarization energy

B (bag parameter) ≈

differene between the perturbative and the non perturbative vacua

vacuum energy density B

gradually decreases with increasing decoherence

* Thermodynamic measure of the entanglement during the phase transition

Fg ≡ Vcolour / Vtotal

On the average, Trapped False vac. Domains (TFVD)

each 1 Orphan Quark

QNNNFVDhorizonvolN oq or ~,

(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 ?

Too good to be true ?Not just a coincidence

Non perturbative : larg г : qq interaction(Plumer & Raha 1987)(Richardson 1976)

(Uniqueness of orphan quark) nq,o ≡ Nq,o / VH = ( 3/ 4) Nq,o /RH3

r ≡ RH / Nq,o1/3

v = ½ nq,o V(r) ~ 4

8

3

Ind. Of density & time, once it is, that is

V(r)=~((r)3-12/ r)

? Hard QCD ~ length scale ~ 1 fm

MeV 100 TFVD (Quark Nugget)

Smallest TFVD ≈ several cm

µ sec epoch nb ~ 1030 cm-3

4-48 GeV 10 ~

GeV 10 ~ -12