3.33 Sspd_chapter 1_part 13_ constituent particles of solid state  (Page 6/14)

V recession = R.H……………………………………………… 1.115

Where H = Hubble Constant and 1/H = Age of the Universe which has been accurately determined to be 13.7Gyears.

If the velocity of recession of the observable horizon ( that is the velocity of recession at 13.7 G light years) is V _recession * then we have three possible scenarios for the final fate of this Universe:

V recession * = V escape : Flat Universe with 0 curvature;…………………….. 1.116

V recession *<V escape : Closed Universe with (+) ve curvature;……………… 1.117

V recession *>V escape : Open Universe with (-)ve curvature;…………………… 1.118

A closed Universe with positive curvature is like a sphere which will ultimately stop receding and collapse on to itself in a final crunch and another big bang leading to the beginning of a new Universe.

A open Universe with a negative curvature is like a saddle which will continue to expand indefinitely. Ultimately everything becomes lifeless, radiationless , dark and cold. It will continue to expand with a whimper.

A flat universe has zero curvature. Here there is steady expansion and no accelerated expansion. This also will end in a cold death.

All these three scenarios have been shown in Figure 1.74.

If we take the flat universe scenario we arrive at the critical mass density Ω _critical .

For Flat Unverse: V _recession * = V _escape

Therefore: RH= √(2GM/R)

Squaring both sides: (RH) ² = (2GM/R)

Therefore: Ω critical = M/{(4π/3)R ^3 } = mass density of the Universe

= 3H ^2 /(8πG) = 10 ^-29 gm/(cm) ^3 = 10 ^-26 Kg/(m) ^3 ………………………. 1.119

where H = 75 Km/(sec.Mparsec);

G = 6.67×10 ^-11 (m ³ /(sec ² .Kg)).

Ω _actual / Ω _critical = Ω ₀ =normalized density of the Universe;

The critical density corresponds to 5 Hydrogen atoms per cubic meter.

Fig. 1.74. The three cosmological models of Universe from the equations of General Theory of relativity.

In Table(1.28), we find that Top quark has the heaviest rest mass, greater than 22GeV/c ² . Therefore it was the last quark to be experimentally verified. In February 1994, it was finally confirmed with definiteness. So it is now a well established fact that there are only three generations of fundamental particles.

1.13.2. THE CREATION OF MATERIAL PARTICLES SUBSEQUENT TO THE BIG BANG.

If we consider the instant of Big Bang to be zero second then during the interval between 0 second and 10 ^-43 second , we have no Physics to explain the events occurring in the given interval. Quantum Gravitation Physics will have to be developed to explain things.

Planck’s time t = (Gћ/c ^5 ) ^1/2 = 10 ^-43 seconds………………………… 1.120

At this instant ,

the radius of the Universe=(Gћ/c ^3 ) ^1/2 = 10 ^-33 cm……………………… 1.121

kT gives temperature in eV. 0.86×10 ^-4 eV corresponds to 1 Kelvin temperature increment;

Planck’s Temperature:

T*(MeV) = 1/√t = 1/√(10 ^-43 ) = 3.16227×10 ^21 MeV~10 ^19 GeV………………….. 1.123

T**(Kelvin) = 10 ^10 /√t = 3.16227×10 ^31 K;

Planck’s Density of the Universe = ρ planck = 10 ^93 gm/(cm) ^3 …………………………. 1.124

Atomic Nucleus density = ρ atomic = 10 ^14 gm/(cm) ^3

From the difference of the two densities, we conclude that matter is not in normal condition at Planck’s Time. In fact it is being created from Photon every moment and instantaneously it is being destroyed: