In addition, we ascribe to the present epoch the condition that the density of matter determined by the use of the present moment

Hubble parameter and from the Friedmann-Einstein equation must be equal.

With solving this equation in terms of H, the obtained value (H) is achieved corresponding to the

Hubble parameter in the inflation time [11].

Therefore, measurements of the

Hubble parameter from the CMB spectrum (r [right arrow] [R.sub.U]) will give a value different from and larger than H = 1/T; we find:

H = [??]/a is the

Hubble parameter and the dot represents the derivative with respect to time.

The

Hubble parameter in Figure 2 rose sharply from 1.0 x [10.sup.-37] to 2.0 x [10.sup.-37] s before undergoing an oscillatory behavior.

The generalized mean

Hubble parameter H can be expressed as H = [??]/R = (1/3)([H.sub.x] + [H.sub.y] + [H.sub.z]), where [H.sub.x] = [[??].sub.1]/[b.sub.1], [H.sub.y] = [[??].sub.2]/[b.sub.2], and [H.sub.z] = [[??].sub.3]/[b.sub.3] are the directional

Hubble parameters in the directions of x, y, and z, respectively.

Now we try to explain how the universe exploded and expanded, we start from our assumptions we made before and find the

Hubble parameter and try to find the dark energy and matter.

The

Hubble parameter is the ratio of a galaxy's recession velocity to its distance and describes the rate at which the universe is expanding.

where H [equivalent to] [??]/a is the

Hubble parameter. For the Hubble volume,

where [beta] = 0.5804 and H0 is the so called Hubble constant, the value of the

Hubble parameter H(t) at t = [T.sub.0], the current age of the Universe.

* The

Hubble parameter, the rate of the universe's expansion today, is 70.1 [+ or -] 1.3 km per second per megaparsec.

where H = [??]/a is the

Hubble parameter, [r.sub.c] = [m.sup.2.sub.pl]/(2[m.sup.3.sub.5]) [20] is the crossover length scale reflecting the competition between 4D and 5D effects of gravity, and [epsilon] = [+ or -]1 corresponds to the two branches of solutions of the DGP model.

where H(t) is time dependent

Hubble parameter, and that pressure [p.sub.m] = 0 (matter is treated as dust), one has

Then, by using independently measured numbers like the

Hubble parameter, they can infer (1) how far away the galaxy was when it emitted the light we see now, (2) how far it now lies from Earth, and (3) how far the light traveled in the interim.

Recently, a large class of flat nonsingular FRW type cosmologies, where the vacuum energy density evolves like a truncated power-series in the

Hubble parameter H, has been discussed in the literature [19-22] (its dominant term behaves like [[rho].sub.[LAMBDA]](H) [varies] [H.sup.n+2], n > 0).