CBR





�QUANTUM COSMOLOGY AND THE COSMIC BACKGROUND TEMPERATURE

*Summary*: a simple equation is found which relates Hubble's constant with other very well known constants of physics, and also an equation for COSMIC BACKGROUND TEMPERATURE .

�1.- Links between the Microcosmos and the Macrocosmos

Louis de Broglie found years ago , that every particle in the Universe has associated with it a wave length given by:

�l = h / mv

�where l is this wave length , h is the Plank's constant , and the product mv is the impulse of the particle. the shortest wave length associated with a particle is call the Compton wave length. In which case the speed v must be replaced by the speed of light C . in this case the Compton wave length is :

�l = h / mC

which drive us to :

�l = hC / mC^2

� The symbol ^ means that the number following the symbol is the power of the previous letter. As the wave length and the frequency of the light are related by : l = C/f then ,as we know we have that :

�f = energy / h

�Now , I shall introduce a an operational mass given by:

m = (me * mp)^(1/2) (1-1)

�which I will call a mason.

�Where me is the mass of the electron and mp is the mass of the proton.

Next, there is what is call the classical radius of an electron given by :

�re = q^2 / me C^2

�Having this in mind and because the electric charge (q) is the same for the proton and for the electron, we calculate the classical radius of the mason as:

�(1-2) r = q^2 / mc^2

�Now , in the Microworld, there is an energy asociated with the fundamental forces in such a way that for the electric fundamental charge the asociate energy for the named mason the energy is e = mC^2 = q^2/r .To this energy corresponds also a frecuency f which value is :

e = h f

therefore:

hf = mC^2 = q^2/r

�and : f = q^2/ hr

As you see the frecuency came from the energy (q^2/r) between the charges of the electron and the proton (with the same value) at the distance r divided by h.

As for the electromagnetic force , the same basic concepts can be used for the gravitational energy between the electron and the proton.

Let us get the gravitatory energy between an electron an a proton at the distance r . we will get:

�(1-3) e = h f = G m^2/ r = G me mp / r

�As all the factors on this last equation are known, we obtain the frequency corresponding the gravitational attraction between an electron and proton at the distance r as :

�(1-4) f = 2.33 e -18 inverse seconds

�using the apropiated changes in the units , we get:

� f = 71.88 km/sec/mparsec

The only custionable assumption made here, is the use of "r" coming from the electric charge on (1-2) and used on (1-3) . I kept this distance " r " on (1-3) just because :

a) it gives me a frecuency equal to the Hubbble's constant.

b) it is the vehicle which relates the electromagnetic force and the gravitational force with the Universe as a whole.

�The Hubble's constant has a measured known value somewhere between 50 and 100 km/sec/megaparsec that have the corresponding values of 1.62 e-18 and 3.24e-18 1/sec. So it is very reasonable to say that this calculated value for the frecuency obtained by mean of (1-3) might be the Hubble's constant. then , using just the allready presented equations we get :

�(1-5) H = Gm^2/hr H = G m^3 / h q^2

�Now we will defined the wave length given by :

�(1-6) R = C/H = 1.284916389E+28 cm

�As you see this two quantities correspond very well to the known values of the Hubble's constant and the radius of the Universe. So , why not to believed that this is so , and that by this mean we are coupling the Macrocosmos with the Microcosmos ?.

�And let us consider that the potential energy of the Universe is equal to its total mass energy , this means :

�(1-7) MC^2 = G M^2 / R (1-8) R = G M / C^2

�(1-9) M = C^3 /G H

�The assumption of (1-7) and therefore (1-8) could be seen as an assumption without any basis. But this is not the case. �Why? . well, first we know that the selfgravitatory energy of an homogeneous spherical mass is :

U = -3/5 GM^2/R

�That in general is very much smaller than MC^2 , but this equation is for masses on which the actual radius is very much greater than the gravitational radius., for the Universe this is not the case.

Here I am making the following assumption :

" The Universe is all what it is, there can not be anything out of it , therefore all the light in the Universe is contained on it , it can't go outside. And because it can't go outside(there is not outside) , then the universe acts as a black hole" .

As it is known , for a black hole ( I am not an expert on black holes) the radius of the event horizon is R = 2GM / C^2 in which except for a factor of 2 the mass-energy of the black hole and the gravitatory energy are almost the same.

�Besides , if you review the equation that A. Einstein developed for the radius of the Universe on which: R = 2GM / pi C^2 which again except for a factor of 2/pi also shows that the mass-energy of the Universe is the same as its gravitatory energy. It should be explain the factor 3/5 is not longer correct for the Universe as a whole , this is because the volume for the spherical space is different than the volume for the flat space ( 2pi^2 R^3 instead of 4pi/3 R^3)

So the assumption of (1-7) is very well supported and if there is any error is of the order of 2 or 3 times . personally I don't think there is an error , I think that the equation is correct as it is , this is because there is another equation which supports the assumption . this is the equation for the gravitational redshift of light :

�f = fo ( 1 - GM/RC^2)

�As you can see on this equation, the only way for the light not to get outside the mass M when the frequency and the energy is cero is when RC^2/GM = 1 that it is precisely my assumption.

�Now lets define the reciprocal of the fine structure constants for the electromagnetic and gravitational forces as :

�(1-10) A = h C / q^2 = 861.0225291 electromagnetic

�(1-11) B = h C / G m^2 = 1.953865716E+42 gravitational

�There is a very important number which represents the ratio of the electromagnetic force to the gravitational force , this number which I will represent by the letter S is :

�(1-12) S = q^2 / G m^2 (1-13) S = B / A (1-14) S = R / L

�if we define the number N as : (1-15) N = M / m we get :

�(1-16) N = A S^2 (1-17) N = B^2 / A

�and we can get the actual mass of the Universe as :

�(1-18) M = h C q^2 / (G^2)( m^3 )

�If we consider that the mass of the neutron and the mass of the proton are almost the same , and that the mass of the electron has a very small contribution to the total mass because they have 1836 less weight than the protons, then the total amount of nucleons in the Universe is :

�(1-19) Nn = (B^2 / A)x m / mp

(1-20) P = H^2 / G k ( density ) k = 4 pi /3

note: I am suppousing an euclidian Universe.

Therefore , we can put all the main parameters of the Universe as a function of nature constants only :

(1-21) P = (G/k )*(m^3 C^2 / h q^2 ) ^2

(1-22) M = h C q^2 / (G^2)( m^3 )

(1-23) m = (me * mp)^(1/2)

(1-24) R = h q^2 / ( G m^3 C )

(1-25) N = hC q^2 / (G m^2 )^2

(1-26) Nn = h C q^2 / ( G^2 m^3 mp )

(1-27) H = G m^3 C^2 / (h q^2 )

these are the values I use for the above results :

�a ) Data :

h = 6.62607554 e-27 erg-sec Plank' s constant

C = 2.997924562 e+10 cm/sec light speed

q = 4.8032067848 e -10 e.u elementary electric charge

mp = 1.67262311 e-24 grams proton mass

me = 9.109389754 e- 28 grams electron mass

G = 6.6725985 e-8 cm^3/ gram- sec^2 Newton gravity constant

�b) Calculations : present values

�M = 1.730687266 e+56 grams Universe actual mass

P = 1.947661213 e-29 grams/ cm^3 density of the Universe

m = 3.903405669 e-26 grams mason mass

R = 1.284916389 e+28 cm radius of the Universe

N = 4.4337787859e+81 number of masons

Nn = 1.034714429e+80 number of nucleons

H = 2.333181419 e-18 1/ sec. Hubble's constant

�2.- Cosmic background temperature :

It is known by everyone interested on Cosmology that the Universe is filled with a thermal radiation of very low temperature that is a fosil of the begginig of it.

It is supposed that this radiation is the consecuence of the annhilition of the particles and antiparticles which existed at the very begginig of time.

Here I am not going to discuss if this is so or not. What I am to expose here is an equation which I got, to know what are the values of the Cosmic background temperatures at different epochs .

I must confess that I got this equation by mean of a not very scientific method, and this is because I used what I have been using on all the papers I wrote about Cosmology and the four fundamental forces, that is : looking for relationships between different constants of the branches of physics.(this paper is just a very small part of my papers).

Because the results are very accurate I think they have great chances of been right.

The equation for the Cosmic Background Temperature is :

(2-1) �T = 2mC^2/ ZK B^(1/4)

�m is as before m = (mp x me)^(1/2) see (1-1)

m = 3.903405669 e-26 grams (actual value)

Z is the solution to the equation (5-Z)e^Z = 5 Z = 4.965114231

B = hC/Gm^2 as (1-11) B = 1.953865716E+42 (actual value)

K = 1.38065812E-16 erg/Kelvin. Boltzman' constant

If you make the calculation for the actual epoch with the actual values of m and B , you will get a Cosmic Background Temperature of :

�T = 2.737637938 Kelvins

�which fits pretty well with the known value.

�Now , I made the following assumptions which are not hard to accept.

a) the four fundamental forces where unified at the "Plank's time" when the unification mass was : mu = (hC/G)^(1/2).

This mass was obtained by just making B = 1 on (1-11)

b) unification means not just that the forces had the same value but that this value was exactly 1.

As mu came from (1-11) where m = (mp x me)^(1/2) , then we can now see that the operational mass "m" (the mason)has an specific meaning, it is the mass that was the unification mass at the Plank's time.

So , to know what was the Cosmic Background Temperature on the Plank's time , you just replace on (2-1) m by (hC/G)^(1/2) and B by the number 1 , and you have that the temperature was :

Tu = 1.430694953E+32 Kelvins.

�I still have to much to say about this same item , but it will be needed to much to say before, like : there is a way to define how does the CBT varies with time , how it is related with the values of the four fundamental forces , how this forces vary with the CBT , what was the mass of the Universe at that time, etc, etc.

�BY : R. Garza e-mail : [email protected] or [email protected]

MONTERREY, N.L, MEXICO SEPTEMBER 30 OF 1998

The previous abstract can be used by anyone , but because it is of my own ideas , if the equations or concepts are used my name must be cited .

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