Documents 1,2 and 1,3 of this website page describe the Cosmic Background Radiation predicted by the Yilmaz Cosmology Model, which is derived from the Yilmaz theory of Gravity. The original analysis of cosmic background radiation published in the year 2000 was based on a rough approximation.  An accurate analysis is presented in Appendix F of page 4, Cosmology, of this website. (Click here for Page 4.) The following summarizes this material of page 4, Appendix F.

        The Yilmaz Cosmology Model assumes that the average density of matter is constant throughout the universe, and so the average luminosity per unit volume is constant. This analysis assumes the following average luminosity density, which was derived from data in the Revised Shapely-Ames Catalogue:

        P/v = 4.103*10⁶ L_sun/MLyr³                                         (1)

Where P/v is the light power P radiated from a volume v. This is expressed in terms of the luminosity of the sun L_sun , which is the light power radiated from the sun. The parameter MLyr represents one million light years.

        The photon rate radiated by the sun is 1.53*10⁴⁵ photons per second. We assume (as an approximation) that the sun luminosity in Eq. 1 can be replaced by the sun’s photon rate to obtain the average photon rate radiated by stars. This gives the following for the average photon rate radiated per unit volume of the universe:

        N*/v = 7.85*10³³ (photon/sec)/Lyr³                                 (2)

where N* represents the photon rate in photons per second. The volume is expressed in terms of cubic light years (Lyr³). Applying this value of photon-rate density to the Yilmaz Cosmology Model yields the following formula for the photon rate N* that is received locally (per unit of receiver area A) from the radiation by stars lying at a distance r within an increment of distance Dr:

        N*/A = 2.625*10⁷ (Dr/r_o) exp[(r/r_o)²]                             (3)

The parameter r_o is the apparent radius of the universe (derived from the Hubble constant), which we assume to be 15 billion light years.

        The Yilmaz Cosmology Model predicts that the frequency f of locally received radiation is related as follows to the corresponding frequency F that is radiated by a star lying at the distance r:

        f/F = ½ exp[-(r/r_o)²/2]                                                     (4)

This is an approximation, which is highly accurate for very distant stars.

        The spectrum of an ideal blackbody can be conveniently expressed as:

    (dP/df) = (P/1.388f_h) (f/f_h)³ [exp(3.501) - 1]/[exp(3.501 f/f_h) - 1]         (5)

where f_h is the mid-power (or half-power) frequency of the spectrum. Half of the spectral power lies at lower frequencies, and half lies at higher frequencies. The frequency variable is denoted f, the total power is P, and dP/df is the power spectral density. Equation 2-5 shows that, at the mid-power frequency f_h , the power spectral density is equal to

        (dP/df) at f_h = P/1.388f_h                                                             (6)

The mid-power wavelength l_h is equal to c/f_h and is related as follows to the blackbody temperature T:

        l_hT = 0.4107 cm-° K                                                             (7)

Equation 4 shows that if the stars radiate a single frequency F, the radiation received from stars that lie within an increment of distance Dr would vary in frequency by an amount Df given by

        |Df/f| = (r/r_o)|Dr/r|                                                                 (8)

The absolute-value marks | | for Df/f and Dr/r are used, because a positive value of distance (Dr/r) produces a negative variation of frequency (Df/f). We make the approximation that all of the distant stars are blackbodies with the same blackbody temperature T_star. For the radiation received from stars that lie over an increment of distance Dr , the ratio |Df/f| in Eq. 2-8 gives the variation of the mid-power frequency f_h of the received radiation. By Eq. 2-7, the blackbody temperature T is proportional to the mid-power frequency f_h. Hence for the radiation received from stars that lie within an increment of distance Dr, the blackbody temperatures of the received radiation lie within a temperature range DT that is given by

        DT/T = |Df_h/f_h| = (r/r_o)|Dr/r|                                                 (9)

We separate the distance r into a series of Dr increments, selected so that each produces the same |Df_h/f_h| frequency interval. The interval |Df_h/f_h| is set sufficiently small (at a value of about 0.1) to achieve approximately a single blackbody spectrum for each interval. We calculate for each of these spectra the value of the photon-rate spectral-density d(N*/A)/df at a particular frequency f_x. The spectral density values are summed for all of these intervals, to obtain the total photon-rate spectral-density at the frequency f_x. The resultant sum is (to a very good approximation):

 d(N*/A)/df = 1.025*10⁷(F_star/f_x)²/1.388f_{x Ö}[ln(F_star/2f_x)] (photon/sec)/cm²     (10)

It is convenient to regard the total d(N*/A)/df spectral density at any frequency f_x as being the spectral density of a single equivalent blackbody spectrum having a mid-power frequency f_h equal to f_x . By Eq. 6, the total photon-rate of this equivalent blackbody spectrum is

        N*/A = 1.388f_x d(N*/A)/df

                  = 1.025*10⁷(F_star/f_x)²/ Ö[ln(F_star/2f_x)]   (photon/sec)/cm²         (11)

For a blackbody, the mid-power frequency is proportional to the blackbody temperature. Hence Eq.11 can be expressed as

        N*/A = 1.025*10⁷(T_star/T)²/ Ö[ln(T_star/2T)]   (photon/sec)/cm²         (12)

The variable T is the blackbody temperature of the received Cosmic Background Radiation, and the parameter T_star is the equivalent blackbody temperature for the spectra of the distant stars. We assume that T_star is the blackbody temperature of the sun, which is 5770 ° K. This photon rate per unit area of Eq. 12 is plotted as the solid curve in Fig. 2-1 versus the received blackbody temperature T. The parameter T_star is set equal to 5770 ° K.

        The dashed curve in Fig 2-1 shows the photon rate of an ideal blackbody, which is related as follows to the blackbody temperature T:

        N*/A = 1.306*10¹¹ T³ (photon/sec)/(cm²-°K³)                     (13)

The photons radiated from an ideal blackbody are in thermal equilibrium with random motion of molecules at the surface of the blackbody. We postulate that this photon rate cannot be exceeded by blackbody radiation in space. Otherwise diffuse molecules would rapidly absorb this radiation. The two curves intersect at a temperature of 3.99 °K. Hence the analysis predicts that radiation from distant stars should produce Cosmic Background Radiation with a blackbody temperature of 3.99 degrees Kelvin. These stars are at a distance of 56 billion light years.

        The COBE satellite measured a blackbody temperature of 2.73 degrees Kelvin. Our computed value exceeds this measured value by 46 percent, which is remarkably good agreement.

        Our analysis would match the measured COBE temperature if the computed photon rate were decreased by a factor of 6.52. An important issue ignored in this analysis is the loss due to the absorption of radiated energy by diffuse molecules in space. The factor 6.52 is equivalent to a signal loss of 8.14 decibels. Since the radiation from distant stars travels over a distance of 56 billion light years, a total loss of 8.14 decibels is equivalent to an attenuation of only 0.145 decibels per billion light years. One light year is a distance of 9.47*10¹² kilometers, and so one billion light years is equal to 9.47*10²⁴ meters.

        The Yilmaz Cosmology Model predicts a density of matter equivalent to 9.6 hydrogen atoms per cubic meter, if we assume a uniform distribution of mass. It predicts a density of half this value if we assume a statistical distribution of point masses. The author initially endorsed the latter assumption, because he believed that most of the universe mass is contained within the stars. However, astronomical observations appear to show that there is very much more matter (in the form of diffuse molecules) in the enormous spaces between stars, than there is within the stars themselves. Hence the uniform distribution of mass seems a much better model.

        Let us consider a volume with a cross section of one square meter, and a length of one billion light years (9.47*10²⁴ meters). Assuming an average mass density equivalent to 9.6 hydrogen atoms per cubic meter, this mass within this volume would be equivalent to 9.09*10²⁵ hydrogen atoms. The mass of one hydrogen atom is 1.67*10^-24 gram. Hence the mass within this volume is 152 grams. Let us consider a volume one billion light years long with a cross section of one square centimeter. The mass within this volume would then be 0.0152 gram.

        Thus we ask: How much signal loss should we expect by feeding radiation through a volume, with a cross section of one cm², that contains a mass of 0.0152 grams in the form of diffuse ionized molecules? The answer to this question will indicate whether or not the signal attenuation is significant. A signal attenuation of 0.145 decibels within this volume would result in a predicted blackbody temperature for Cosmic Background Radiation that matches the COBE data