exchemist, **you have to **read this short article from NASA, of which I'll extract an excerpt.

There, you'll find ground for your position and I find ground for my position (and maybe we just have

a communication problem, and that's the basis of our differences).

https://map.gsfc.nas..._tests_cmb.html

I extracted from the article this picture, as I found it very didactical, among the complexities we are dealing here.

What I found as **extraordinary **is that this article is the first one from NASA (or ESA) that has the **courage**

to risk numbers about **the size of the universe when CBR started to permeate it**, from a site different from

academic places, where I found more daring and precise numbers.

Excerpt from the link provided above: **Tests of Big Bang: The CMB **------------------------------------------------------------------------

*The Origin of the Cosmic Microwave Background*

*One of the profound observations of the 20th century is that the universe is expanding. This expansion implies the universe was smaller, *

*denser and hotter in the distant past. When the visible universe ***was half its present size**, the density of matter **was eight times higher **

*and the cosmic microwave background ***was twice as hot**. When the visible universe **was one hundredth of its present size**, the cosmic

*microwave background ***was a hundred times hotter** (273 degrees above absolute zero or 32 degrees Fahrenheit, the temperature at

*which water freezes to form ice on the Earth's surface). In addition to this cosmic microwave background radiation, the early universe *

*was filled with hot hydrogen gas with a density of about 1000 atoms per cubic centimeter. When the visible universe ***was only one **

**hundred millionth its present size,** its temperature **was 273 million degrees **above absolute zero and the density of matter was

*comparable to the density of air at the Earth's surface. At these high temperatures, the hydrogen was completely ionized into free *

*protons and electrons.*

End of excerpt --------------------------------------------------------------------------------------------------------------------------------------------------

As far as I researched about theories for black bodies **being used currently in astrophysics **(as sacred dogmas), I found that

the three main theories (converted in laws, actually) were originated between Kirchoff's theorem (1859) and Planck's theory (1900).

During those 41 years, three theories (two of them with a Nobel Prize awarded to their authors) are:

1) Stefan's Law (or Stefan-Boltzmann Law): It is applied since 1877 to perfect black body surfaces (watts per square meter **units**).

2) Wien's Displacement Law: It is applied since 1893 to perfect black body cavities (peak micrometers **.** °Kelvin **units**).

3) Planck's Black Body Cavity Radiation Law: It is applied since 1901 to perfect black body cavities (Joules per cubic meter per Hertz **units**).

**1. Part of this post using the Wien's Displacement Law:**

Using NASA's article data:

Peak wavelength of CBR (380,000 years after the BB) = 2,900/3,000 micrometers = **0.9667 micrometers**.

Peak wavelength of CBR (13.7 billion years after the BB) = 2,900/2.75 micrometers = **1.05 millimeters**.

So, peak wavelength of the CBR has increased **almost 1,000 times **since it appeared. Explanations that are

given, relate this displacement to the expansion of the universe.

**2. Part of this post using the Stefan-Boltzmann's Law:**

*j** = **T*^{4}

where is **5.67x10**^{-8} Watt.m^{-2}.K^{-4}

At this link: https://physictheories.blogspot.com/ , there is a complete explanation of the three theories.

As **j** is power per unit area, it allows to calculate (astrophysics and industrial applications) the total power emitted by a perfect BB surface.

So,** j = P/A** and, in the case of the inner surface of an spherical shell, **j = P/(4.PI.r**^{2}), where r is the radius of the spherical shell.

It can be derived that

**P = (4.PI.r**^{2}),**.T**^{4}

and a quotient between two different values is (dividing side by side)

**P**_{M}/P_{N} = (r_{M}/r_{N})^{2} . (T_{M}/T_{N})^{4}

From NASA's article, we can write down the given data in a different form:

1) Visible universe (r_{1}: 13.7.10^{9} yl): density 10^{-5} atoms/cm^{3} and T_{1} = 2.73 ºK

2) Visible universe (r_{2}: 6.85.10^{9} yl): density 8.10^{-5} atoms/cm^{3} and T_{2 }= 5.46 ºK

3) Visible universe (r_{3}: 137.10^{6} yl): density: 1000 atoms/cm^{3} and T_{3 }= 273 ºK

4) Visible universe (r_{4}: 137 yl): density: 2.53 x 10^{31} atoms/cm^{3} and T_{4 }= 273 millions ºK

In this way, using Stefan-Boltzmann's Law, we can calculate (for the entire Universe):

P_{1}/P_{2} = (r_{1}/r_{2})^{2} . (T_{1}/T_{2})^{4 }= 2^{2} . 0.5^{4} = 0.25 (It means decrease in CBR energy, in joules per second units)

Atomic density decrease (per cm^{3}): 1/8

Missing parameter: Time elapsed between 1) and 2). If expansion was linear, the value is 6.85 billion years.

P_{1}/P_{3} = (r_{1}/r_{3})^{2} . (T_{1}/T_{3})^{4 }= 100^{2} . 0.01^{4} = 10^{-4} (It means decrease in CBR energy, in joules per second units)

Atomic density decrease (per cm^{3}): 10^{-8}

Missing parameter: Time elapsed between 1) and 3). If expansion was linear, the value is 13.56 billion years.

P_{1}/P_{4} = (r_{1}/r_{4})^{2} . (T_{1}/T_{4})^{4 }= (10^{8})^{2} . (10^{-8})^{4} = 10^{-16} (It means decrease in CBR energy, in joules per second units)

Atomic density decrease (per cm^{3}): 3.95 . 10^{-37}

Missing parameter: Time elapsed between 1) and 4). If expansion was linear, the value is almost 13.7 billion years.

------------------------------------------------------------------------------------------------------------------------------------------------

**CONCLUSION**: According to data supplied by NASA at the above link, the total energy of the initial CBR is **NOT A CONSTANT**.

Apparently, this energy is dissipating as time passes by, so the conclusion is: **The Universe doesn't behave as a perfect **

**black body cavity**.

**Maybe I'm wrong in my extrapolation of power into energy along the time passed**, but the application of **two out of the **

**three **fundamental laws for perfect black bodies is correct as they are widely used in astrophysics and cosmology.

The **third law for BBR **(Planck's one) could be applied in the form of a double integral of the spectral flux density (first in spheric space

units and then in Hertz units). The result has to be equal to the Stefan-Boltzmann's law (area under Planck's curve and over 4PI radians).

L_{ʋ}(ʋ,T) = (c/4).W_{u}(ʋ,T) = 2hʋ^{3}c^{-2}(e^{h}^{ʋ}^{/kT}-1)^{-1} [**units**: *Watt.m*^{-2}.Hz^{-1}.sr^{-1}]

Anyone can check this on the section Radiometric Quantities of the given blog link, which is unrelated with astrophysics or cosmology,

and deals only with theories of classic thermodynamics applied to black bodies.