Chapter 5 - The uniformity of the CMB modified 20110926

Introduction

The cosmic microwave background Go back to - Chapter 4 - Dark Matter

Go back to - Chapter 1 - Introduction The ellipse is the path of point that moves, so that the

Light acts the same, with the same geometry, with ellipsoidal mirrors. The two foci can be called the origin and the destination. Light leaves the origin as an expanding sphere and reflects at the ellipsoidal surface as a ring. It is a ring because it is the intersection of a sphere and ellipsoid. This reflection focuses the light on to the destination. The overall travel time from the origin, to reflection, to destination, is always the same for all angles of light departing from the origin.

If we retain the origin and destination and change to a luminous expanding sphere we can eliminate the mirror and reflection while keeping the geometry of the intersection of an expanding sphere and ellipsoid. The

A ray of **CMB** reaches us, after **two distinct intervals**.

The **first interval** starts at the center focus, at the origin, at point **o**, on figure 3. It is with the expanding and cooling spherical
shell, before the ray of CMB, which we will be observing, is emitted. Examples on figure 3; are the lines **oa**, **ob** and **oc**. The **temperature **and** watts/meter ^{2}**, of the expanding sphere is
proportional to the inverse square of the radius.

The **second interval**, is the travel of the ray of CMB through space, after it leaves the expanding spherical shell. Examples on figure 3; are the lines **ad**, **bd** and **cd**. It ends with the
reception of the CMB, at the observer at point **d**. The temperature and watts/meters^{2}, of the CMB during the second interval is also proportional to the inverse square of the
radius.

The two intervals always add up to, **c*age** meters in **age** seconds, in any direction the observer looks. For CMB emitted early in the cosmos, there is a shorter interval with the expanding
sphere, and a much longer path through space interval to reach the observer. For CMB emitted later, there is a longer spherical expansion interval, before the CMB is emitted, but a shorter path
through space interval to the observer. The expanding spherical shell, the CMB which it emits, and the CMB during its travel through space, all have a temperature proportional to, the inverse
square of the distance traveled from the origin, **o**.

When the radius of the cosmos was **oa**, it emitted CMB from the entire spherical surface. Only that from the ring, on the sphere at **aa**, will reach **d** at the same time, as the other rings on the
same ellipsoid. A similar argument can be seen in the rings bb and cc. All the CMB from the various rings, which intersect the ellipse, arrive at point **d**, at the same time and temperature. **oa +
ad = ob + bd = oc + cd = or = c*age**.

The formulas in the next section, show the relationship between radius and temperature in the CMB.

The temperature at point **a** when the cosmos was **1/4** its age and size was **5.4_K**.

The CMB arrived at point **d** **at 2.7_K** after expanding for **3/4** the age of the cosmos.

The temperature at point **b** when the cosmos was **1/2** its age and size was **3.8_K**.

The CMB arrived at point **d** **at 2.7_K** after expanding for **1/2** the age of the cosmos.

The temperature at point **c** when the cosmos was **3/4** its age and size was **3.2_K**.

The CMB arrived at point **d** **at 2.7_K** after expanding for **1/4** the age of the cosmos.

When one sees something, it is in terms of

The ** W/m^{2} times the area of the cosmos = wattage of the CMB**, because as we saw in figure 3, the temperature at point

The CMB has the luminosity of a

This is the same as

The CMB is emitted from the expanding radiant shell which is where light orbits at the perimeter of the Cosmos. The scattering of photons along this thin spherical shell is the source of the CMB. The light was accumulated as the Cosmos gained mass and light through the merging of Black holes. The energy emitted in 15 billion years by the CMB, if the energy output is constant, is **7.9E47_Watts*age = 3.7E65_J**. For comparison, the energy of the cosmos, **Mc*c ^{2}=1.7E70_J is
46,000 times bigger**. If the CMB is the remnant energy from the Big Bang, why is it so feeble? However, if the CMB is emitted instead throught the scattering of photons at the perimeter of the Cosmos then this small value of energy makes sense.

The gravitational and centrifugal accelerations on the photon in orbit are **c/age**. As the cosmos expands, the photons orbit at a larger radius and the orbital accelerations decrease. The rate
of change of the acceleration is **1/age ^{2}**. The

We can map the power of the CMB onto the smaller spheres and higher temperature when the cosmos was younger, as long as we keep well clear of infinities.

**(7.9E47/(5.5698E-8*4*pi)) ^{1/2} /(temperature_K^{2}) = radius in meters**

1.0615E27_m/(temperature_K^{2}) = radius in meters

The radius, of the expanding sphere of the shell, is proportional to the inverse square of the temperature.

The following examples map temperature and radius.

At a temperature of

Another way of looking at it is;

Conclusions

A ledger might have beliefs on the left side, and evidence for those beliefs on right side. The dynamics described here are mathematically consistent beliefs, which don’t require
physical infinities. The evidence is the values presented by the mass, radius and density of the cosmos, uniformity of the CMB, the flat rotation curves of galaxies and prevalence of dark
matter. All the parts slip together seamlessly, and the dynamics locks all the parts together. There are no free parameters which might be adjusted to reflect a point of view.
References

- Ellipse graphic @ http://blackholeformulas.com/files/ellipse2.png
- Polarized in a non-random direction @ http://www.spie.org/web/oer/june/jun97/axis.html
- WMAP satellite @ http://map.gsfc.nasa.gov/m_mm.html