Nikolaus Copernicus

Cosmological Principle

Three Views of the CMB

We do not occupy a preferred place in the Universe (Copernican belief). Further, at a given time, the Universe looks homogeneous and isotropic to all observers as is supported by the smoothness of the cosmic microwave background (CMB) radiation.

Homogeneity and Isotropy of the Universe

Homogeneous means that in an average sense, the Universe looks the same to all observers regardless of location. This is true for the left hand figure in the left panel (the brick wall) but not for the right hand figure in the left panel (the diverging lines from the center of the image).

Isotropic means that the Universe appears the same in whatever direction one looks. If one is at the center of the figure on the right in the left hand panel, this is true and so the Universe appears isotropic for an observer at the center of this Universe. The figure on the left in the left hand panel does not appear isotropic for any observer!

The suggestion that the Univere is Homogeneous and Isotropic is consistent with the smoothness of the CMB (more on this later).

The CMB is 2.7 Kelvin to within 0.003 Kelvin everywhere

The Universe is homogeneous and isotropic on the scale of the CMB, but not on smaller scales such as this room, the Solar System, the Galaxy, and so on. We must specify the size of the region over which the Universe should be averaged. The scale over which the Universe should appear homogeneous and isotropic is not well-defined, outside of the requirement that it is large (e.g., see Abell 2218 , Hubble Deep Field Photograph Great Wall),

There is structure in the Universe, but it is small compared to the overall size of the Universe and so, in a sense, the imperfections can be averaged over ===> the Cosmologoical Principle is apparently valid on large scales.

The homogeneous and isotropic requirements are tough. The CMB is homogeneous and isotropic which causes problems. The CMB from regions in the Universe which are in opposite directions are not causally connected and so really have no reason why they should have the same properties. Why?

Speed of Light and Communication

Galileo performed an experiment to measure the speed of light (the maximum speed at which information can travel). The simple experiment was shown to the left. Because of the great speed at which light traveled, he could not measure the speed of light. Later, Roemer was able to measure the speed of light. Roemer determined the orbital periods of the Galilean moons of Jupiter (say Io). Consequently, he was able to predict when Io would come out of eclipse. He found that at points L and G, his predictions matched observation. However, at K and F, discrepancies arose. Were the observations early or late compared to the predicted times? From this observation, Roemer was able to determine the speed of light. Today, the accpeted value for the speed of light is c = 300,000 kilometers per second.

Heat Flow and the CMB

Because the fastest that information can travel through the Universe is limited by the speed of light, information does not propagate instantaneously from one point to another. See the picture of a bar heated on one end shown to the right. As the bar is heated at its right end, a finite amount of time is required for the energy to flow from one point to another. The heat flows in the sense that the bar tries to make everything come to the same temperature. This requires time because of the finite speed at which information travels. This fact makes the observation that the CMB is Homogeneous and Isotropic perplexing. Why?

Why is it perplexing that the CMB homogeneous and isotropic? When I look in one direction on the sky and observe the CMB, I see light that has traveled over the lifetime of the Universe to reach me. When I look behind me, in the opposite direction, I see light that has also traveled over the lifetime of the Universe to reach me. That is, the part of the Universe in front of me and the part behind me are so far apart that they have never been in thermal contact (and, in fact, in principle do not even know of the other's existence). Given this, how can they have the same temperature?

This problem is known as the Horizon Problem.

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