## Sachs-Wolfe Effect

##
The Sachs-Wolfe effect refers to the statistical energy gain and loss of
photons as they pass through time dependent density pertubartions.

Suppose a photon enters a density perturbation. What happens? The photon
initally gains energy? To escape the density pertubration the photon has
to lose energy. If there is no change in the state of the density
pertubation, then there is no net change in photon energy.

But what happens if, during the photon transit time, the density perturbation
** decreases ** in amplitude. That means the photon has a smaller
density pertubation to climb out of, than the one it initially entered.
In this case, the photon experiences a net energy gain. In the opposite
case where the density pertubation ** increases ** in amplitude then
the photon experiences a net energy loss.

The end result of this will be an observed anistropy in the temperature
of the Universe (e.g. not all microwave background photons will have
exactly the same temperature). The temperature distribution of the photons
be modified by the statistical occurence of photons traversing density
enhancements. Now this does not happen to all photons, but since there
are so many photons per density enhancement, then many photons are subject
to this modification. This is what we measure in the WMAP data as
a temperature anisotropy.

The r.m.s. tempearture fluctuations as measured by WMAP are on the order
of 10^{-5}. This is very small, but its sufficient to produce
the observed large scale structure.

In addition, the angular scale over which the fluctuations are measured
is quite sensitive to the geometry of the Universe. The WMAP scale
strongly indicate that the Universe is flat. This is a critical Universe
where the total mechanical energy is 0. What is intriguing about this
situation, is that it seems there is now a need for "dark energy" to
help insure this condition of 0 total mechanical energy. Weird ...
(more on this weirdness later)

The WMAP Tempearture Flucuations:

Mapping the angular scale of the flucutations on to the large
scale geometery of the Universe.