HW #14 (Due 12/11/09)_Answers
1) Explain why the Hubble constant tells us the age of the universe.
When we make a Hubble plot we plot recessional velocity on the y-axis and
distance on the x-axis. The data for galaxies is well represented by a straight line
in this plot. The equation for a straight line is y = mx + b , where m is the slope
of the line and b is the y-intercept. The galaxy data passes through the origin, so
b = 0 and if we replace the y with v and the x with d, the equation is v = md.
The slope is given the name the Hubble constant (Ho), since the slope is constant.
The equation is then
v = Ho d
This looks very similar to the normal velocity equation v = d/t , where
Ho = 1/t. In the case of the Hubble constant, t, is the time it would take for all
the galaxies in the universe to return to one single point. Or the age of the
universe. So the age of the universe is
tage = 1/Ho
2) Why is it necessary to introduce dark energy into our understanding of the universe?
In other words, how do we know dark energy must be real?
Today we are able to observe objects out to a distance where the Hubble relation is
no longer linear. If gravity is the only force that effects the expansion of the
universe, then we would expect to see that in the distant past the expansion rate of
the universe was faster than it is today. This is because gravity is attractive and
should act to slow the expansion. Instead, we find that the universe was expanding
more slowly in the distant past than it is today. The only way this can happen is if
there is a repulsive force in the universe that has overcome the attractive force of
gravity. This new universal repulsive force is called Dark Energy.
3) Why was it only possible for the big bang to create hydrogen and helium? Why not
all the rest of the elements that we see in nature?
This was a battle between the expansion of the universe and the temperature and
density that is needed to form new elements. In the first minute or so after the big
bang, protons and neutrons were unable to combine to make nuclei because the high
energy radiation would split the nuclei apart as soon as they formed. When the
expansion of the universe was great enough to lower the energy of the radiation, the
particles began to make helium. But this was very short lived, because the
expansion also lowered the density needed to fuse particles together. The
nucleosynthesis stage only last a couple minutes. Just long enough to make some
helium and a trace amount of Lithium.
4) What is the microwave background radiation and how is it related to the time of
recombination?
After nuclei formed, the universe was filled with light, nuclei, and electrons. The
light still had very high energy and would not allow the electrons to combine with
the nuclei to form normal, neutral matter. During this time, the free electrons acted
like particles and absorbed and re-emitted all wavelength of radiation. When the
universe had expanded to the point where the energy in the light dropped below the
ionization energy for the atoms, electrons combined with the nuclei to make normal
atoms. At this point the electrons acted like waves and could only absorb very
specific energies of light. The rest of the light from the Big Bang was free to move
through the universe and not interact with matter. The universe became
transparent. This radiation that was set free during the time of recombination, is
now seen as the microwave background radiation.
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