More on time, look back and otherwise

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More on time, look back and otherwise
t in R(t) starts from beginning of big bang
Everywhere in universe starts aging
simultaneously
Observational consequences gt
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An object at high redshift 1z 1.5 (for
example) R(t0)/R(t) 1.5 where t age of
universe when the light we are just seeing now
left the object If this is galaxy, and we assume
all galaxies formed at the same t in the
universe, then The galaxy we observe at 1z 1.5
is younger than ours (we are at t t0) and must
be younger than other galaxies formed at the same
time but seen at lower 1z This assumes an
expanding universe and a finite speed for light
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General consequence observing to higher and
higher 1z is like time travel to a younger and
younger part of the universe.
Look back to 1z 1000 see universe just
beginning to form clumps which will evolve into
galaxies and clusters of galaxies (see slide 6
for age versus 1z)
As universe ages and expands, the part of the
brick wall we were observing now has aged and
becomes transparent gt the material just behind
it becomes the new brick wall!
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We see more and more of Universe as time goes on
until acceleration makes effective redshift too
high for us to see the light
The part behind the brick wall in this model was
younger. This is why when it ages, it evolves to
the t of the brick wall and becomes the new brick
wall. Since time itself is moving forward, R(t0)
is now larger and so the 1z we observe the brick
wall at is less and the universe is cooling off!
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Can see OK, from brick wall
Cant see this because behind the brick wall
brick wall
Behind brick wall
Think of needing to lead a moving target to hit
it with a gun
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Another Example Assume we have 3 planets in row
separated by 25 light years each A 25 lt yrs
B 25 lt yrs C
Assume A and C can watch a patch of ground
continuosly
B sends out a signal at the speed of light to
plant an acorn. Somebody at both of these patches
has an acorn the signal. Assume C is Earth and
the signal is received in 1908
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Assume also people on both A and C plant the
acorn when they receive the message
In 1908 we will still see on A bare ground
because it takes it takes 50 years for light to
get here, so we wont see the acorn planting
until 1958. Now you, are born circa 1981-1984
when you see the tree on A to be 23-26 years old
while your tree is 76-73 years old! gt The tree
on A looks younger. gt Look at high 1z, look
far away, see younger (on average) galaxies
(assumes galaxies arent forming now
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Now the standard fare
Einsteins model of the universe geometry is
defined by mass
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Prologue
Assume General Relativity works
gt Tests!
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Prologue (cont)
Deflection predicted for star light as it passes
close to the sun with ordinary physics gives
wrong answer by factor of 2 Equate energy to
mass and calculate orbit using Newtons law of
gravity gives wrong answer GR gets it right
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Prologue (cont)
No deflection if no gravity
Deflection due to gravity, angle twice as large
due to GR
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Prologue (cont)
Use a solar eclipse!
Very first try may have fudged results, but
truly verified and it does give the factor of two
larger effect predicted by GR.
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Prologue (cont)
Another effect The motion of Mercury about the
sun is affected by GR in a noticeable way because
Mercury is so close to the sun.
The effect is called the precession of the
perihelion.
The direction of its axis changes at the rate of
43 (arc seconds)/century

Sun
Mercury
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Prologue (cont)
gt GR seems pretty good
Move on
Cosmological Principle The Universe is
homogenous and isotropic, i.e. everywhere is the
universe is the same as everywhere else and all
directions are the same
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Distance measure
The path of light (a geodesic the most direct
shortest) Define a proper time to travel
between two points is calculated from
dt2 (cdt)2-(dx2 dy2
dz2) 0 for light
Never mind the books comments of the LONGEST path
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Roberston-Walker Metric
Use dt 0 and space-time curvature and
get (cdt)2 R2(t)(dr2/(1-kr2)
R(t) is the scale factor of universe
If we take r 0 to be here, then r not 0 is
the coordinate of a point relative to us and
R(t)r is the distance (not corrected for rapid
near c 0.1 c velocity of recession
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If know R(t) as function of t and can calculate
distance.
The time we use is the time at R since the big
bang see slide 6 for relationship between 1z
(R(to)/R(t)) and t
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Comments on math and notation
d in front of symbol indicates that this is a
small (enough) change in that variable that if
something is changing as variable (or thing) ,
the change is negligible over that small change.
Also we some times write this with a dot above
the variable instead as in R

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Comments on notation continued
Example velocity ds/dt change in distance
with respect to time or v s

And if there is no acceleration, then v s/t or
vt s or velocity x time distance
Expanding surface, take into account the
geometry of the surface and the time!
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Co-moving coordinates and Redshift
R(10-43 sec)r 10-43 x c at the beginning
R(today)r 13 billion years x c 1.2 1028 cm
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Co-moving coordinates and Redshift
So, R(to)r/R(10-43 sec)r 15x109 x 3.17x 107
/10-43 to get all in seconds, and remember the
co-moving rs cancel out about 5 x 1060
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Key features and concepts
R(t) is the scale factor for this surface.
little r only tells us relative distances R(t)
sets the scale
k is the curvature that weve used before
we see something bad happens when k is equal to
1 and r 1! gt