1. Harrison B. Prosper Florida State University YSP
Cosmology 1
Harrison B. Prosper
Florida State University
YSP

2. Topics Island Universes The Expanding Universe
The Universal Scale Factor
Models of the Universe
Summary

3. Cepheid Variables She deserved, but did not get, a Nobel Prize
Luminosity-Period Relation of Cepheid Variables
Henrietta Leavitt
1912
She deserved,
but did not
get, a
Nobel Prize
Figure 18–11 The period-luminosity relation of Cepheid variable stars. Long-period Cepheids have higher average luminosities than short-period Cepheids.

4. Island Universes 1924 – Edwin Hubble
Using the work of Henrietta Leavitt, Hubble measured the distances to several galaxies and found that they are immense star systems very far from Earth

5. The Expanding Universe
1929 – Red Shift
Drawing on his own observations and those of others, Edwin Hubble discovered that the red shift,
z = (o - e) / e
of the light from distant galaxies increases with distance D.
e = emitted wavelength
o = observed wavelength

6. The Expanding Universe
Hubble’s Law
v = H0 D
The Hubble Time
D = v T
D = (H0 d) T
T = 1/H0
For H0 = 70 km/s / Mpc
T ~ 14 billion years.
1 Mpc (Mega-parsec) = 3.26 x 106 light years (ly)

7. The Universal Scale Factor
D(t1)
t1 = past
a(t) is the scale factor
of the Universe
D(t0) λo
a = 1
t0 = today
a > 1
D(t2)
t2 = future
λe = a(t) λo
D(t) = a(t) D(t0)
z = (λo - λe) / λe
t is cosmic time

8. The Hubble Parameter t2 = future d(t2) a > 1
H(t) is called the Hubble parameter
The Hubble constant H0 is simply the
Hubble parameter H(t0) at the present epoch

9. Why Can We Assign a Cosmic Time?
We have learned that your now and my now do not coincide as we move relative to each other. However, since our relative speeds are small relative to c, it is a very good approximation to take our nows to be the same. The same is true for galaxies. Their motions relative to space are << c. Consequently, we can assign each galaxy approximately the same cosmic time.

10. Models of the Universe General Relativity
Einstein’s theory describes the evolution of spacetime. It can therefore be used to describe the evolution of the Universe
The Cosmological Principle (Albert Einstein)
The Universe is isotropic (looks the same in all directions) from every vantage point, at all times
Such a Universe is necessarily homogeneous, that is, contains matter and energy uniformly distributed

11. Distribution of Galaxies
APM Galaxy Survey,
Steve Maddox, Will Sutherland, George Efstathiou & Jon Loveday

12. Models of the Universe – II
The Friedmann-Lemâitre-Robertson-Walker Metric
This describes a universe in which the proper distance,
that is the distance between two events that are simultaneous
(dt = 0), changes with cosmic time, t. The proper distance D(t)
between simultaneous events in the Universe is given by
where t0 is the lifetime of
the Universe

13. How Far Is Far ? D0, t0 L = c (t0 – t1) D1, t1
t0 – t1 is the look-back time
d0 = D(t0) proper distance between galaxies now
d1 = D(t1) proper distance between galaxies then

14. Models of the Universe – III
According to Newton’s laws, the total
energy E of a galaxy of mass m at a
distance D is given by v D
where M is the total mass enclosed
within the sphere of radius D
writing
gives

15. Models of the Universe – IV
Alexander Friedmann
The Friedmann Equation
We can write this differential equation as
where

16. Models of the Universe – IV
Problem 7:
Using H0 = 70 km/s/Mpc, calculate the (critical) density
ρ0 in kg/m3 as well as in the number of protons/m3.
Calculate how much mass would be contained in a
volume equal to that of the Earth. Give the answer in kg

17. Models of the Universe – V
Since the Friedmann equation is a 1st order differential equation we can re-write it as follows where C is a constant determined by the initial conditions
where

18. Models of the Universe – VI
Georges Lemâitre
1927
Assume
Ω0 = 1
a(0) = 0
Ω(a) = Ω0 / a3
and remember that
a(t0) = 1
Problem 8:
Using the above, and H0 = 70 km/s/Mpc, calculate
the age of the Universe t0 in Gy according to the Lemâitre
model

19. Summary Expansion of Space
In 1929, Hubble discovered the expansion of the Universe.
The Friedmann Equation
This equation describes how the scale factor a(t) varies with cosmic time.
Different cosmological models give different predictions for a(t)