Download Cosmology

ASTR 113 – 003
Lecture 12 April 19, 2006
Spring 2006
Introduction To Modern Astronomy II
Review (Ch4-5): the Foundation
1.
2.
3.
4.
5.
6.
7.
Sun, Our star (Ch18)
Nature of Stars (Ch19)
Birth of Stars (Ch20)
After Main Sequence (Ch21)
Death of Stars (Ch22)
Neutron Stars (Ch23)
Black Holes (Ch24)
Star (Ch18-24)
Galaxy (Ch 25-27)
Cosmology (Ch28-29)
Extraterrestrial Life (Ch30)
1. Our Galaxy (Ch25)
2. Galaxies (Ch26)
3. Active Galaxies (Ch27)
1. Evolution of Universe (Ch28)
(EXAM 3 on April 26)
2. Early Universe (Ch29)
ASTR 113 – 003
Lecture 12 April 19, 2006
Spring 2006
Cosmology:
The Origin and Evolution of the Universe
Chapter Twenty-Eight
Guiding Questions
1. What does the darkness of the night sky tell us about the
nature of the universe?
2. As the universe expands, what, if anything, is it
expanding into?
3. Where did the Big Bang take place?
4. How do we know that the Big Bang was hot?
5. What was the universe like during its first 380,000
years?
6. What is “dark energy”? How does the curvature of the
universe reveal its presence?
7. Has the universe always expanded at the same rate?
8. How reliable is our current understanding of the
universe?
Olbers’s Paradox:
Why is the night sky dark?
• If the universe is infinite in
space and time, and
static (the Newtonian
universe), Olbers
expected that the night
sky is bright, since one
would always see a star
in any direction
• The resolution: the
universe we can see is
finite
The universe is expanding
•The Hubble law: the more distance a galaxy, the greater its
redshift and the more rapidly it is receding from us.
v = H0 d
V: velocity in unit of (km/s)
D: distance in init of Mpc
H0, Hubble constant, ~ 71 km/s/Mpc, but not certain
The universe is expanding
•The receding motion of galaxies is due to the expansion of
the universe; the galaxies are locked into the space fabric
The universe is expanding
•Expansion is not an explosion; there is no center, and
there is no surrounding space
•Expansion involves all space
Cosmologic redshift
•Cosmologic redshift is caused by the expansion of space
itself
•Normal Doppler redshift is caused by the motion of objects
through space
Cosmologic redshit
•For example, observed redshift Z=1
z = (λ – λ0)/λ0
λ = 2 λ0
the wavelength is doubled
•It means that the universe has expanded by a factor of 2
during the period that takes light to travel from the emitting
galaxy to the Earth
•The larger the redshift, the greater the distance, and the
greater the travel time
•Lookback time: cosmological redshift is also an indicator of
the lookback time
e.g., Z=1, distance=5 billion light-year, lookback 5 billion years
Big Bang
• The universe is created by the Big Bang
• Big Bang is a cataclysmic event originated from a cosmic
singularity with infinite density
• The universe started its expansion after the Big Bang
• The Big Bang marks the beginning of time
• Before the Big Bang, the law of physics we know can not
apply
• After the Big Bang, space and time began to behave in
the laws of physics we know
The age of the Universe
• The age of the Universe is measured from the Big Bang
• It is approximately the time taking all galaxies back to the
singularity point at the expansion velocity, that is
– T=d/v
– Hubble law says v = H0 d
– T = d / H0 d or simply
– T = 1 / H0
T = 1 / 71 (km/s/Mpc) = 3.09 X 1019 / 71 = 4.4 X 1017 s
and 1 year = 3.16 X 107 s
• The age of our universe is 13.7 (+- 0.2) billion years
Cosmic Light Horizon
•We cannot see objects whose distance is beyond 13.7 lightyears because light from these objects has not had enough time
to reach us
•Cosmic light horizon is the surface of the sphere with a radius
of 13.7 light-years
•It defines the size of the observable universe, even the
universe itself may be even bigger, or infinite
Cosmic Microwave Background Radiation
•There is a background radiation in microwave in all
directions from the sky; the peak of radiation is about 1 mm
•Cosmic background radiation is virtually a blackbody with a
temperature of 2.7 K (or more accurately, 2.725 K)
Mass Densities of Matter and Radiation
• Mass density of matter (including dark matter) in our
universe (from observations of galaxy clusters) at present
day is about
ρm = 2.6 X 10-27 kg/m3
or about 1 single hydrogen atom per m3
• Mass density of radiation (2.7 K microwave) in our universe
at present day is about
ρrad = 4.6 X 10-31 kg/m3
• Because of E=MC2, radiation is equivalent to mass in
terms of energy
• At present day, the universe is dominated by matter
Evolution of Densities
• As the universe expands,
the volume gets bigger. As
a result, both density of
matter and density of
radiation decrease with
time
• At 2500 years after the Big
Bang (redshift Z=25000),
the two densities are equal
• Before 2500 years, the
universe is dominated by
radiation
• After the 2500 years, the
universe is dominated by
matter
Epoch 380000 years: era of recombination
• At 380,000 years after the
Big Bang (Z=1100), the
temperature of the universe
dropped to 3000 K
• Because photon ionization is
sufficient weak at this
temperature, electrons start
to combine with protons to
form neutral hydrogen atoms
• The time when the first
atoms formed is called the
era of recomnination
Epoch 380000 years: era of recombination
Epoch 380000 years: era of recombination
Cosmic background radiation is the
afterglow of the Big Bang
• The cosmic microwave background radiation,
corresponding to a temperature of 2.7 K at the present
day, is the greatly redshifted remnant of the hot
universe as it existed about 380,000 years after the Big
Bang
• During the first 380,000 years of the universe, radiation
and matter formed an opaque plasma called the
primordial fireball
• The microwave background radiation we see today are
the same photons of the Universe at 380,000 years
when the photons started to move freely in the
transparent universe.
Three possible types of the Universe
• Universe could be closed, flat and open
• What type the Universe could be depends on the density
parameter, the combined mass density ρ0 (including all
mass and energy) compares to a critical density ρc
• Critical density ρc = 9.5 X 10-27 kg/m3
• Density parameter Ω0 = ρ0 / ρc
Flat Universe
•Flat universe: parallel light beams remains parallel forever
converge
•Flat geometry
•Curvature of space is zero
•The sum of the three angles is equal 180 degree
•The combined density equals the critical density
•Density parameter equals 1
Closed Universe
•Closed universe: parallel light beams converge; if travel in
a straight line, you will return to your starting point
•Spherical geometry
•Curvature of space is positive
•The sum of the three angles is more than 180 degree
•Combined density larger than the critical density
•Density parameter is more than 1
Open Universe
•Open universe: parallel light beams diverge
•Hyperbolic geometry
•Curvature of space is negative
•The sum of the three angles is less than 180 degree
•Combined density less than the critical density
•Density parameter is less than 1
Cosmic background radiation reveals the
type of our universe
•Cosmic microwave background radiation shows very small
(1 over 10000) variations in the temperature across the
entire sky
•It has hot spots and cooler temperature regions
Our Universe is flat
•The theoretically predicted hot spot size (about 1 degree) is
very close to what is observed
•Therefore, our universe is flat, or density parameter is 1.0
Dark Energy
•The combined mass density should be equal to critical
density
ρc = 9.5 X 10-27 kg/m3
•The observed mass density of matter in our universe is
ρm = 2.6 X 10-27 kg/m3
• The
matter density parameter is 0.27
•The energy density parameter should be 0.73 in order to
keep the universe flat.
•However, the mass density of radiation is almost negligible
•Therefore, 73% of the universe is made of dark energy
State-of-the-Art of the Universe
•Age: 13.7 billion years
•Composition: 73% dark energy, 23% dark matter, 4%
ordinary matter
Key Words
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average density of matter
Big Bang
closed universe
combined average mass density
compression
cosmic background radiation
cosmic microwave background
cosmic light horizon
cosmic singularity
cosmological constant
cosmological principle
cosmological redshift
cosmology
critical density
dark energy
dark energy density parameter
dark-energy-dominated universe
density parameter
era of recombination
flat space
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homogeneous
hyperbolic space
isotropic
lookback time
mass density of radiation
matter density parameter
matter-dominated universe
negative curvature
observable universe
Olbers’s paradox
open universe
Planck time
plasma
positive curvature
primordial fireball
radiation-dominated universe
rarefaction
relativistic cosmology
spherical space
zero curvature