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Cosmology

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Title: Cosmology


1
Cosmology
2
Cosmology
Observation 1 universe is homogeneous and
isotropic at large scales
It cannot be stationary! It should expand or
contract
Observation 2 universe is expanding (Hubble)
It should have a beginning!
Hot or cold??
Observation 3 Cosmic microwave background
radiation
Hot Big Bang!
3
Observation 4 Abundance of light elements
Confirms Hot Big Bang
Fate of the universe depends on mass
distribution (or curvature)
Observation 5 density measurements
Observation 6 Fluctuations of background
radiation
Universe is nearly flat it contains dark matter
and dark energy
4
Problems with standard Big Bang model
Theory of inflation
Formation of structure Planck scale, Theory of
Everything
WHY our universe has the parameters that we
observe?
Anthropic Principle and beyond
5
Observation 1 universe is very inhomogeneous
and anisotropic at smaller scales
6
Groups
clusters
superclusters
7
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8
but homogeneous and isotropic at large
scale (The Cosmological Principle)
The universe is homogeneous. This means there is
no preferred observing position in the universe.
The universe is also isotropic. This means you
see no difference in the structure of the
universe as you look in different directions.
9
The Cosmological Principle
Considering the largest scales in the universe,
we make the following fundamental assumptions
1) Homogeneity On the largest scales, the local
universe has the same physical properties
throughout the universe.
Every region has the same physical properties
(mass density, expansion rate, visible vs. dark
matter, etc.)
2) Isotropy On the largest scales, the local
universe looks the same in any direction that one
observes.
You should see the same large-scale structure in
any direction.
3) Universality The laws of physics are the same
everywhere in the universe.
10
The universe cannot be stationary!
11
Conclusion the universe should either contract
or expand with decreasing speed, because the
gravity slows down the expansion
What is in reality?
12
Hubble and Humason 1931 Vrecession H0 R
The universe expands!
13
Hubbles Law
Distant galaxies are receding from us with a
speed proportional to distance
14
Necessity of the Big Bang
Velocity distance / time
The time of expansion is T 1/H0 14 billion
years
14 billion years ago all distances R were equal
to 0
Current value of the Hubble constant H0 ? 70
km/s/Mpc
15
Fig. 15-12, p.307
16
Olbers' Paradox and the Dark Night Sky IF the
universe is infinite, eternal, and static, then
the sky should be as bright as the surface of the
Sun all of the time! Heinrich Olbers (lived
1758--1840) popularized this paradox in 1826, but
he was not the first to come up with this
conclusion. Thomas Digges wrote about it in 1576,
Kepler stated it in 1610, and Edmund Halley and
Jean Philippe de Cheseaux talked about it in the
1720's. If the universe is uniformly filled with
stars, then no matter which direction you look,
your line of sight will eventually intersect a
star (or other bright thing).
Solved by finite size of the expanding universe
17
Olberss Paradox
Why is the sky dark at night?
If the universe is infinite, then every line of
sight should end on the surface of a star at some
point.
  • The night sky should be as bright as the surface
    of stars!

Solution to Olberss Paradox
If the universe had a beginning, then we can only
see light from galaxies that has had time to
travel to us since the beginning of the universe.
  • The visible universe is finite!

18
Newtonian model of the universe
Mass within radius r(t)
Energy per unit mass
Hubble law
19
Hubble constant changes with time!
20
Main equation
Critical density
Indefinite expansion
Expansion will be replaced by contraction
Indefinite expansion but with speed approaching
zero
Solution for k 0
21
T 2/3H0 9.5 billion years
But the age of globular clusters is 13 billion
years!
Fig. 15-12, p.307
22
Cosmology and General Relativity
According to the theory of general relativity,
gravity is caused by
the curvature of space-time.
The effects of gravity on the largest
cosmological scales should be related to the
curvature of space-time!
The curvature of space-time, in turn, is
determined by the distribution of mass and energy
in the universe.
Space-time tells matter how to move
matter tells space-time how to curve.
23
General relativistic models
Matter (mass, energy, pressure)
Einsteins equations
Geometry of space-time
24
The Expanding Universe
On large scales, galaxies are moving apart, with
velocity proportional to distance.
Its not galaxies moving through space. Space is
expanding, carrying the galaxies along!
The galaxies themselves are not expanding!
25
2D analogy with houses on the balloon
26
No center and no edge
Now add another dimension and you have our
situation. Just like there is not new balloon
material being created in the 2D analogy, new
three-dimensional space is not being created in
the expansion. Like any analogy, though, the
balloon analogy has its limits. In the analogy,
the balloon expands into the region around
it---there is space beyond the balloon. However,
with the expanding universe, space itself is
expanding in three dimensions---the whole
coordinate system is expanding. Our universe is
NOT expanding into'' anything beyond''.
27
The Expanding Universe (2)
Hubble law does not mean that we are at the
center of the universe!
You have the same impression from any other
galaxy as well.
28
Expanding Space
Analogy A loaf of raisin bread where the dough
is rising and expanding, taking the raisins with
it.
29
Raisin Bread
(SLIDESHOW MODE ONLY)
30
Cosmological redshift
31
General relativity picture
Galaxies are at rest in the comoving (expanding)
frame
Due to the presence of matter, the universe is
non-stationary all distances change scale
factor R(t) is a function of time
Curvature
32
Metric of the homogeneous and isotropic Universe
Robertson, Walker, Friedman, Lemaitre
Compare with metric for empty flat space
Scale factor R(t) describes expansion or
contraction
33
Finite, But Without Edge?
2-dimensional analogy Surface of a sphere
Surface is finite, but has no edge.
For a creature living on the sphere, having no
sense of the third dimension, theres no center
(on the sphere!) All points are equal.
Alternative Any point on the surface can be
defined as the center of a coordinate system.
34
k 1 positive curvature (sphere)
finite volume
k -1 negative curvature (saddle)
k 0 zero curvature (flat)
35
Shape and Geometry of the Universe
Back to our 2-dimensional analogy
How can a 2-D creature investigate the geometry
of the sphere?
Measure curvature of its space!
Flat surface
(zero curvature)
Closed surface
Open surface
(positive curvature)
(negative curvature)
36
p.309
37
p.309
38
p.309
39
The Necessity of a Big Bang
If galaxies are moving away from each other with
a speed proportional to distance, there must have
been a beginning, when everything was
concentrated in one single point
The Big Bang!
?
40
The Age of the Universe
Knowing the current rate of expansion of the
universe, we can estimate the time it took for
galaxies to move as far apart as they are today
Time distance / velocity
velocity (Hubble constant) distance
T d/v 1/H 14 billion years
41
Einsteins equations
Equation of state relation between pressure P
and energy density ?c2
? 0 for dust (no pressure)
? 1/3 for radiation (very hard pressure)
Critical parameter
42
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43
Hot or cold universe??
Any signatures of the past around us?
Microwave background radiation!
George Gamow (lived 1904--1968) predicted in 1948
that there should be a faint glow left over from
when the universe was much hotter and denser. The
entire universe would have glowed first in the
gamma ray band, then the X-ray band, then to less
energetic bands as the universe expanded. By now,
about 14 billion years after the start of the
expansion, the cold universe should glow in the
radio band.
44
George Gamow
Born 1904 in Russia Studied and worked at
St.-Petersburg University Fled Russia in
1934 Worked at GW University and University of
Colorado
Proposed the concept of the Hot Big
Bang Explained the origin of chemical elements
in the universe Built the theory of
radioactivity and explained the nucleosynthesis
in stars Proposed a concept of genetic code and
explained how the code is implemented in DNA by
the order of nucleotides
The cosmogenesis paper with Alpher (The origin
of chemical elements) was published as the
Alpher-Bethe-Gamow theory, Gamow had added the
name of Hans Bethe to make a pun on the first
three letters of the Greek alphabet, alpha beta
gamma.
45
Looking Back Towards the Early Universe
The more distant the objects we observe, the
further back into the past of the universe we are
looking.
46
Fig. 15-9, p.304
47
The Cosmic Background Radiation
The radiation from the very early phase of the
universe should still be detectable today
R. Wilson A. Penzias
Was, in fact, discovered in mid-1960s as the
Cosmic Microwave Background
Blackbody radiation with a temperature of T
2.73 K
48
Arno Penzias and Robert Wilson observed in 1965 a
radio background source that was spread all over
the universe---the cosmic microwave background
radiation. The radiation has the same intensity
and spectral character as a thermal continuous
source at 3 K (more precisely, 2.728 0.004 K)
as measured by the COBE satellite in every
direction observed. To a high degree of precision
the sky is uniformly bright in radio. The
uniformity of the background radiation is
evidence for the cosmological principle.
From 3000 K to 2.7 K The redshift of 1000!
49
Fig. 15-6c, p.301
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