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A (very) Short Story of the Big Bang
Andrzej Radosz
Institute of Physics
Wroclaw University of Technology
[email protected]
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Introduction: night sky’ paradox
How big is Universe?
Hubble’s discovery
Three principles
Scale parameter
Closed , open or flat.
How old is Universe?
What was before Big Bang?
WHAT IS THE FATE OF THE UNIVERSE?
I.
Night sky - paradox
1692 - I. Newton: the Universe is infinite otherwise it should
have collapsed (gravitational attraction)
1736 - E. Halley: the Universe is finite otherwise the night
sky should be bright
1821 - W. Olbers: in the infinite, homogenous universe
energy reaching the Earth should be infinite (night
sky paradox)
1990 - S. Hawking: at the beginning of the XX century the
night sky- paradox was the only cosmological
observation
II.
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How big is Universe
Solar system: Planets and the Sun
Stars
Milky Way
Galaxies
Clusters and Super-clusters of galaxies
Cosmological principle
Eerie, dramatic pictures
from the Hubble
telescope show newborn
stars emerging from
"eggs" — not the
barnyard variety — but
rather, dense, compact
pockets of interstellar
gas called evaporating
gaseous globules
(EGGs). Hubble found
the "EGGs,"
appropriately enough, in
the Eagle nebula, a
nearby star-forming
region 7,000 light-years
from Earth in the
constellation Serpens
View all images
One of the nearest
globular star
clusters, called
NGC 6397,
resembles a
treasure chest of
glittering jewels.
The cluster is
located 8,200
light-years away
in the
constellation Ara.
View all images
Stellar swarm, M80
(NGC 6093), one of
the densest of the
147 known globular
star clusters in the
Milky Way Galaxy.
Located about
28,000 light-years
from Earth, M80
contains hundreds
of thousands of
stars, all held
together by their
mutual gravitational
attraction.
View all images
Large Magellanic Cloud
165 000 LY
NGC 1313, (13.5 M light years)a bright but rather isolated galaxy classified as a
barred spiral galaxy (although with very short and irregular spiral arms). This
galaxy has recently (within the past billion years) collided with a satellite galaxy,
and the material at the bottom-right of this picture are the remains of the
satellite galaxy.
Spiral galaxy NGC 4414
19.1 megaparsecs 60 M LY
Our galaxy is just one of thousands that lie within 100 million
light years. Galaxies tend to cluster into groups, the largest
nearby cluster is the Virgo cluster a concentration of several
hundred galaxies which dominates the galaxy groups around it.
Collectively, all of these groups of galaxies are known as the
Virgo Supercluster. The second richest cluster in this volume of
space is the Fornax Cluster, but it is not nearly as rich as the
Virgo cluster.
Number of galaxy groups within 100 million light years = 200
Number of large galaxies within 100 million light years = 2500
Number of dwarf galaxies within 100 million light years = 25000
Number of stars within 100 million light years = 200 trillion
The Virgo Cluster
The Virgo cluster is a massive cluster of galaxies which
dominates the Virgo supercluster. There are roughly 2000
galaxies in this cluster (although ninety percent of them are
dwarf galaxies). This cluster has a diameter of approximately
15 million light years which is not much larger than our Local
Group but it contains fifty times the number of galaxies.
It is not possible to get a good photograph of the entire Virgo
cluster because the galaxies are rather faint and small objects
scattered across 15 degrees of the sky. Below is photograph of
the centre of the cluster showing the inner 4°x4° region. Most
of the brightest objects in this picture are galaxies. The
elliptical galaxy in the centre is M87. On the right can be seen
two other large elliptical galaxies - M86 and M84. To the left of
M87 is another large elliptical galaxy M89 and above M89 is
the large spiral galaxy M90.
M87 from the Hubble Space Telescope
View all images
Hubble telescope was used to observe 19 galaxies out to 108 million lightyears. They discovered almost 800 Cepheid variable stars, a special class of
pulsating star used for accurate distance measurements. Here is a picture of
one of those galaxies. It is the spiral galaxy NGC 4603, the most distant galaxy
in which Cepheid variables have been found. It is associated with the
Centaurus cluster, one of the most massive assemblages of galaxies in the
nearby universe.
A rare and spectacular head-on collision between two galaxies appears in this Hubble
telescope picture of the Cartwheel Galaxy, located 500 million light-years from Earth in
the constellation Sculptor. The striking ring-like feature is a direct result of a smaller
intruder galaxy — possibly one of two objects to the right of the ring — that careened
through the core [close-up image at lower left] of the host galaxy.
Number of super-clusters in the visible universe = 10 million
Number of galaxy groups in the visible universe = 25 billion
Number of large galaxies in the visible universe = 100 billion
Number of dwarf galaxies in the visible universe = 10 trillion
Number of stars in the visible universe = 20 billion trillion
The Hubble Deep Field
Almost every object in this image is a galaxy typically lying 5 to 10 billion light years away.
The galaxies revealed here are all shapes and colors, some are young and blue,
whereas others are old, red and dusty.
It is probable that our universe is infinite and has been filled with
matter everywhere since the Big Bang There is also good
evidence that in the early universe that the universe may have
expanded much faster than the speed of light. It is possible to
inflate space so that although particles are not traveling fast, the
space between particles increases enormously.
The Visible Universe
III Hubble’s discovery
1929 - E. Hubble’s discovery : nebulae, the distant galaxies, similar to our
own Galaxy, Milky Way, are receding.
First cosmological law (Hubble’s law) : velocity of distant galaxy is
proportional to its distance from the Earth
v=Hr
(Hubble constant H=50-100 km/s/Mpsc)
1946 - F. Hoyle: “big bang” - beginning of the Universe
1948 - G. Gamow: the Universe appeared from the hot phase;
remnant of this transition should be a presence of the
radiation (blackbody radiation) of T=5K
1964 – A. Penzias and R. Wilson discovered a homogenous and isotropic
radiation, T=2.73 K, Cosmic Microwave Background
1993 – Wrinkles of spacetime
III. 1. Cosmic Microwave Background
Cosmic Microwave Background, CMB, was discovered by Penzias and
Wilson in 1964. This is isotropic and homogeneous radiation which
T0  2.73K blackbody radiation, i.e. radiation
corresponds to the
emitted by a black body of temperature T0  2.73K .
During the expansion the temperature of CMB diminishes inversely
proportionally to the size of/distances in the Universe.
In fact it was emitted 12 billion years ago when the Universe was
300 000 years old.
At that time the Universe was 1100 times smaller and CMB temperature
was 1100 times higher, Ts  3000 K .
At more early stages the temperature of that radiation was even higher.
What was its value just after Big Bang?
IV.
Three principles
1. Cosmological principle: the Universe is isotropic and
homogenous (in a large scale!)
2. The Universe is expanding according to Hubble’s law:
v=Hr
3. A ratio of an average number of photons (in CMB) to
the average number of protons equals one billion,
10 9
This is an entropy of the Universe;
(is it constant?)
V. Scale parameter
Einstein’s General Theory of Relativity
In the homogeneous and isotropic Universe there is only one timedependent parameter, which scales the distances, a t . The actual
distance between points (super-clusters of galaxies !) in the Universe is
proportional to this scale parameter

r t   at   r t   at 0
 a t 
dr t 
 rt   a t 0  
a t 0  Hr

dt
 at 
a t 
H
at 
v
This scale parameter is determined by a dynamical equation. That equation
comes out from equations of general relativity
VI. Closed, open or flat?
Homogeneous and isotropic universe is evolving according to the laws of
General Theory of Relativity (GTR). The prediction of that theory is that
there are three possible ways of the expanding universe
1. Closed (k=1)
2. Open (k=-1)
3. Flat (k=0)
- the expansion will be stopped and contraction
will follow
- expansion will not be stopped
- in between
The first case, k=1, corresponds to finite Universe – it has got a sense to
speak about a radius of Universe.
The other two cases are associated with an infinite Universe – a Universe
has always been infinite.
VII.
Hubble’s constant or how old the Universe is?
First estimation of the age of the Universe is an inverse Hubble constant:
1

 15  30 109 y.
H0
However, assuming that the matter domination era has been the
only period of the Universe history one finds a very precise (how
precise?) estimation of the age of the Universe expressed via Hubble
constant:
2
at   t 2 / 3  a t   t 1/ 3
3
a
2 1
 H 0  t0
a0
3
t0 
2
 10  20 109 y.
3H 0
VIII. What was before Big Bang?
Approaching to the original singularity, moment of creation, one can see
more and more dense, hotter and hotter plasma. This plasma should
eventually reach extreme stage at the initial moment t=0.
Before that, at the very early stage the special circumstances are reached,
at the so-called Planck’s time
t P  1043 s
At that time one came across the quantum limit of classical Big Bang
scenario. We could not continue our trip back in time to the initial singularity
because our tools (mathematical tools of general theory of relativity) should
be substituted by tools of quantum gravity. According to quantum gravity
(which in fact has not been yet fully designed) there is no time at all and
there is no sequence of events and there is no “before” or “after”.
At the Planck’s era there is no way to go before because there is no
such a meaning.
IX.
Expanding forever?
GTR claims that
8
Ga 2     C 
3
3
c 
H2
8G
kc 2 
Therefore, depending on k three scenarios for expansion are possible:
a)
Closed k = 1, density is larger than the critical,    C
universe reminds three dimensional sphere in four dimensional space;
expansion will be stopped and contraction will follow
b)
Open k = -1, density is smaller than the critical one    C
universe reminds three dimensional hyperboloid in four dimensional space
expansion will not be stopped it will continue forever
c)
Flat
k= 0, density is equal to the critical value    C
geometry of the universe is Euclidean one but the space is expanding
IX.
Expanding forever?
C  10
25
kg / m
3
27
3
(Luminous) Matter density is 1 proton per cubic meter, 10 kg / m
and is 1000 times larger than radiation (CMB!) density (energy density of
matter and radiation are compared). But it is still 5-10% of its critical value...
What our Universe is then: closed, open or flat ?