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A ( very ) Short Story of the Big Bang. Andrzej Radosz Institute of Physics Wroclaw University of Technology 1. Introduction: night sky’ paradox 2. How big is Universe? 3. Hubble’s discovery 4. Three principles 5. Scale parameter 6. Closed , open or flat.

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A (very) Short Story of the Big Bang

Andrzej Radosz

Institute of Physics

Wroclaw University of Technology

1. Introduction: night sky’ paradox

2. How big is Universe?

3. Hubble’s discovery

4. Three principles

5. Scale parameter

6. Closed , open or flat.

7. How old is Universe?

8. What was before Big Bang?



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



II.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


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.


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.


View all images

Hubble telescope was used to observe 19 galaxies out to 108 million light-years. 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

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


(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. Penziasand R. Wilsondiscovered 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

corresponds to the blackbody radiation, i.e. radiation

emitted by a black body of temperature .

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, .

At more early stages the temperature of that radiation was even higher.

What was its value just after Big Bang?


IV. Three principles

  • Cosmological principle: the Universe is isotropic and
  • homogenous (in a large scale!)
  • The Universe is expanding according to Hubble’s law:
  • v=Hr
  • A ratio of an average number of photons (in CMB) to
  • the average number of protons equals one billion,

This is an entropy of the Universe;

(isit constant?)


V.Scale parameter

Einstein’s General Theory of Relativity

In the homogeneous and isotropic Universethere is only one time-

dependent parameter, which scales the distances, . The actual

distance between points (super-clusters of galaxies !) in the Universe is proportional to this scale parameter

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
  • Closed (k=1) - the expansion will be stopped and contraction
  • will follow
  • Open (k=-1) - expansion will not be stopped
  • Flat (k=0) - in between

The first case, k=1, corresponds to finiteUniverse – it has got a sense to

speak about a radius of Universe.

The other two cases are associated with an infiniteUniverse – a Universe

has always been infinite.

vii hubble s constant or how old the universe is
VII. Hubble’s constant or how old the Universe is?

First estimation of the age of the Universe is an inverse Hubble constant:

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



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

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

  • Therefore, depending on k three scenarios for expansion are possible:
  • a) Closed k = 1, density is larger than the critical,
  • 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
  • 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
  • geometry of the universe is Euclidean one but the space is expanding

IX. Expanding forever?

(Luminous) Matter density is 1 proton per cubic meter,

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 ?