Andrzej RadoszInstitute of Physics

Wroclaw University of Technologyaradosz@if.pwr.wroc.pl

A (very) Short Story of the Big Bang

1. Introduction: night sky’ paradox2. How big is Universe?3. Hubble’s discovery4. Three principles5. Scale parameter 6. Closed , open or flat.7. How old is Universe?8. What was before Big Bang?9. 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 bright1821 - 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. How big is Universe

1. Solar system: Planets and the Sun2. Stars3. Milky Way4. Galaxies5. Clusters and Super-clusters of galaxies6. Cosmological principle

                                                                                    

                

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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

                                                                                 

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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.

                                                                               

                 

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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.

Large Magellanic Cloud165 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

                                                                                               

    

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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 FieldAlmost 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 Earthv=Hr(Hubble constant H=50-100 km/s/Mpsc)

1946 - F. Hoyle: “big bang” - beginning of the Universe1948 - 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 whichcorresponds 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?

KT 73.20 KT 73.20

KTs 3000

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,

910

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 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

ta

This scale parameter is determined by a dynamical equation. That equationcomes out from equations of general relativity

tata

H

Hrtata

tatatr

dt

tdrv

tatrtatr

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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) - the expansion will be stopped and contraction will follow

2. Open (k=-1) - expansion will not be stopped3. Flat (k=0) - 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?

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

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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:

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

stP4310

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 singularitybecause 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.

VIII. What was before Big Bang?

IX. Expanding forever?GTR claims that

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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 oneuniverse reminds three dimensional hyperboloid in four dimensional spaceexpansion will not be stopped it will continue forever

c) Flat k= 0, density is equal to the critical valuegeometry of the universe is Euclidean one but the space is expanding

C

C

C

IX. Expanding forever?

325 /10 mkgC

(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 ?

327 /10 mkg