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Cosmology

Syllabus ----------------------------------------

--------------------------------------------------

--------------------------- Special theory of

relativity. General theory of relativity. Friedman

n universe models, Hubble constant, cosmological

red shift Elementary particles and

interactions. Modern cosmology, phases and

processes near after the Big Bang. Evolution of

the Universe with dark matter and dark

energy. -----------------------------------------

--------------------------------------------------

--------------------------

Cosmology

The study of the Universe at large, its origins

and evolution. It is distinct from cosmogony,

which is the study of the origin and evolution of

objects within the Universe, such as

galaxies. Although the roots of cosmology can be

traced back to ancient myths and legends, and the

Greek study of the way the planets move, modern

cosmology is essentially a mathematical

description of the behaviour of spacetime on the

largest scale, using equations derived from

Albert Einsteins general theory of relativity.

So the date on which modern cosmology was born

can be set very precisely, as 1917, the year

Einstein first applied those equations to

describe the Universe at large. Although some

theorists have developed alternative theories of

gravity and spacetime, which have led to

cosmological models different from those derived

from Einsteins theory, these alternative

cosmologies have now been ruled out by

observations. Within the framework of Einsteins

theory, there have been two great cosmological

hypotheses, the Big Bang and the Steady

State. Both these models conform to the

observational evidence that the Universe is

expanding as spacetime stretches, but in the big

bang model this is seen as evidence that the

Universe was born out of singularity a finite

time ago, while in the Steady State model it was

required that new matter should be created

continuously to fill the gap between the galaxies

as they moved apart, so that the overall

appearance of the Universe stayed the same.

Cosmology

The simple Steady State hypothesis has been found

to be incorrect, because there is now clear

observational evidence that the Universe changes

as time passes. This leaves a variety of possible

Big Bang models, which can be considered as

possible descriptions of the real Universe. To

within the limits of observational accuracy, our

Universe is indistinguishable from flat model

which obeys the laws of Euclidean geometry. This

is the simplest possible Universe allowed by

Einsteins equations.

Theory of the relativity

Newtons mechanics

Electromagnetic field theory

Special theoryof relativity

Gravitation

General theory of relativity

Relation between classical mechanics,

electromagnetic field theory and theory of

relativity

Special theory of relativity

Special theory of relativity Description of the

relationship and interactions between moving

object, developed by Albert Einstein early in the

20th century. The theory was first published in

1905, in a mathematical form based on equations

its implications can be more clearly visualized,

however, using a geometrical description of

events taking place In a fourdimensional

spacetime, first applied in this context by

Herman Minkowski in 1908. The special theory

gets its name because it applies only to be the

special case of objects moving at constant speeds

in straight lines that is, at constant

velocities. It does not deal with accelerated

motions, including the acceleration caused by

gravity. The later extensions of Einsteins

theory to deal with gravity and other

accelerations (the general theory of relativity)

developed the geometrical model of spacetime

further. The key features of the special theory

are that, from the point of view of an observer

who is regarded as stationary (in his or her own

inertial frame), time recorded on a moving clock

will run slow, a moving object will shrink in the

direction of motion, and the moving object will

gain mass. The speed of light is the same for any

observer in any inertial frame, no matter how he

or she is moving relative to the source of the

light, and it is impossible to accelerate an

object from below the speed of light up to the

speed of light. All of these predictions have

been tested and verified many times in

experiment. It is the special theory that says

that mass and energy can be interchanged in line

with Einsteins equation E0 m0c2 this too has

been confirmed by experiments.

General theory of relativity

General theory of relativity Theory of gravity

developed by Albert Einstein in the early part of

the 20th century, and presented to the Prussian

Academy of Sciences in 1915. Because gravity is

the dominant force in the universe at large

(thanks to its very long range), the theory is

also a theory of cosmology, and underpins all

modern models of how the Universe got to be the

way it is. Einsteins special theory of

relativity, published in 1905, deals with the

dynamical relationships between objects moving at

constant speeds in straight lines. It does not

deal with accelerations, or with gravity, which

is why it is called the special (meaning

restricted) theory. Einstein always intended to

generalize his theory to deal with accelerations

and gravity, but it took him ten years (not all

the time devoted exclusively to the general

theory) to find a satisfactory mathematical

description of the dynamics of the Universe and

everything in it. Indeed, the whole point about

Einsteinss theory is that it gives us a physical

picture of how gravity works Isaac Newton

discovered the inverse square law of gravity, but

explicitly said that he offered no explanation of

why gravity should follow an inverse square law.

The general theory of relativity also says that

gravity obeys an inverse square law (except in

extremely strong gravitational fields), but it

tells us why this should be so. That is why

Einsteins theory is better than Newtons even

thought it includes Newtons theory within

itself, and gives the same answers as Newtons

theory everywhere except where the gravitational

field is very strong.

Practices, demonstrations

Practices in special theory of relativity -

Lorentzs transformation, Lorentzs matrix,

relativistic factor, Practices in general

theory of relativity - description of the curved

spacetime, metric tensor, Schwarzschilds

solution,

some demonstrations http//demonstrations.wolfram

.com/SchwarzschildSpaceTimeEmbeddingDiagram/

http//demonstrations.wolfram.com/GravitationVers

usCurvedSpacetime/ http//demonstrations.wolfram.c

om/BendingOfLightByAStar/

General theory of relativity

- Observed effects of general theory of relativity
- advance of perihelion
- of Mercury
- of binary pulsars
- deflection of light
- by Sun, observed first in 1919 by Arthur

Eddington - gravitational lensing, from stars (low

probability) and galaxies often observed - gravitational time dilatation
- gravitational redshift direct observed by

Pound Rebka experiment - atomic clock shift by flight experiments
- GPS in fact permanent operating general

relativity experiment - gravitational radiation
- indirect observations in binary pulsars

General theory of relativity

Advance of perihelion of Mercury The orbit of

Mercury around the Sun does not trace out the

same path every time, but shifts slightly from

one orbit to the next. Each orbit is an ellipse,

with the Sun at one focus of the ellipse. In each

orbit, at the closest approach of Mercury to the

Sun (perihelion), the ellipse shifts sideways by

a tiny amount. This advance of the perihelion was

predicted by Albert Einsteins general theory of

relativity but cannot be explained by Isaac

Newtons theory of gravity. The perihelion

precession of Mercury is 5600 arc seconds per

century. Newtonian mechanics, taking into account

all the effects from the other planets, predicts

a precession of 5557 seconds of arc per century.

In the early 20th century, Albert Einsteins

General Theory of Relativity provided the

explanation for the observed precession. The

effect is very small the Mercurian relativistic

perihelion advance excess is just 42.98

arcseconds per century, similar, but much

smaller, effects operate for other planets 8.62

arcseconds per century for Venus, 3.84 for Earth,

1.35 for Mars (http//en.wikipedia.org/wiki/Mercur

y_(planet))

In 1859, the French mathematician and astronomer

Urbain Le Verrier reported that the slow

precession of Mercurys orbit around the Sun

could not be completely explained by Newtonian

mechanics and perturbations by the known planets.

He suggested, among possible explanations, that

another planet (or perhaps instead a series of

smaller 'corpuscules') might exist in an orbit

even closer to the Sun than that of Mercury, to

account for this perturbation. (Other

explanations considered included a slight

oblateness of the Sun.) The success of the search

for Neptune based on its perturbations of the

orbit of Uranus led astronomers to place faith in

this possible explanation, and the hypothetical

planet was even named Vulcan. However, no such

planet was ever found. (http//en.wikipedia.org/wi

ki/Mercury_(planet))

General theory of relativity

Deflection of light One of first key tests of

the general theory of relativity which predicted

that light from a distant star passing close by

the Sun would be bent by a certain amount. The

only way to observe this is during an eclipse,

when the bright light of the Sun itself is

blocked by the Moon, and stars can be seen on the

sky around the eclipsed Sun. Albert Einstein

published his paper predictihg this effect in

1916, abd British astronomer Arthur Eddington

organiyed an expedition to observe the eclipse

from Principe, off the west coast of Africa,

while a second team observed it from Brazil.

Photographs of the positions of the stars near

the Sun on the sky were then compared with

photographs of the same part of the sky taken 6

months earlier, when the Earth was on the other

side of the Sun in its orbit and those stars were

visible at night. The comparison showed that the

stars photographed during the eclipse seemed to

have been shifted sideways slighthly by the

deflection of light by exactly the amount that

Einstein had predicted. In principle, this

deflection occurs whenever light passes near a

massive object, although usually the effect is

too small to be measurable. It is caused by the

curvature of spacetime associated with the mass.

A more extreme version of the same effect causes

the gravitational lens phenomenon, and in the

ultimate extreme light is trapped completely

within a black hole.

General theory of relativity

Gravitational time dilatation, gravitational red

shift Slowing down of clocks caused by a

gravitational field, as predicted by the general

theory of relativity.

?2

?1

F2

F1

(linear approximation)

With this effect must be for example calculated

also by GPS navigation system ?1 10,23000000000

MHz ?2 10,22999999543 MHz (also included

effect of special theory of relativity

transversal Doppler shift).

General theory of relativity

- Binary pulsars
- A binary pulsar exists when two neutron stars,

one of which is a pulsar, are in orbit around one

another, forming a binary star system. The term

is also used to refer to a pulsar in orbit about

any other star for example, a white dwarf. More

than twenty binary pulsars are now known, but

astronomers reserve the term the binary pulsar

for the first one to be discovered, which is also

known by its catalogue number, as PSR 191316.

This pulsar has provided the most accurate test

yet of Albert Einsteins general theory of

relativity, and is the most accurate clock yet

discovered. - The binary pulsar was discowered in 1974 by

Russell Hulse and Joseph Taylor, of the

University of Massachusetts, working in the

Arecibo radio telescope in Puerto Rico. - Measured effects
- advance of the perihelion
- time dilatation (STR effect)
- losing energy as a result of gravitational

radiation - Fro this results Hulse and Taylor won the 1993

Nobel Prize in Physics. - For other information see http//en.wikipedia.org/

wiki/PSR_B19132B16

Equivalence principle

Equivalence principle That the effects of

acceleration are indistinquishable from the

effects of a uniform gravitational field. This

equivalence results from the equivalence between

gravitational mass and inertial mass. It led

Albert Einstein to the development of general

theory of relativity, when he realized that a

person falling from a roof would not feel the

effects of gravity the acceleration of their

fall would exactly cancel out the feeling of

weight.

Acceleration is equivalent to a uniform

gravitational field

In modern language, the equivalence is best

described in terms of a spaceship being

accelerated through space by constant firing of

its rocket motors. When the motors are not

firing, everything inside the spaceship floats

about in free fall, just as weightless as the

person falling from a roof. In principle, the

acceleration of the rocket could be adjusted so

that everything inside felt a force exactly as

strong as the force of gravity on Earth (or any

other strength you chose), pushing things to the

back of the vehicle as it moved forward through

space. Any scientific experiments carried out in

this accelerating frame of reference would give

exactly the same results as if the spaceship were

standing on its launch pad on Earth, and not

accelerating at all.

Schwarzschild metric

Eukleidian metric in kartesian and polar

coordinates

Schwarzschild metric (space out of spherical

symetrical spread matter)

Minkowski metric in polar coordinates (space

without matter or in special theory of relativity)

Where is the

Schwarzschild

radius.

You can see that the Minkowski metric is limit of

the Scwarzschild metric for for r gtgt rg.

Friedman metric

Friedman metric (space with matter regularry

spreded with constant density)

You can see that the Minkowski metric is limit of

the Scwarzschild metric for for r gtgt rg.

The final test

will take place the last week of semester, on

Tuesday 17.5.2001 at 1615 after the last

lecture, during the time for practise in the room

T2C2-81. Later you can only arrange the

alternative date and time of the final test with

me individually For other information see

http//www.aldebaran.cz/zacek/education/astroph

ysics_final_test.html 12 questions, each have 4

possibilities, maximum gain is 48 points,

Grading scale in per cent in per cent in points in points

Grading scale from to from to

Excellent (A) 90 100 43 48

Very good (B) 80 90 38 42

Good (C) 70 80 33 37

Satisfactory (D) 60 70 28 32

Sufficient (E) 50 60 24 27

Fail (F) 0 50 0 23