D.V. FursaevJINR, DubnaMysteries of

the Universe

Problems of the Modern Cosmology

facts about our Universe

mathematical model, Friedman universe

consequences, the Big Bang

recent observational data

problem of the dark energy and dark matter

inflation and the problem of initial data

plan of the lecture

What do we know about our Galaxy (Milky Way)?

diameter – 120 000 light years width - 6 500 light years

(1 light year is about 10 000 billions km)

Other facts:

Number of stars – 100 billions

Distance to the star which is closest to the Earth (Alfa Centauri) - 4,3 light years

Distance to a black hole which is closest to the Earth -1600 light years

Distance from the Earth to the center of the Galaxy -30 000 light years

What do we know about our Universe?

- Age – about 14 billions years

- Number of galaxies – 100 billions

- Average number of stars per galaxy - 100 billions

Key facts about the Universe

- the Universe is isotropic and homogeneous at scales -100 millions pc (1 pc = 3,26 light year), this scale is 1000 larger than the syze of a galaxy

- the Universe is expanding and the acceleration rate is increasing!

- the Universe is filled with a highly homogeneous cosmic microwave backgrond radiataion (CMBR) with temperature 2.7 K

Mathematical model: Friedman Universe

2 2 2 2

22 2 2 2 2

2

18

2

( )

(sin )1

0

1

1

R g R GT

G

T

ds dt a t dl

drdl r d d

kr

k

k

k

-Einstein equations for gravitational field

-the Newton constant

-stress-energy tensor of matter

-space-time metric

-metric on a maximally symmetric space

-plane

-3-sphere

-Lobachevsky space

Friedman equations and their consequences (developed by A. Friedman in 1922-1924)

2

2

2/3

1/ 2

8

3

3( ) 0

0 ( )

1( )

3

k GH

a

aH

a

p

p w

p H

w a t t

w a t t

initial cosmological singularity- the Big Bang

- one of the Einstein equations

-Hubble parameter

- density of matter- pressure of matter

- equation of state- “conservation law”- flat Universe with a dust matter

- flat Universe with a radiation

the redshift factor – characteristic of a distance

In the Friedman universe all lengths grow proportionally to the scale factor

the wave length of the photons is stretched together with the scale factor

- the redshift factor

time of emission

time of observation

the wavelength of a photon at the time of emission

the wavelength of a photon at the time of observation

( )1 1

( )

o o

e e

o

e

o

e

a tz

a t

t

t

The Hubble law(1929)

The rate of the distance increase between galaxies due to expansion of the Universe is

V=H R=z c

H= 71 (km/s)/Mpc – the Hubble constant

R – the distance

E. Hubble(1889-1953)

The law is valid for “close” objectswith redshifts z << 1

consequences The expansion of the Universe and the presence of the cosmic

singularity indicate that the “young” Universe was very dense and very hot

When the temperature decreased the Univese underwent a number of phase transitions

At the temperature of the order of 1000 degrees the recombination of the ionized plasma occured and the matter became “transparent” for the radiation (“relic photons” or CMBR)

The temperature of the relic photons lowered during the expansion

Cosmic Microwave Background Radiation(discovered by A. Penzias & R.W. Wilson in 1965)

The spectrum of CMBR is

Planckian with the

temperature about 2,7 К(radioband)

It is important for physicists that the temperature distribution is slightly inhomogeneous

510T

T

fluctuations of the CMBR temperature

The power spectrum

the angular syze of a typicalinhomogeneity is 1 degreewhich is equivalent to l=200

«Snapshot» of the young Universe

(when it was 300 thousands years old)

CMBR data tell that the Universe is spatially flat (k=0)!

this yields the value of the density for the present

value of the Hubble parameter:

gramm /cubic meter

to compare: the mass of the proton is

gramm

250.8 10

241.6 10

23

8crit

H

G

This means that the average density of matter in the Universe is

beyond the Hubble law

Luminosity distance 1/ 2

0

4

( ) ( 1)( )

( ) ( )

( )1

( )

L

z

L

o

LD

F

L

F

dzD z z

H z

H z H t

a tz

a t

-luminosity of the object (totalenergy emitted per unit time)

-brightness of the object, asmeasured by an observer

redshift of the object

one can extract the information about the scale factor if the luminosity distance and the redshift of different objects

are known

How do we measure the (luminosity) distance to the most remote objects in the Universe?

We use supernovae as “standard candles”-the objects with the known luminosity

Quiz

the answer:

the question:

A supernova explosion

Remnants of a supernova (its explosion was observed by Kepler)

the redsift is aboutz=1

the universe expands with some acceleration (antigravity)

Acceleration means that the second derivative of the scale factor is positive

0a

To measure second and higher derivatives one needs information about expansion at large

distances (where the Hubble law does not hold)

4 4( 3 ) (1 3 )

3 3

1

3

a G Gp w

a

w

What is our Universe composed of?

1

M

M

crit

M MM

crit

M

-the density of an unknown form of matter which ensures acceleration, this matter is called “the dark energy”

-the density of matter with a usual equation of state

What are the proportions between the two forms of matter in the Universe?

0.7

0.3M

The mystery of the Universe:

Only 5 % of the Universe is composed of the known matter:

0,03 % - heavy elements (matter of planets)0,5% - stars0,3 % - relativistic particles (neutrino)4 % - free Helium and Hydrogen

MThe rest part of is directly unobservable form of matter (the dark matter)

How can we know about the existence of the «other» forms of

matter?

galaxy rotation curves

gravitational lenseing

observation of velocities of distant galaxies

Effects of gravity!

galaxy rotation curves

One could expect: the further the object from the center the slower its rotation

The observed behaviour

(NB: rotation velocity of the Solar System around the centerof the Milky Way is 250 km/s)

gravitational lenses

the gravitational field distorts trajectories of the light rays

effects of gravitational lenses

25% matter of the universe is concentrated in the

galaxies and galaxy clusters in the form which we cannot directly observe, this form of the matter is

called

«the dark matter»

Dark matter candidates?

Massive compact objects (black holes, white dwarfs?)

New stable particles weakly interacting with quarks, leptons, photons ...?

New physics at accelerators of the next generation?

the dark energy

homogeneously distributed throughout the Universe,

makes 70% of total density of the matter

Cosmological constant (negative pressure)?

Quintessence (a new field or a fifth essence)?

Modification of the Einstein theory at large distances?

The vacuum energy (equation of state with w=-1)

4

1 1

2 2vac bosons fermions

bosons fermions

vac

E w w

w

E

V

single-particle frequences

- the leading order

-is an ultraviolet cutoff associated to some physical scale

The problem

19

1/ 42

35 18

10

1000

100

310 10

8

QG Planck

SUSY

EW Z

DE Planck Z

m Gev

Gev

m Gev

Hm m

G

-a quantum gravity scale (?)

- a supersymmetry scale (?)

- the electroweak scale

- cosmological (dark energy) scale

inflation and the problem of “initial data” in the Friedman model

horizon problem

the problem of the size of the universe

the problem of flatness

horizon problem

for a power law expansion the part of the Universe (which became observable now) consists of a large number of casually independent regions;

Why (according to CMBR data) those regions are in thermal equilibrium?

size of the universe

if the size of the universe at the Planckian moment

was then the size of the

universe at the present time would be

43 3510 10Pl Plt s l m 410oL m

the problem of flatness

3010

cr

cr

-to get the density at the present moment close to the critical density

one has to finetune the density at the Planckian moment

the idea of inflation

very rapid expansion of the universe after the birth

2

( )

1

70

tH

Pl

Pl

p

a t e

Hm

t t

A.Guth, A.Linde,...

de Sitter-like stage after the birth

exponetial change of the scale factor

Hubble parameter is determined by the Planckian scale

after this time the universe may havethe Friedman evolution

Conclusions

next 10-20 years may become a revolutionfor our understanding of which the universe is made of