Mysteries of D.V. Fursaev JINR, Dubna the Universe Problems of the Modern Cosmology
plan of the lecture 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
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
R 1 g 2 R 8 GT G T ds dt a () t dl 2 2 2 2 Mathematical model: Friedman Universe 2 2 dr 2 2 2 2 dl r (sin d d ) 2 1 kr k 0 -plane k k 1 1 -Einstein equations for gravitational field -the Newton constant -stress-energy tensor of matter -space-time metric -3-sphere -Lobachevsky space -metric on a maximally symmetric space
Friedman equations and their consequences (developed by A. Friedman in 1922-1924) 2 k H a a H a p p 2 w 8 G 3 3( p ) H 0 w 0 a( t) t 1 w a() t t 3 2/3 1/ 2 - 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 initial cosmological singularity- the Big Bang
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 z t t o e o at ( o) 1 1 at ( ) o e e time of emission time of observation e - the redshift factor the wavelength of a photon at the time of emission the wavelength of a photon at the time of observation
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 objects with 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 T T 10 5
fluctuations of the CMBR temperature The power spectrum «Snapshot» of the young Universe (when it was 300 thousands years old) the angular syze of a typical inhomogeneity is 1 degree which is equivalent to l=200
CMBR data tell that the Universe is spatially flat (k=0)! This means that the average density of matter in the Universe is this yields the value of the density for the present value of the Hubble parameter: 0.810 25 crit gramm /cubic meter 2 3H 8 G to compare: the mass of the proton is 1.610 24 gramm
beyond the Hubble law
Luminosity distance D L L L 4 F 1/ 2 -luminosity of the object (total energy emitted per unit time) F -brightness of the object, as measured by an observer z dz DL ( z) ( z 1) H ( z) H ( z) H ( t) 0 z at ( ) o 1 redshift of the object at () one can extract the information about the scale factor if the luminosity distance and the redshift of different objects are known
Quiz the question: How do we measure the (luminosity) distance to the most remote objects in the Universe? the answer: We use supernovae as standard candles - the objects with the known luminosity
A supernova explosion the redsift is about z=1 Remnants of a supernova (its explosion was observed by Kepler)
the universe expands with some acceleration (antigravity)
Acceleration means that the second derivative of the scale factor is positive a 0 a 4G 4G ( 3 p) (1 3 w) a 3 3 w 1 3 To measure second and higher derivatives one needs information about expansion at large distances (where the Hubble law does not hold)
What is our Universe composed of? M -the density of an unknown form of matter which ensures acceleration, this matter is called the dark energy M -the density of matter with a usual equation of state crit M M crit M 1 M What are the proportions between the two forms of matter in the Universe?
0.7 M 0.3
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% - stars 0,3 % - relativistic particles (neutrino) 4 % - free Helium and Hydrogen The rest part of M is directly unobservable form of matter (the dark matter)
How can we know about the existence of the «other» forms of matter? Effects of gravity! galaxy rotation curves gravitational lenseing observation of velocities of distant galaxies
galaxy rotation curves (NB: rotation velocity of the Solar System around the center of the Milky Way is 250 km/s) One could expect: the further the object from the center the slower its rotation The observed behaviour
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 Dark matter candidates? «the dark matter» 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) 1 1 E w w 2 2 vac bosons fermions bosons fermions w single-particle frequences E vac V 4 - the leading order -is an ultraviolet cutoff associated to some physical scale
The problem QG m Planck 10 19 Gev -a quantum gravity scale (?) SUSY 1000 Gev - a supersymmetry scale (?) EW m Z 100 Gev - the electroweak scale 2 1/ 4 3H 35 18 DE 10 mplanck 10 mz 8G - 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 43 35 t was then the size of the Pl 10 s lpl 10 m 4 universe at the present time would be L o 10 m cr cr 10 30 the problem of flatness -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 A.Guth, A.Linde,... very rapid expansion of the universe after the birth p a() t H t m 70t e 1 th 2 Pl Pl 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 have the Friedman evolution
Conclusions next 10-20 years may become a revolution for our understanding of which the universe is made of