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INTRODUCTION TO

ALEXEY GLADYSHEV (Joint Institute for Nuclear Research & Moscow Institute of and Technology)

RUSSIAN LANGUAGE TEACHER PROGRAMME CERN, November 2, 2016 Introduction to cosmology

 History of cosmology. Units and scales in cosmology.

 Basic observational facts. Expansion of the . Cosmic microwave background radiation. and of the Universe.

 The Model. . Friedmann-Robertson- Walker metric. The Hubble law. Einstein equations. Equations of state. . Basic cosmological parameters.

 The history of the Universe from Particle physics point of view.

 The idea of . Problems and puzzles of the Big Bang Model.

 The Dark .

 Cosmology after 1998. The accelerating Universe. The and .

November 2, 2016 A Gladyshev “Introduction to Cosmology” 2 What is Cosmology ?

 COSMOLOGY – from the Greek κοσμος – the World, the Universe λογος – a word, a theory

studies the Universe as a whole, its history, and evolution

November 2, 2016 A Gladyshev “Introduction to Cosmology” 3 Cosmology before XX century

 ~ 2000 BC

Babylonians were skilled astronomers who were able to predict the apparent motions of the Moon, planets and the Sun upon the sky, and could even predict eclipses

 ~ IV century BC

The Ancient Greeks were the first to build a “cosmological model” within which to interpret these motions. They developed the idea that the stars were fixed on a celestial sphere which rotated about the spherical every 24 hours, and the planets, the Sun and the Moon, moved between the Earth and the stars.

November 2, 2016 A Gladyshev “Introduction to Cosmology” 4 Cosmology before XX century

 II century BC

Ptolemy suggested the Earth-centred system. Stars and planets rotate around the Earth. The model was very successful at reproducing the apparent motion of the planets.

November 2, 2016 A Gladyshev “Introduction to Cosmology” 5 Cosmology before XX century

 XVI century

Copernicus proposed a heliocentric system. The Earth rotated and, together with the other planets, moved in a circular orbit about the Sun. But the observational evidence of the time favoured the Ptolemaic system!

November 2, 2016 A Gladyshev “Introduction to Cosmology” 6 Cosmology before XX century

Tycho Brahe realised that if the Earth was moving about the Sun, then the relative positions of the stars should change as viewed from different parts of the Earth's orbit. But there was no evidence of this shift, called parallax. Either the Earth was fixed, or else the stars would have to be fantastically far away.

 Beginning of the XVII century

Galileo discovered Jupiter’s moons. And if moons could orbit another planet, why could not the planets orbit the Sun?

November 2, 2016 A Gladyshev “Introduction to Cosmology” 7 Cosmology before XX century

 Kepler discovered the key to building a heliocentric model. The planets moved in ellipses, not circles, about the Sun.

 Newton later showed that elliptical motion could be explained by his inverse-square law for the .

 1750

Thomas Wright noticed that the luminous stripe observed in the night sky and called the Milky Way could be a consequence of spatial distribution of stars: they could form a thin plate, what we call now a galaxy.

November 2, 2016 A Gladyshev “Introduction to Cosmology” 8 Cosmology before XX century

 At that time many faint and diffuse objects were known and listed. The generic name was nebulae. Soon after the proposal of Wright Emmanuel Kant suggested that some of these nebulae could be some other clusters of stars far outside the Milky Way.

 XIX century

Bessel finally measured the distance to the stars by parallax. The nearest star turned out to be about 15 million, million km away from the Earth! (The Sun is 150 million km away.)

November 2, 2016 A Gladyshev “Introduction to Cosmology” 9 Cosmology before XX century

 At the beginning of the century some observed the first spectral lines.

 1842 Johann Christian Doppler argued that if an observer receives a wave emitted by a moving body, the wavelength that he will measure will be shifted proportionally to the speed of the emitting body with respect to the observer

 1868 Sir William Huggings found experimentally that the spectral lines of some neighboring stars were shifted towards the red or blue end of the spectrum

November 2, 2016 A Gladyshev “Introduction to Cosmology” 10 Cosmology in the XX century

 1910-1922 Vesto Melvin Slipher discovered the red shift in galactic spectra.

 1916 discovered the General

 1922-1924 found solutions of Einstein equations which could describe the expanding Universe.

November 2, 2016 A Gladyshev “Introduction to Cosmology” 11 Cosmology in the XX century

 1929 Edwin Powell Hubble established that some of the nebulae in the sky were indeed distant galaxies comparable in size to our own Milky Way. He also made the remarkable discovery that these galaxies seemed to be moving away from us, with a speed proportional to their distance from us.

 1933 discovered the hidden mass in galactic clusters, later called “the ”

November 2, 2016 A Gladyshev “Introduction to Cosmology” 12 Cosmology in the XX century

 40’s of the XX century

Ralph Alpher, Hans Bethe, and others developed a hypothesis of the Hot Big Bang and predicted a cosmic microwave background radiation and calculated the relative abundances of the elements and helium that might be produced in a Hot Big Bang

November 2, 2016 A Gladyshev “Introduction to Cosmology” 13 Cosmology in the XX century

 1965

Arno Penzias, Robert Wilson discovered the pridicted cosmic microwave background radiation with a temperature around 3 К

 1979-1980

Alan Guth, Alexei Starobinsky, Andrei Linde, David Kirzhnitz suggested a hypothesis of inflating Universe

November 2, 2016 A Gladyshev “Introduction to Cosmology” 14 Cosmology in the XX century

 1986

Margaret Geller and discovered the large-scale structure of the Universe at distances 25-100 Mpc

 1992-1993

COBE (COsmic Background Explorer) satellite detected the first anisotropies in the CMBR: slight fluctuations in the temperature of the radiation, about 10-5 at scales 10°

November 2, 2016 A Gladyshev “Introduction to Cosmology” 15 Cosmology in the XXl century

 1998 Collaborations “Supernova Cosmology Project” and “The High-Z Supernova Search” discovered that at large scales the Universe expands with acceleration

 1998-2003 Missions BOOMERANG (Balloon Observations Of Millimetric Extragalactic Radiation ANd Geophysics) and MAXIMA (Millimeter Anisotropy eXperiment IMaging Array) confirmed that the geometry of the Universe is very close to the flat one

November 2, 2016 A Gladyshev “Introduction to Cosmology” 16 Cosmology in the XXl century

 2001-2010 A NASA Explorer mission WMAP (Wilkinson Microwave Anisotropy Probe) made fundamental measurements of cosmology. WMAP has been extremely successful, producing our new Standard Model of Cosmology. Full analysis of the data is now completed.

 2009-2015 Plank – a European Space Agency observatory – mapped the anisotropy of CMB at microwave and infra-red frequencies, with high sensitivity and small angular resolution. November 2, 2016 A Gladyshev “Introduction to Cosmology” 17 System of units in Cosmology

 The system of units one selects for a problem often reveals much about physics of the problem. In cosmology one uses the “natural” system

ck B 1

Plank Speed Boltzman constant of light constant

-1 -1  In this system [ ENERGY ] = [ MASS ] = [ TEMPERATURE ] = [ LENGTH] = [ TIME ]

1 GeV = 1.16  1013 К 1 К = 0.8  10–13 GeV 1 GeV = 1.8  10–24 g 1 GeV–1 = 2  10–14 cm 1 cm = 5  1013 GeV–1 1 GeV–1 = 6.6  10–25 s 1 s = 1.5  1024 GeV–1

November 2, 2016 A Gladyshev “Introduction to Cosmology” 18 Measuring distances / Parallax

 Units of length in cosmology: A is defined as the distance from the Sun which would result in a parallax of 1 second of arc as seen from Earth. The word "parsec" is an abbreviation and contraction of the phrase "parallax per second."

 1 pc = 3.262 light years = 3.086  1018 cm 1 Mpc = 106 pc

November 2, 2016 A Gladyshev “Introduction to Cosmology” 19 Scales in the Universe

 Stars – surrounding astronomical objects

30 Typical masses M ~ 1 – 10 M M= 2  10 kg

 Galaxies – the basic building blocks in the Universe

6 12 Typical masses M ~ 10 – 10 M

Typical size L ~ 0.1 Mpc

Typical distance D ~ 1 Mpc

November 2, 2016 A Gladyshev “Introduction to Cosmology” 20 Scales in the Universe

 Many galaxies are gravitationally bound to groups or clusters with 2 – 1000 galaxies. Big clusters are the biggest objects in the Universe bound by gravitation. Typical size L ~ 10 Mpc

 Conglomerations of galaxies – regions of space with higher than average

 On scales bigger than 100 Mpc the matter distribution is known to be homogenious

 The – the distant the light has travelled since the Big Bang, L ~ 104 Mpc – the biggest distance we can observe

November 2, 2016 A Gladyshev “Introduction to Cosmology” 21 Basic observational facts

The most important cosmological observations are:

 Expansion of the Universe

 Cosmic microwave background radiation

 Large scale isotropy and homogeneity

 Light element abundances in the Universe

November 2, 2016 A Gladyshev “Introduction to Cosmology” 22 Measuring velocities / The red shift

 Galaxies have a set of absorption and emission lines identifiable in their spectra, whose characteristic frequencies are well known.

 If a galaxy is moving towards us, the light waves get crowded together, raising the frequency, this is known as a .

 If the galaxy is receding from us, the characteristic lines move towards the red end of the spectrum and the effect is known as a .

November 2, 2016 A Gladyshev “Introduction to Cosmology” 23 Measuring velocities / The red shift

observed  emitted  observed  The red shift is defined by z   1 emitted emitted

 Due to the expansion of the universe the observed wavelenghts of photons coming from distant objects is greater than when they were emitted

 The red shift can be also used to describe time, distance and even temperature

November 2, 2016 A Gladyshev “Introduction to Cosmology” 24 Expansion of the Universe

 In 1929 E.Hubble

 measured red shifts of distant galaxies

 used the angular size as a measure of distance (he considered all galaxies had roughly the same physical size

 found a linear correlation between radial velocity away from us and the distance to the galaxy

 Hubble observation was correctly interpreted as mainly due to the expansion of the Universe.

November 2, 2016 A Gladyshev “Introduction to Cosmology” 25 Expansion of the Universe

 Hubble’s estimation was

v = HR H ~ 500 km sec-1 Mpc-1

now one usually uses

H ~ 70 km sec-1 Mpc-1

 The dependence of the red shift on the apparent magnitude has a universal character and does not depend on the type of the object, on the frequency of the emitted light or on the direction in the sky

November 2, 2016 A Gladyshev “Introduction to Cosmology” 26 Cosmic microwave background radiation

 In 1946 G. Gamow theoretically predicted the cosmic microwave background radiation. He knew that 3  The Universe expands d dI  The Universe is isotropic  exp 1 and homogeneous T

 The Universe was hot and dense, and reactions between particles were rapid enough. The system was in thermal equilibrium, characterized by a specific spectrum (Plank distribution for photons)

 Gamov’s estimation T ~ 10 K

November 2, 2016 A Gladyshev “Introduction to Cosmology” 27 Cosmic microwave background radiation

 In 1946 A.Penzias & R.Wilson observed a weak isotropic background signal at a radio wavelength of 7.5 cm, corresponding to a blackbody temperature T ~ 3.5 ± 1 K

 Nowadays, the photon spectrum confirmed to be a blackbody spectrum with a temperature

T ~ 2.725 ± 0.002 ± 7×10-6 K

 The cosmic microwave background radiation – the equlibrium spectrum of relic photons red-shifted to the present time November 2, 2016 A Gladyshev “Introduction to Cosmology” 28 CMB measured by COBE

THE CMBR SEEN BY COBE (COsmic Background Explorer)

Monopole radiation

T0 ~ 2.725 ± 0.002 K

Dipole radiation

T1 ~ 3.372 ± 0.014 mK

Quadrupole radiation

T2 ~ 18 ± 2 K

 The cosmic microwave background radiation is extraordinarily isotropic T/T ~ 10-5 K

November 2, 2016 A Gladyshev “Introduction to Cosmology” 29 CMB measured by COBE

A large diagonal asymmetry due to our motion with respect to the cosmic microwave background – the Doppler shift

The temperature fluctuations after subtraction of the velocity contribution, showing primordial fluctuations and a large radio signal from nearby sources in our own galaxy (the horizontal strip)

The primordial fluctuations after subtraction of the galaxy signal

November 2, 2016 A Gladyshev “Introduction to Cosmology” 30 CMB measured by WMAP

A large diagonal asymmetry due to our motion with respect to the cosmic microwave background – the Doppler shift

The temperature fluctuations after subtraction of the velocity contribution, showing primordial fluctuations and a large radio signal from nearby sources in our own galaxy (the horizontal strip)

The primordial fluctuations after subtraction of the galaxy signal

November 2, 2016 A Gladyshev “Introduction to Cosmology” 31 CMB measured by PLANK

A large diagonal asymmetry due to our motion with respect to the cosmic microwave background – the Doppler shift

The temperature fluctuations after subtraction of the velocity contribution, showing primordial fluctuations and a large radio signal from nearby sources in our own galaxy (the horizontal strip)

The primordial fluctuations after subtraction of the galaxy signal

November 2, 2016 A Gladyshev “Introduction to Cosmology” 32 CMB measurements

November 2, 2016 A Gladyshev “Introduction to Cosmology” 33 CMB measurements

November 2, 2016 A Gladyshev “Introduction to Cosmology” 34 Homogeneity and isotropy

 The isotropic microwave background tells us that the Universe in the past was very homogeneous

 Today it is not: we observe galaxies, clusters and superclusters

 However at large scales L > 100 Mpc the Universe is believed to be isotropic and homogeneous

November 2, 2016 A Gladyshev “Introduction to Cosmology” 35 Homogeneity and isotropy

 A thin slice through the Universe containing nearly 10,000 galaxies (according to the Center for astrophysics (CFA) redshift survey).

 The observer is situated at the narrow end of the slice. Distances radially outward indicate the observed redshift of a galaxy.

November 2, 2016 A Gladyshev “Introduction to Cosmology” 36 Homogeneity and isotropy

November 2, 2016 A Gladyshev “Introduction to Cosmology” 37 The Cosmological Principle

Theoretical basis of the Standard Cosmological Model:

 Cosmological principle

The Universe looks the same to all observers, that is the Universe is homogenious on large distance scales

November 2, 2016 A Gladyshev “Introduction to Cosmology” 38 The Cosmological Principle

 The cosmological principle can be summarized by two principles of spatial invariance:

 Translational invariance  homogeneity

In cosmology this means that galaxies are uniformly distributed through the universe, and this uniformity is independent of the location of the observer

 Invariance under rotations  isotropy

Different directions can not be distinguished, there is no special ones

November 2, 2016 A Gladyshev “Introduction to Cosmology” 39 The Standard Cosmological Model

Theoretical basis of the Standard Cosmological Model:

 Einstein’s general theory of relativity

The dynamics of the expanding Universe is described by the Einstein equations

 Classical description of matter

Matter is described by a classical ideal fluid (consisting of galaxies !)

November 2, 2016 A Gladyshev “Introduction to Cosmology” 40 Friedmann-Robertson-Walker metric

 The geometry of the space-time is described by metric

 Examlpes: 2 2 2  2-dimensional Eucledian space ds dx dy

2 2 2 2  3-dimensional Eucledian space ds dx1  dx 2  dx 3

 4-dimensional 1 0 0 0  4 0 1 0 0 2   ds g dx dx g  ,1 0 0 1 0  0 0 0 1

November 2, 2016 A Gladyshev “Introduction to Cosmology” 41 Friedmann-Robertson-Walker metric

 The most general metric satisfying the cosmological principle (isotropy and homogeneity), consistent with a spherical symmetry and allowing a uniform expansion of the Universe is the Friedmann – Robertson – Walker metric with the line element

2 2 2 2dr 2 2 2 2 ds dt  a( t )2  r d  sin  d   1 kr

Universal , which determines Constant, which characterizes the the physical size of the universe and spatial of the Universe describes its expansion k = 1 closed Universe k = 0 flat Universe a(t) is the only time-dependent quantity k = –1 open Universe

November 2, 2016 A Gladyshev “Introduction to Cosmology” 42 Friedmann-Robertson-Walker metric

 In matrix form it looks

4 2  ds  g dx dx ,1

1 0 0 0 2 at() 0 2 0 0 g  1 kr 0 0a22 ( t ) r 0  2 2 2 0 0 0a ( t ) r sin 

November 2, 2016 A Gladyshev “Introduction to Cosmology” 43 Friedmann-Robertson-Walker metric

2 2 2 2dr 2 2 2 2 ds dt  a( t )2  r d  sin  d   1 kr

 r,  and  are dimensionless ‘comoving’ polar coordinates, which remain fixed for objects that have no other motion than the general expansion of the Universe r dr  The measurable physical distance is R a() t  2 1/ 2 0 1 kr 

 For the flat Universe one simply has R a() t r

November 2, 2016 A Gladyshev “Introduction to Cosmology” 44 The Hubble Law

 Consider the case of the flat universe. The ‘physical’ velosity of an object in the 3-dimensional space is

dR a dr Peculiar velosity of the object, V  R  a The velosity with respect to the dt a dt ‘comoving’ coordinate system

 For zero peculiar velosity one immediately gets the Hubble law

All objects run away from each other a with velocities proportional to their distances V R H() t R a

 The Hubble law is valid at distances The Hubble parameter, L > 100 kpc which depends on time

November 2, 2016 A Gladyshev “Introduction to Cosmology” 45 Einstein Equations

 The dynamics of the expanding Universe is determined by

Einstein equations for the metric g (= for the scale factor a(t) )

Ricci Metric Scalar Newton Energy-momentum tensor tensor curvature constant tensor

1 R g R 8 GT 2  

The geometry is determined by its energy of the Universe content

November 2, 2016 A Gladyshev “Introduction to Cosmology” 46 Einstein Equations

 Matter / energy is described by the energy-momentum tensor T

 Consistency with the symmetry of the Friedmann-Robertson-Walker metric implies that T has a diagonal form

 Isotropy implies equality of spatial components of T

 The simplest realisation is the energy-momentum tensor of a perfect fluid

T  diag(,,,)  p  p  p

where (t) and p(t) are the matter/energy density and

November 2, 2016 A Gladyshev “Introduction to Cosmology” 47 Friedmann Equation

1  From the Einstein equations R  g R 8  GT 2  

one gets for ==0 the Friedmann equation

2 a k8 G 2 aa 3

 Friedmann equation shows how the scale factor evolves with time given the total density  (amount of energy and matter, and hence geometry), and curvature k

November 2, 2016 A Gladyshev “Introduction to Cosmology” 48 Friedmann equation (simple derivation)

 Consider the energy conservation law for a particle of mass m at the surface of an expanding sphere of radius R

Kinetic Potential enegy energy 4 G R3 m 1GMm 1 1 4 U mR2   mR 2 3  mR 2  G R 2 m 2RR 2 2 3 2 RGU82  Multiplying by 2 one gets 2 mR2 R3 mR

November 2, 2016 A Gladyshev “Introduction to Cosmology” 49 Friedmann equation (simple derivation)

2 RGU82 2 R3 mR

2U  Now recall that and denote we easily get R a() t r 2  k the Friedmann equation mr

2 a k8 G 2 aa 3

November 2, 2016 A Gladyshev “Introduction to Cosmology” 50 Matter and energy in the Universe

2  Matter and energy are convertible according to E  mc In our “natural” system Em 

Matter and energy density in the Universe can be classified into three species

 Dust (or non-relativistic matter) – particles with speed small compared with the (, electrons, etc.)

 Radiation – relativistic particles moving with the speed close to that of light (photons, neutrinos)

 Cosmological constant (the vacuum energy ? ) / Dark energy (the repulsive gravity ?)

November 2, 2016 A Gladyshev “Introduction to Cosmology” 51 Matter and energy in the Universe

 The μ=0 component of the conservation of the energy-momentum dT   0 dx

gives the 1st law of thermodynamics with a physical meaning:

The change in energy in a comoving volume element is equal to minus pressure times the change in the volume d()() a33 pd a

or equivalently d[ a33 (  p )] a dp

November 2, 2016 A Gladyshev “Introduction to Cosmology” 52 Equations of state

 The relation between density (t) and pressure p(t) for the homogeneous and isotropic perfect fluid is described by the equation of state. The simplest one is pw 

 Then for the density dependence on the scale factor one has

3(1w ) a  0  a0

November 2, 2016 A Gladyshev “Introduction to Cosmology” 53 Equations of state

 The equation of state for the non-relativistic matter has the form pw0 ( 0)

 An adequate description for 'matter-dominated Universe', t > 105 years

3 a  0  a0

 This can be interpreted as a mere dilution of a fixed number of particles in a 'comoving' volume due to the Hubble expansion

November 2, 2016 A Gladyshev “Introduction to Cosmology” 54 Equations of state

 The equation of state for the radiation is pw /3 ( 1/3)

 An adequate description of photons, massless neutrinos and, in general, for any type of particle if its kinetic energy is much greater than its rest mass 4 a  0  a0

 The extra factor of a(t) is due to the red-shifting of all wave lenghts by the expansion

November 2, 2016 A Gladyshev “Introduction to Cosmology” 55 Equations of state

 The equation of state pw  (   1)

describes the so-called vacuum energy

0 const

 In general there can be more complicated equation of state: there can be more than one type of material, or the combination of radiation and non-relativistic matter, etc.

November 2, 2016 A Gladyshev “Introduction to Cosmology” 56 Solution of the Friedmann equation

 The Friedmann equation

2 a k8 G 2 aa 3

now can be easily solved (for simplicity assume that the Universe is flat, k=0)

2 3(1w ) a88 G   G a 0  aa330 2 t 3(1w ) a() t a0  t0

November 2, 2016 A Gladyshev “Introduction to Cosmology” 57 Solution of the Friedmann equation

2 t 3(1w ) a() t a0  t0

 For the matter-dominated Universe (w=0) one has

2/3 aM ()/ t a00 t t 

 For the radiation-dominated Universe (w=1/3) the solution is

1/ 2 aR ()/ t a00 t t 

November 2, 2016 A Gladyshev “Introduction to Cosmology” 58 Cooling down with expansion

 The temperature of the present Universe is T ~ 2.73 K

 The CMBR has a black-body spectrum, therefore the energy density is

4 2 4 3 5 RB T   k/15 c

4  Comparing to   00  aa /  one may conclude that Ta1/

2 2  or, using a ()/ t  a t t 3(1  w ) we have 3(1w ) 00  Tt

 This implies that matter or radiation-dominated Universe should be hotter and smaller at earlier time.

 This is the main concept of the Hot Big Bang model

November 2, 2016 A Gladyshev “Introduction to Cosmology” 59 Time evolution of density

3(1w )  Putting together expressions  a for density evolution  0  a0

2 and for time dependence  t 3(1  w ) of the scale factor a() t a0  t0

one gets the expression for the time evolution of density

2 t  0  t0

regardless of the value of w (i.e. the same for matter and radiation)

November 2, 2016 A Gladyshev “Introduction to Cosmology” 60 The

 Consider again the time dependence of the scale factor

2 t 3(1w ) a() t a0  t0 Differentiating this equation with respect to time and dividing by a the Hubble parameter evolves with time as

21 Ht() 3(1 wt )

November 2, 2016 A Gladyshev “Introduction to Cosmology” 61 The age of the Universe

 Assuming that the Universe is matter-dominated (w=0)

2 Ht() 3t

and using the today value of the Hubble parameter

(the Hubble constant) H0=70 km/s/Mpc one can estimate the age of the Universe

2 17 10 t0 2.9  10 s  10 yr 3H0

Since dust has been dominating the Universe longer than other type of matter, therefore our approximation is quite reasonable

November 2, 2016 A Gladyshev “Introduction to Cosmology” 62 Basic cosmological parameters

 The Hubble constant – the today value of the Hubble parameter H0

determines the rate of the Universe expansion H0 =H(t0)

 The first measurement (Hubble - 1929) H ~ 500

 For decades the parameter H has been measured to be in the range 40 < H < 100, and later 50 < H < 80

 The most recent measurement (Plank, 2015) gives H = 67.3 ± 0.7

 A grain of salt: direct measurements give H = 73.00 ± 1.75

We have 3.2 σ discrepancy. Systematics or hint of new physics?

November 2, 2016 A Gladyshev “Introduction to Cosmology” 63 Basic cosmological parameters

 The critical density – the density corresponding to the flat Universe. From the Friedmann equation 2 a k8 G 2 aa 3 one has 3H 2   0 = 1.88 h2  10-29 g/cm3  10-29 g/cm3 c 8G which corresponds to a few protons per cubic meter

2 17 10  The age of the Universe. Our estimation t0 3  10 s  10 yr 3H0

is in agreement with recent (Plank) data: t0=13.81 0.03 billion years

November 2, 2016 A Gladyshev “Introduction to Cosmology” 64 Basic cosmological parameters

 Density parameters – ratios of contributions of different components (matter, radiation, etc.) to the critical density

2 i 3H0 ic   c 8 G

 Consider the Friedmann equation in the most general form (including the cosmological constant)

2 a k 8 G 2   aa33

November 2, 2016 A Gladyshev “Introduction to Cosmology” 65 Basic cosmological parameters

 Then we can define density parameters corresponding to the matter, radiation, cosmological constant, and even spatial curvature

88GG MR   MR 22   33HH00  k  2 k  2 2 3H0 a 0 H 0

 The Friedmann equation can be rewritten then in the form

4 3 2 22a0 a 0 a 0 H() a H0  RMK4   3   2   a a a

November 2, 2016 A Gladyshev “Introduction to Cosmology” 66 Basic cosmological parameters

4 3 2 22a0 a 0 a 0 H() a H0  RMK4   3   2   a a a

 For today (a= a0 , H = H0 ) it corresponds to the cosmic sum rule

1 RMK      

In the context of the Friedmann-Robetrson-Walker metric the total fraction of radiation, matter, curvature and cosmological constant must add up to unity

November 2, 2016 A Gladyshev “Introduction to Cosmology” 67 Basic cosmological parameters

 In the year 2000, two CMBR missions, BOOMERANG and MAXIMA confirmed that the Universe’s geometry should be very close to flat.

 The BOOMERANG result of 2001  1.02  0.05

 The most recent data (2015)

1   0.0008  0.004 i i

November 2, 2016 A Gladyshev “Introduction to Cosmology” 68 The Standard Model

 The Standard Model summarizes the current knowledge in particle physics. It is the gauge theory

based on the SU(3)c×SU(2)ew×U(1)y group and includes the theory of strong interactions (quantum chromodynamics) and the unified theory of weak and electromagnetic interactions (electroweak theory).

November 2, 2016 A Gladyshev “Introduction to Cosmology” 69 The Standard Model

 Particles of the Standard Model are three generations of fermions (quarks and leptons), gauge and Higgs bosons.

November 2, 2016 A Gladyshev “Introduction to Cosmology” 70 Grand Unification

 The idea of Grand Unification (Georgi, Glashow - 1970) is based on the observation that three gauge coupling constants of the Standard Model evolve according to the renormalization group equations towards the same point

 The gauge group is wider than the Standard Model one and includes the latter as a subgroup

November 2, 2016 A Gladyshev “Introduction to Cosmology” 71 Grand Unification

 Particles of the Standard Model belongs to the representations of the Grand Unification group

 Examples of GUTs:

SU(5) SO (10)

 New particles: heavy gauge and Higgs bosons, monopoles

November 2, 2016 A Gladyshev “Introduction to Cosmology” 72 Supersymmetry

 The idea of supersymmetry (Golfand, Likhtman, Volkov, Akulov, Wess, Zumino - 1972-1973) is to unify particles with different spins (bosons and fermions)

 Bosons and fermions belong to the same supermultiplets

 New particles – superpartners (usually heavy)

November 2, 2016 A Gladyshev “Introduction to Cosmology” 73 Supersymmetry

FERMIONS (s=1/2) BOSONS (s=0,1)

Quarks Electron, Muon, Tau Neutrinos

Photon Z-boson W-boson

Higgs

November 2, 2016 A Gladyshev “Introduction to Cosmology” 74 Supersymmetry

FERMIONS (s=1/2) BOSONS (s=0,1)

Quarks Squarks Electron, Muon, Tau Sleptons Neutrinos Sneutrinos

Photino Photon Zino Z-boson Wino Charginos W-boson Neutralnos Higgsino 1 Higgs 1 Higgsino 2 Higgs 2 November 2, 2016 A Gladyshev “Introduction to Cosmology” 75 The first instant

t < 10-44 sec  At the instant of the Big Bang T > 1032 K t = 0 , the Universe was E > 1019 GeV infinitely dense  =  and unimaginably hot T = 

 Cosmologists believe that all forms of matter and energy, as well as space and time itself, were formed at this instant.

 One cannot ask what came before and therefore "caused" it, at least not within the context of any known physics November 2, 2016 A Gladyshev “Introduction to Cosmology” 76 The first instant

t < 10-44 sec  The only meaningful statement 32 T > 10 K is that E > 1019 GeV The Universe, after a yet unknown initial stage, has

emerged at t ~ tPL with T ~ MPL

 And the question we can ask is

What conditions at that early time and what history thereafter would lead to the observed features of today´s Universe ?

November 2, 2016 A Gladyshev “Introduction to Cosmology” 77 Grand Unification era

t ~ 10-37 - 10-35 sec  The Universe is still very hot T ~ 1032 - 1029 K and filled with the particles E ~ 1019 - 1016 GeV predicted in the theories of Grand Unification - massless at first leptoquarks, and gauge and Higgs bosons

 GUT gauge group breaks down

to the SU(3)C×SU(2)EW×U(1)Y

 GUT gauge and Higgs bosons

aquire masses ~ MGUT

November 2, 2016 A Gladyshev “Introduction to Cosmology” 78 Grand Unification era

t ~ 10-37 - 10-35 sec  Production of topologically 32 29 T ~ 10 - 10 K stable extended objects - 19 16 E ~ 10 - 10 GeV monopoles, cosmic strings, domain walls, etc

 The strong interaction decouples and exists independently from now on.

 If there is supersymmetry supersymmetric partners also present

November 2, 2016 A Gladyshev “Introduction to Cosmology” 79 Electroweak phase transition

t ~ 10-10 sec  The Standard Model gauge T ~ 1015 K E ~ 100 GeV group SU(3)C×SU(2)EW×U(1)Y breaks down to SU(3)C×U(1)EM

 The electroweak interaction splits to weak and electromagnetic

 Gauge and Higgs bosons aquire

masses ~ MEW ~ 100 GeV

November 2, 2016 A Gladyshev “Introduction to Cosmology” 80

t ~ 10-4 sec  The electroweak baryogenesis - matter-antimatter asymmetry

 Quark confinement

November 2, 2016 A Gladyshev “Introduction to Cosmology” 81 Neutrino

t ~ 1 sec  The weak interactions have already decoupled and can not keep neutrinos in the state of thermal equilibrium

 Below the decoupling temperature neutrinos decoupled from the rest of the plasma, and their temperature continued to decay inversely proportional to the scale factor

 Estimations for the neutrino background temperature give

TK 1.95 November 2, 2016 A Gladyshev “Introduction to Cosmology” 82 Primordial nucleosynthesis

t ~ 1 sec – 3 min  Primodrial nucleosynthesis - T ~ 1010 - 109 K formation of the first nuclei. E ~ 1 - 0.1 MeV In a chain of nuclear reactions taking protons and neutrons and making Deuterium 2H, Helium 3He and 4He, and Lithium 7Li

 If the temperature of the Universe is greater than the binding energies of nucleons in nuclei ( >> 1 MeV ), the primordial plasma consists of protons and neutrons November 2, 2016 A Gladyshev “Introduction to Cosmology” 83 Electron-positron annihilation

t ~ 1 min  Electron-positron pairs annihilate and all their energy goes into photons

November 2, 2016 A Gladyshev “Introduction to Cosmology” 84 Electron-positron annihilation

t ~ 5 x 104 years  At this moment the densities of radiation and matter have the same value

 From this equidensity point the Universe is matter-dominated

November 2, 2016 A Gladyshev “Introduction to Cosmology” 85 Recombination

t ~ 105 years  The temperature of the Universe has decreased enough and electrons could become bound to protons to form neutral hydrogen

November 2, 2016 A Gladyshev “Introduction to Cosmology” 86 Photon decoupling. Formation of CMBR

t ~ 105 years  Photons are no longer interact with matter, since their energy is not sufficient to ionize atoms and there are no free electrons to interact with photons

 Photons are effectively decoupled and propagate freely.

 We observe them as the cosmic microwave backgroung radiation with T ~ 2.7 K

November 2, 2016 A Gladyshev “Introduction to Cosmology” 87 Large scale

t ~ 108 - 109 years  Small inhomogeneities generated during inflation have grown, via gravitational collapse, to become galaxies, clusters of galaxies, and superclusters

November 2, 2016 A Gladyshev “Introduction to Cosmology” 88 The present time

t ~ 1010 years  Formation of the Sun and the solar system

 Life on the Earth

November 2, 2016 A Gladyshev “Introduction to Cosmology” 89

Success of the Hot Big Bang Model

 The model is successful theory which passed crucial observationsl tests

 The expansion of the Universe. The expansion was discovered and it has an explanation within the Big Bang theory (the Hubble law)

 Cosmic microwave background radiation. The CMB was accidentally discovered and its spectrum is very close to the predictions

 Primordial nucleosynthesis. The predicted abundances of light elements in the Universe agree very well with observations

 The age of the Universe. The predicted age of the Universe is comparable with direct age measurements of objects in the Universe

November 2, 2016 A Gladyshev “Introduction to Cosmology” 91 Problems of the Hot Big Bang Model

 However, there are puzzles that can not be explained within the model

 Flatness (fine-tuning) problem. Why the Universe today is very flat ?

 Horizon (causality) problem. Different regions in the Universe never had causal contact in the past. Why the Universe (and CMBR) is homogeneous and isotropic ?

 Monopole problem. Particle physics predicts many exotic particles that could be created in the early Universe. Where they are ?

 Origin of structure problem. There is no mechanism to account for tiny density perturbations, the “seeds” of the large-scale structure

 Monopole problem. The Universe has passed through stages described by different theories, which predict some new particles and topological objects. Where they are ? November 2, 2016 A Gladyshev “Introduction to Cosmology” 92 Inflation

 Inflation is a general term for models of the very early Universe which involve a short period of extremely rapid (exponential) expansion, blowing the size of what is now the observable Universe up from a region far smaller than a proton to about the size of a grapefruit (or even bigger) in a small fraction of a second.

November 2, 2016 A Gladyshev “Introduction to Cosmology” 93 Inflation

t ~ 10-35 sec

November 2, 2016 A Gladyshev “Introduction to Cosmology” 94 Inflation

 Phases of the inflationary Universe

The reheating time Equidensity point

att  1/2 ate  Ht att  1/2 att  2/3

Inflation

Radiation domination Matter domination November 2, 2016 A Gladyshev “Introduction to Cosmology” 95 Inflation

 After the reheating the standard Big Bang theory works perfectly

November 2, 2016 A Gladyshev “Introduction to Cosmology” 96 Inflation and the Big Bang model

 Inflation can solve the Big Bang model problems. However, it does not substitute the Big Bang idea but adds some ideas and also modifies the Big Bang model.

 We still have unsolved problems even in the inflationary cosmology

 What is the state of the Universe before inflation?

 Can the initial singularity be avoided?

November 2, 2016 A Gladyshev “Introduction to Cosmology” 97 Matter content of the Universe

 The matter content of the Universe is determined by the mass density

parameter M . the possible contributions are

M   B,, lum   B dark   CDM   HDM

The luminous baryonic matter The hot dark matter (stars in galaxies) (massive neutrinos ? )

The dark baryonic matter The (MAssive Compact Halo Objects - (Weakly Interacting Massive MACHOs ? ) Particles - WIMPs - neutralinos ? )

November 2, 2016 A Gladyshev “Introduction to Cosmology” 98 Evidence for the Dark Matter

 The most direct evidence for the existence of large amount of the dark matter (of baryonic or non-baryonic nature) are the flat rotation curves of spiral galaxies (the dependence of the linear velocity of stars on the distance to the galactic center)

November 2, 2016 A Gladyshev “Introduction to Cosmology” 99 Evidence for the Dark Matter

 Spiral galaxies consist of a rather thin disc and a spherical bulb in the galactic center

 From the equality of forces one gets the linear velocity of the star

G M M M v2 FFr   gravrr2 centr GM vr() r r November 2, 2016 A Gladyshev “Introduction to Cosmology” 100 Evidence for the Dark Matter

 Assuming spherical distribution of mass in the core one gets 4 Mr 3 r 3 v() r r for the inner part of the galaxy 1/ 2 v() r r for the outer part of the galaxy

Observation tell us that for large radii r v() r const

which means linear distribution of mass Mrr 

November 2, 2016 A Gladyshev “Introduction to Cosmology” 101 Evidence for the Dark Matter

 This points to the existence of the huge amount of dark matter surrounding the visible part of the galaxy

Contribution of the dark matter halo alone

Contribution of the disc (visible stars) alone

November 2, 2016 A Gladyshev “Introduction to Cosmology” 102 Evidence for the Dark Matter

 Nowadays, thousands of galactic rotation curves are known, and they all suggest the existence of about ten times more mass in the halos than in the stars of the disc

 The rotation curve of the Milky Way has been measured and confirms the usual picture

 Measurements of velocities of Magellanic Clouds tells that the Milky Way has very large and massive halo

 Elliptic galaxies and cluster of galaxies also contain a large amount of the dark matter

November 2, 2016 A Gladyshev “Introduction to Cosmology” 103 Dark Matter candidates

 Baryonic Dark Matter (MACHOs – MAssive Compact Halo Objects)

 Normal stars No, since they would be luminous

 Hot gas No, since it would shine

 Burnt-out stellar remnants seem implausible, since they arise from normal stars, there is no trace in the halo

 Neutron stars No, since they arise from supernova explosions and eject heavy elements into the galaxy

 White dwarfs (stars with a mass not enough to reach the supernova phase): possible, since white dwarfs are known to exist and to be plentiful.

 Brown dwarfs (stars ten times lighter than the Sun): possible

November 2, 2016 A Gladyshev “Introduction to Cosmology” 104 Dark Matter candidates

 Non-baryonic “hot” dark matter

 Massive neutrinos 2 3 2 The measured quantity – mass-squared difference m10 eV If neutrino mass m 0.1 eV the contribution to the total density is comparable to the contribution of the luminous baryonic matter!

0.001 HDM ()  0.18

 Non-baryonic “cold” dark matter

 The most reasonable explanation – weakly interacting massive particles (WIMP’s). WIMP’s could have been produced in the Big Bang origin in right amounts and with right properties to explain the Dark Matter BUT: we do not know WHAT the WIMP IS

November 2, 2016 A Gladyshev “Introduction to Cosmology” 105 Dark Matter candidates

 Neutralino – a mixture of superpartners of photon, Z-boson and neutral Higgs bosons is a good candidate for WIMP

 Neutral

 The lightest supersymmetric particle (LSP)

 Stable !!!

 Experimental lower mass limit m  45 GeV

 Typical WIMP-nucleon cross section lies in the range

10 5 10 pb n 10 pb

November 2, 2016 A Gladyshev “Introduction to Cosmology” 106 Searches for the Dark Matter

 Optical observations from the Earth (EROS, MACHO, … )  Underground searches (DAMA, EDELWEISS, CDMS, … )  Underwater searches (ANTARES, BAIKAL… )  Searches in space (AMS, … )  Collider searches (LHC)

November 2, 2016 A Gladyshev “Introduction to Cosmology” 107 Searches for the Dark Matter

November 2, 2016 A Gladyshev “Introduction to Cosmology” 108 Cosmology after 1998

 In 1998 collaborations “Supernova Cosmology Project” and “The High-Z Supernova Search” discovered that at large scales the Universe expands with acceleration

 The conclusion is based on the supernovae of type Ia observations

November 2, 2016 A Gladyshev “Introduction to Cosmology” 109

Cosmological constant

 The most general form of the Einstein equations (with cosmological term) 1 R g R   g  8 GT 2    leads to the Friedmann equation 2 a k 8 G 2   aa33 -5  Neglecting the radiation contribution R= 4.8  10 , and curvature

contribution k= 0 (the Universe is flat!) we get

1  M  

 ? ? ? Cosmological constant = Dark energy

November 2, 2016 A Gladyshev “Introduction to Cosmology” 111 Cosmology after 1998

 The result of fitting cosmological parameters

0.8M  0.6   0.2  0.1

 Assumning that the Universe is

flat (M+ Λ=1) this gave

0.09 0.05 M 0.28 0.08 0.04 0.08 0.04 0.72 0.09  0.05

November 2, 2016 A Gladyshev “Introduction to Cosmology” 112 Cosmology after 1998

 The result was improving during the years and the 2003 values are

0.07 M 0.250.06  0.04 0.06 X 0.750.07  0.04

 The most recent values from the Plank data (2015) are

M 0.316  0.09

X 0.684  0.09

November 2, 2016 A Gladyshev “Introduction to Cosmology” 113 Cosmology after 1998

 The results are in good agreement with data on cosmic microwave baground radiation and large-scale structure

0.07 M 0.250.06  0.04 0.06 X 0.750.07  0.04

 The is a well established experimental fact. One has to believe

November 2, 2016 A Gladyshev “Introduction to Cosmology” 114

Composition of the Universe

Heavy elements ~ 0.03 %

Massive neutrino ~ 0.3 %

Luminous stars ~ 0.5 %

H and He ~ 4 %

Dark Matter ~ 27 %

Dark Energy ~ 68 %

November 2, 2016 A Gladyshev “Introduction to Cosmology” 116 ΛCDM Model

The standard model of cosmology now is a model based on:

 Idea of the Hot Big Bang

 Idea of Inflation

 Cosmological constant (Λ-term in the Einstein equation) as Dark Energy

 Cold (non-relativistic) Dark Matter

Within this set of assumptions practically all cosmological phenomena can be described. Though cosmology is hardly testable branch of physics.

November 2, 2016 A Gladyshev “Introduction to Cosmology” 117 Short summary

 Basic observational facts:

 Expansion of the Universe

 Cosmic microwave background radiation

 Homogeneity and isotropy of the Universe at large scales

 Cosmological Principle. Einstein Equation

 Friedmann-Robertson-Walker metric

 Friedmann equation. The Hubble law

 Soluiton of the Friedmann equation

 Matter and radiation density evolution

 The age of the Universe

 Success of the Big Bang model

November 2, 2016 A Gladyshev “Introduction to Cosmology” 118 Short summary

 Problems of the Big Bang model

 Inflation

 Solution of the Big Bang model problems

 The Dark Matter

 Evidence , Candidates, Experimental searches

 The modern picture of the Universe

 Matter density M ~ 0.32  Accelerating expansion of the Universe

 The dark energy, Λ ~ 0.68  Cosmological constant as dark energy

November 2, 2016 A Gladyshev “Introduction to Cosmology” 119 Thank you for your patience !

November 2, 2016 A Gladyshev “Introduction to Cosmology” 120