1. Cosmological Inflation: History and Present Status

2. Motivated by the book : Breakthrough Beyond the Edge of the World Valery Rubakov Alexei Starobinsky Andrei Linde Vyacheslav Mukhanov Vladimir Lukash

3. The first cosmological revolution 1916 - 1929 R  – ½ R g  – 8  g  = 16  c -4 G T 

4. The universe is not just a containment of everything that exists – This is a physical object! -Geometry: a closed 3D space + time -Size: unknown but > 10 12 light years -Dynamics: accelerating expansion -Density: 10 -29 g/сm 3 -Equation of state: pressure = 0 (dust) -Temperature: 2.7 о К -Total energy: 0 (Zero!)

5. Big Bang problems -Horizon problem (Charles Misner): Universe is the same in the causally unconnected regions -Flatness problem (  = 1), or  =  c -Cosmic junk problem: lack of monopoles, cosmic strings etc. -Entropy problem: ~ 10 90 particles within horizon

6. Vladimir Lukash about 1970-ies: They worked in the frames of “Cosmological postulate”: all problems come from initial conditions that we have to postulate. Nobody was happy (except theologists) but how to work otherwise? Observations:  is at most 10% of the critical value (Peebles & Tali). However it was clear that any value of  degrades very fast to 0 or infinity except  = 1 exactly (Dicke) The anthropic principle was treated in Zeldovich school as a bad style science Mid 70-ies: Gunn & Tinsley: the negative deceleration parameter derived from the Hubble diagram (acceleration) The issue of H: H ~50 km/s/Mpc versus ~75 km/s/Mpc (too young Universe)

7. Reincarnation of the  -term (cosmological term) R  – ½ R g  – 8  g  = 16  c -4 G T  - 8/3  Vacuum (p = -  ) p = 

8. The first hint: Brout, Englert & Gunzig 1961 Creation of Universe ex nihilis with a massive scalar field (a toy model) The next attempt: Erast Gliner 1969: non-singular bounce due to “heavy vacuum” with p = -e Contraction -> expansion through de-Sitter stage Gliner & Dymnikova 1975: It solves problems of flatness (big Universe) and of a large entropy

9. 1980 – The start of the second cosmological revolution 1980 – Starobinsky presents his model and meets criticism for a wrong scenario 1980 Mukhanov & Chibisov claim that de-Sitter stage is necessary to get galaxies from quantum fluctuations 1981 Mukhanov & Chibisov - primordial scalar perturbations and their spectrum 1981 Guth publishes his famous paper 1982 Linde - New inflation (slow roll) + Steinhardt & Albercht (3 month later) 1983 Linde - Chaotic inflation 1986 Linde - Eternal inflation

10. Alexei Starobinsky: modified gravitation R 2 appears as a result of Kazimir effect at a large curvature Scenario: Universe has started from a pure de-Sitter world which existed indefinite time. Then it dissipated into hot Friedman Universe. Mukhanov & Others: de-Sitter world is unstable because of quantum fluctuations and incompatible with contraction stage. Zeldovich: The model can be interpreted as a way of Universe creation from nothing Vilenkin has formalized this as a tunnel transition.

11. Mukhanov & Chibisov: primordial scalar perturbations Virtual quantum fluctuations produce real perturbations under variable metric Gravitational waves – Leonid Grischuk Gravitational waves (tensor perturbations) in Starobinsky model – Starobinsky Production of scalar perturbations – Lukash (general formalism), Mukhanov & Chibisov – the concrete result for the concrete model (of Starobinsky), including the spectrum of perturbations: First approximation – ns = 1 (flat spectrum) Next approximation – ns = 0.96

12.  V( , T) Alan Guth: Scenario of inflation 1.Thermal equilibrium 2.Phase transition 3.Supercooling + Exponential expansion 4. “Boiling” – reheating

13. Answers: 1.The flatness problem is evidently solved with expansion by many orders of magnitude (  k ~ 10 -100, e.g) 2.The horizon problem disappears because all we see inside the horizon was a causally connected piece of a uniform heavy vacuum. 3.All exotic “defects” were swept away during inflation out of the horizon 4. A huge entropy results from the decay of self- reproducing scalar field

15. New inflation  + 3 H  + V’  = 0... Linde 1982 Albrecht & Steinhardt 3 months later

17. Chaotic inflation Linde 1983  > M pl f(x) – homogeneous at ~ 10 R hor

18. Starobinsky model in terms of a scalar field V(  ) ~ log 2 (  )

19. Ethernal inflation Linde 1986 Planck limit

20. Andrei Linde

22. Predictions (According to Slava Mukhanov) 1.Flatness  =1 2.Spectral slope of primordial perturbations ns ~ 0.96 – 0.97 3.Gaussianity 4.Adiabaticity 5.Gravitational waves

23. WMAP 2001 – 2010 Band 0.32 – 1.3 см Thermal equilibrium in the shadow ~40К Mirror 1.4 Х 1.6 м The data were opened in 2002 «Планк» 2009 – 2013 Band 0.035 – 1см Liquid helium Mirror 1.5 Х 1.9 м Data opening: 2013?

24. What one can see on this picture? Cold spot, “fingers”, concentric rings. Also “SH”, Zuntz, Zibin, Zunkel & Zwart, 01/04/2014

25. What we have to search in this map? A.D. Sakharov 1963. Primordial perturbations produce acoustic waves with common phase. (Standing waves) Waves coming to recombination with the phase , 2 , 3  have maximal amplitudes - With the phase  /2, 3p/2, 5p/2 – minimal amplitudes Sakharov assumed a wrong model (cold universe) where peaks were of a very short scale Reconsidered for correct model Sunyaev & Zeldovich + Peebles & Yu Sakharov oscillations are observable!

26. Silk effect

27. Fit of the multipole spectrum Free parameters: 1.The amplitude of primordial perturbations (normalization) 2. The spectral slope (with a deviation from a flat) 3. The share of the baryonic matter (affects the height of the first peak) 4. The share of the dark matter (affects the ratio between peaks) 5. The curvature parameter  (defines the angular scale of the whole picture) 6. Free electron optical depth (reionization z) affects the curve at low L -----------------------

28. Curvature  k = 0.001+-0.006 Dark matter  c = 0.259+-0.005 Baryonic matter  b = 0.048+-0.001

29.  = 1 (Flat Universe) ++!! Planck + other data:  = 0.001 +/- 0.007 2.. Ns = 0.96 – 0.97 ++! n s = 0.96 +/- 0.07 3.Adiabaticity Confirmed (position of acoustic peaks) 4. Gaussianity Confirmed at the level ruling out complicated models Linde: there was a rumor that WMAP has observed a non- gaussianity. Some people were excited. The rumor had no ground. 5. Gravitational waves Not confirmed yet Predictions / Measurements

30. Starobinsky model BICEP2

31. It was too early to drink champagne! BICEP 2 South pole

32. B-mode at the level r = 0.2 The result is in contradiction with Planck data (too large) Поляризованная пыль?

34. Alternatives Steinhardt & Turok Ekpyrotic model Bounce due to brane collision p > +  Strong criticism by Andrei Linde and others (pyrotechnical model) Rubakov A primordial vacuum with conform invariance No massive particles, no gravity, no scale (… and the Sent Spirit flied over the water) A spontaneous breaking Hot Fridman Universe

35. Linde, Mukhanov, Stasrobinsky: Inflation theory is simple (in ideology), solves all problems and has predicted future observations. Alternatives are more complicated, require additional entities and give no clear predictions Rubakov: Until primordial gravitational waves are detected alternative models have a right for existence (and it is worth to wait with Nobel prize) However, one part of the theory has no alternatives: the quantum production of primordial perturbations by Mukhanov $ Chibisov

36. My impressions: - Inflation theory far exceeds alternatives in ideological simplicity and predictive power. Also the most economical in the sense of extra entities. - Among the inflation models the best is that of Alexei Starobinsky with the same reason. -William Occam probably would agree with me.