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IFIC, 6 February 2007 Julien Lesgourgues (LAPTH , Annecy )

current status of cosmological inflation. IFIC, 6 February 2007 Julien Lesgourgues (LAPTH , Annecy ). 1) « historical arguments » - flatness problem - horizon problem - monopoles & topological defects basic model - slow rolling scalar field - primordial fluctuations

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IFIC, 6 February 2007 Julien Lesgourgues (LAPTH , Annecy )

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  1. current status of cosmological inflation IFIC, 6 February 2007 Julien Lesgourgues (LAPTH, Annecy)

  2. 1) « historical arguments » - flatness problem - horizon problem - monopoles & topological defects • basic model - slow rolling scalar field - primordial fluctuations 3) agreement between CMB maps and inflation - coherence - scale invariance - gaussianity - adiabaticity 4) current constraints on inflation, prospects…

  3. 1) « historical arguments » - flatness problem - horizon problem - monopoles & topological defects • basic model - slow rolling scalar field - primordial fluctuations 3) agreement between CMB maps and inflation - coherence - scale invariance - gaussianity - adiabaticity 4) current constraints on inflation, prospects… 1979-1982: A.Starobinsky A. Guth

  4. Definitions : -scale factor : a(t) ds2 = dt2 - a(t)2 dx2 c=1 -e-fold number : N = ln a e.g. “a stage lasts for DN=10 e-folds” a(t) increases by factor e10=22000 1) « historical arguments » : flatness problem

  5. matter (nr, r) spatial curvature decelerated expansion H 1) « historical arguments » : flatness problem Friedmann equation : or : a-2 a-3, a-4

  6. curvature ? 1) « historical arguments » : flatness problem ln r radiation matter dark energy ln a today

  7. curvature ? 1) « historical arguments » : flatness problem ln r Mp4 1062 radiation matter dark energy ln a today

  8. 1) « historical arguments » : flatness problem ln r TeV4 1032 radiation matter dark energy curvature ? ln a today

  9. 1) « historical arguments » : flatness problem Inflation = stage of accelerated expansion Friedmann Energy cons.ä(t) > 0  r + 3 p < 0  r an, -2 < n < 0

  10. 1) « historical arguments » : flatness problem ln r radiation inflation curvature matter dark energy ln a today

  11. 1) « historical arguments » : flatness problem What is the minimal duration of inflation ?

  12. DNinflation=DNpost-inflation 1) « historical arguments » : flatness problem ln r inflation r~cst radiation a-4 curvature a-2 ln a today

  13. 1) « historical arguments » : flatness problem Minimal duration of inflation : DNinflation DNpost-inflation

  14. 1) « historical arguments » : horizon problem t y x

  15. 1) « historical arguments » :horizon problem t y x photon decoupling last scattering surface (LSS) are all LSS points within causal contact ?

  16. Hubble radius at decoupling: ~1° ↓initial singularity 1) « historical arguments » : horizon problem t y x photon decoupling Last scattering surface (LSS)

  17. 1) « historical arguments » : horizon problem t y x x photon decoupling last scattering surface (LSS) inflation

  18. curvature ? • « historical arguments » : monopoles and other defects ln r phase transition defects radiation matter dark energy ln a today

  19. « historical arguments » : monopoles and other defects ln r phase transition radiation inflation matter curvature dark energy ln a today

  20. Basic model : a slow-rolling scalar field Inflation = stage of accelerated expansion Friedmann + e. c. : ä(t) > 0  r + 3 p < 0 nearly homogeneous slow-rolling scalar fields: r = ½ f‘2 + V(f) p = ½ f‘2- V(f) |dV/df | < V/mP , |d2V/df2|< V/mP2 V f

  21. Basic model : a slow-rolling scalar field Inflation = stage of accelerated expansion Friedmann + e. c. : ä(t) > 0  r + 3 p < 0 nearly homogeneous slow-rolling scalar field: r = ½ f‘2 + V(f) p = ½ f‘2- V(f) |dV/df | < V/mP , |d2V/df2|< V/mP2 V f

  22. end of inflation: field oscillates and decays in particles which finally thermalize • Basic model : a slow-rolling scalar field Inflation = stage of accelerated expansion Friedmann + e. c. : ä(t) > 0  r + 3 p < 0 nearly homogeneous slow-rolling scalar field: r = ½ f‘2 + V(f) p = ½ f‘2- V(f) |dV/df | < V/mP , |d2V/df2|< V/mP2 V f

  23. Basic model:primordial cosmological fluctuations fluctuations today

  24. Basic model:primordial cosmological fluctuations fluctuations at decoupling

  25. Basic model:primordial cosmological fluctuations origin of fluctuations ?

  26. Basic model:primordial cosmological fluctuations decelerated expansion : - causal horizon = Hubble radius ( RH = c/H ) - RH(t) grows faster than a(t) distance RH acausal primodial cosmological perturbations causal L time MATTER DOMINATION RADIATION DOMINATION

  27. Basic model:primordial cosmological fluctuations decelerated expansion : - causal horizon = Hubble radius ( RH = c/H ) - RH(t) grows faster than a(t) distance RH primodial cosmological perturbations no coherent fluctuations phase transition L time MATTER DOMINATION RADIATION DOMINATION

  28. Basic model:primordial cosmological fluctuations accelerated expansion : - causal horizon » Hubble radius - RH(t) grows more slowly than a(t) distance RH primodial cosmological perturbations L time MATTER DOMINATION INFLATION RADIATION DOMINATION

  29. Basic model:primordial cosmological fluctuations - quantum fluctuations of df and hmn grow tomacroscopic scales - normalization and evolution imposed by quantum mechanics 1 distance RH primodial cosmological perturbations 1 L time MATTER DOMINATION INFLATION RADIATION DOMINATION

  30. Basic model:primordial cosmological fluctuations • - Hubble crossing, Bogolioubov transformation • “squeezed state”→ classical stochastic fluctuations 2 distance RH primodial cosmological perturbations 2 1 L time MATTER DOMINATION INFLATION RADIATION DOMINATION

  31. Basic model:primordial cosmological fluctuations - perturbation amplitude frozen since - «primordial spectrum» of scalar and tensor perturbations 2 3 distance RH primodial cosmological perturbations 3 2 1 L time MATTER DOMINATION INFLATION RADIATION DOMINATION

  32. Basic model :primordial cosmological fluctuations • insensitive to microscopical evolution (reheating, phase transition) • primordial spectrum mediated to g, b, n, CDM 4 distance RH primodial cosmological perturbations 4 3 2 1 L time MATTER DOMINATION INFLATION RADIATION DOMINATION

  33. Basic model:primordial cosmological fluctuations • acoustic oscillations and decoupling • CMB anisotropies → primordial spectrum inherited from 5 3 distance RH primodial cosmological perturbations 4 5 3 2 1 L time MATTER DOMINATION INFLATION RADIATION DOMINATION

  34. Agreement between CMB maps and inflation

  35. Agreement between CMB maps and inflation • inflation predict that perturbations are: • coherent • nearly gaussian • adiabatic* • nearly scale invariant* • *for simplest inflationary models

  36. Agreement between CMB maps and inflation time coherence of inflationary fluctuations : distance RH primodial cosmological perturbations decoupling L time MATTER DOMINATION RADIATION DOMINATION INFLATION

  37. Agreement between CMB maps and inflation absence of coherence in the case of topological defects : distance RH primodial cosmological perturbations decoupling L time MATTER DOMINATION RADIATION DOMINATION INFLATION

  38. validated (existence of acoustic peaks) • Agreement between CMB maps and inflation • inflation predict that perturbations are: • coherent • nearly gaussian • adiabatic* • nearly scale invariant* • *for simplest inflationary models

  39. validated (existence of acoustic peaks) validated (statistical analysis of CMB maps) • Agreement between CMB maps and inflation • inflation predict that perturbations are: • coherent • nearly gaussian • adiabatic* • nearly scale invariant* • *for simplest inflationary models

  40. validated (existence of acoustic peaks) validated (statistical analysis of CMB maps) validated (peak scale) • Agreement between CMB maps and inflation • inflation predict that perturbations are: • coherent • nearly gaussian • adiabatic* • nearly scale invariant* • *for simplest inflationary models

  41. validated (existence of acoustic peaks) validated (statistical analysis of CMB maps) validated (peak scale) • Agreement between CMB maps and inflation • inflation predict that perturbations are: • coherent • nearly gaussian • adiabatic* • nearly scale invariant* • *for simplest inflationary models

  42. Agreement between CMB maps and inflation scale invariance : slow rolling scalar field : V f f* AS AT k k amplitude  V3/2/V’ tilt (1-nS)  (V’/V)2 , V’’/V + hider order corrections (tilt running, …) amplitude  V1/2 tilt nT  (V’/V)2 + higher order corrections (tilt running, …)

  43. validated (existence of acoustic peaks) validated (statistical analysis of CMB maps) validated (peak scale) validated (peak amplitudes) • Agreement between CMB maps and inflation • inflation predict that perturbations are: • coherent • nearly gaussian • adiabatic* • nearly scale invariant* • *for simplest inflationary models

  44. current constraints on inflation single field slow-roll inflation : V f f* AS AT k k amplitude  V3/2/V’ tilt (1-nS)  (V’/V)2 , V’’/V + next-order corrections (running of the tilt, …) amplitude  V1/2 tilt nT  (V’/V)2 + next-order corrections (running of the tilt, …)

  45. current constraints on inflation overall amplitude AS AT k k amplitude  V3/2/V’ tilt (1-nS)  (V’/V)2 , V’’/V + next-order corrections (running of the tilt, …) amplitude  V1/2 tilt nT  (V’/V)2 + next-order corrections (running of the tilt, …) = 0.5x10-5 mp3

  46. current constraints on inflation overall slope AS AT k k amplitude  V3/2/V’ = 0.5x10-5 mp3 tilt (1-nS)  2.25 (V’/V)2 - V’’/V = 0.5 mp-2 + next-order corrections (running of the tilt, …) amplitude  V1/2 tilt nT  (V’/V)2 + next-order corrections (running of the tilt, …)

  47. current constraints on inflation absence of tensors AS AT k k amplitude  V3/2/V’ = 0.5x10-5 mp3 tilt (1-nS)  2.25 (V’/V)2 - V’’/V = 0.5 mp-2 + next-order corrections (running of the tilt, …) amplitude  V1/2 < (3.7x1016 GeV)2 tilt nT  (V’/V)2 + next-order corrections (running of the tilt, …)

  48. current constraints on inflation • Energy scale of inflation still unknown !! • Self-consistency relation still not checked !! absence of tensors AS AT k k amplitude  V3/2/V’ = 0.5x10-5 mp3 tilt (1-nS)  2.25 (V’/V)2 - V’’/V = 0.5 mp-2 + next-order corrections (running of the tilt, …) amplitude  V1/2 < (3.7x1016 GeV)2 tilt nT  (V’/V)2 + next-order corrections (running of the tilt, …)

  49. current constraints on inflation • Energy scale of inflation still unknown !! • Self-consistency relation still not checked !! • future CMB experiments (B-polarization) : r ~ 10-2 (factor 50 pour V) • future space-based GW interferometers : r ~ 10-4 (BBO) (factor 5000 pour V) • measure r, nt : inflationary energy scale • + self-consistency r=-8nt • measure r: inflationary energy scale • no GW detected : inflation unconstrained new physics at 1016 GeV (extra-D ?) ordinary QFT (SUSY, PNGB…)

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