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Inflationary Cosmology

Inflationary Cosmology. Jerome Martin CNRS/Institut d’Astrophysique de Paris. International School of Physics Enrico Fermi, “Gravitational Waves and Cosmology” , Varenna, July 3-12, 2017. Outline. Lecture I: “problems” of the standard hot Big Bang model, a motivation for inflation.

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Inflationary Cosmology

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  1. InflationaryCosmology Jerome Martin CNRS/Institut d’Astrophysique de Paris International School of Physics Enrico Fermi, “Gravitational Waves and Cosmology” , Varenna, July 3-12, 2017

  2. Outline Lecture I: “problems” of the standard hot Big Bang model, a motivation for inflation. • The hot Big Bang Model • The Horizon problem Lecture II: the inflationary scenario, theoretical and observational status • Inflation with scalar fields • Cosmological perturbations of quantum-mechanical origin • Constraints on the inflationary scenario

  3. Lecture I Lecture I: “Problems” of the standard hot Big Bang model, a motivation for inflation.

  4. The standard model The « hot Big Bang phase » is the standard cosmological model and provides a convincing description of the Universe on a wide range of energy scales. The model is based on three assumptions: 1- Gravity shapes the Universe and is described by General Relativity 2- Cosmological principle: the Universe is homogeneous and isotropic (on large scales) 3- Matter/energy is given by different sources to be listed in the following

  5. The standard model The model is based on three assumptions 1- Gravity shapes the Universe and is described by General Relativity Geometry Matter/energy c, G: Relativistic theory of gravitation

  6. The standard model The model is based on three assumptions 1- Gravity shapes the Universe and is described by General Relaltivity 2- Cosmological principle: the Universe is homogeneous and isotropic (on large scales)

  7. The standard model The model is based on three assumptions 1- Gravity shapes the Universe and is described by General Relaltivity 2- Cosmological principle: the Universe is homogeneous and isotropic (on large scales) One can use the FLRW metric

  8. The FLRW Universe Cosmological Principle : the Universe is (on large scales …) homogeneous and isotropic.Technically, this implies that the metric is of the FLRW type space of constant curvature cosmic time only one (time-dependent) undetermined function: the scale factor a(t) In conformal time, the same metric reads flat (Euclidean) space k=0 conformal time In conformal time, space time diagrams look as in Minkowski!

  9. The standard model The model is based on three assumptions 1- Gravity shapes the Universe and is described by General Relaltivity 2- Cosmological principle: the Universe is homogeneous and isotropic (on large scales) 3- Matter/energy is given by different sources to be listed in the following One can use the FLRW metric - The size of the Universe is described by a single function of time, the scale factor a(t) - The spatial curvature of the Universe can be zero (flat) positive or negative

  10. Composition of the Universe • - Photons • - Neutrinos • - Baryons • - Cold dark matter • - Dark Energy Radiation Matter Cosmological constant??

  11. Composition of the Universe - Each species is described by a perfect fluid • - Photons • - Neutrinos • - Baryons • - Cold dark matter • - Dark Energy Radiation Matter Cosmological constant?? pressure energy density velocity

  12. Composition of the Universe • - Each species is described by a perfect fluid • - To close the system we need the equation of • state • - Photons • - Neutrinos • - Baryons • - Cold dark matter • - Dark Energy Radiation Matter Cosmological constant?? pressure energy density velocity

  13. Composition of the Universe • - Photons • - Neutrinos • - Baryons • - Cold dark matter • - Dark Energy Radiation Matter Cosmological constant??

  14. Composition of the Universe • - Photons • - Neutrinos • - Baryons • - Cold dark matter • - Dark Energy Conservation of energy Radiation Matter Cosmological constant?? Hubble parameter= Expansion rate of the Universe

  15. Composition of the Universe • - Photons • - Neutrinos • - Baryons • - Cold dark matter • - Dark Energy Conservation of energy Radiation Matter Cosmological constant??

  16. The standard model: solutions radiation energy density rad-matter equality pressureless matter Dark energy time Radiation dominated era Matter dominated era Dark energy era

  17. The standard model The model is based on three assumptions 1- Gravity shapes the Universe and is described by General Relaltivity 2- Cosmological principle: the Universe is homogeneous and isotropic (on large scales) 3- Matter/energy is given by different sources to be listed in the following The Einstein equations reduce to ordinary non-linear differential equations Their integration allows us to find the function a(t)

  18. The standard model: solutions The fact that a=a(t) implies that the Universe is expanding. This expansion is now measured with very high accuracy The Universe is measured to be spatially flat

  19. The standard model: solutions radiation energy density rad-matter equality pressureless matter Dark energy time Radiation dominated era Matter dominated era Dark energy era

  20. The standard model: solutions Hubble radius: c/H characteristic length beyond which the expansion matters matter Dark energy Slope 3/2 radiation Slope 2 Radiation dominated era Matter dominated era DE era time

  21. A good model! The standard model, though it is a simple construction, can account for a large number of observations and/or experimental tests - Expansion (Hubble diagram) - Cosmic Microwave Background (CMB) - Nucleosynthesis - etc …

  22. Standard Model of Cosmology aka “Lambda” CDM ЛCDM model is confirmed by Planck • Hubble parameter • Photons energy density • Neutrinos energy density • Baryons energy density • Cold Dark Matter (CDM) energy density • Dark energy (CC) energy density • Amplitude of the fluctuations • Tilt of the primordial spectrum • Reionization depth

  23. Standard Model of Cosmology ЛCDM model is confirmed by Planck • Hubble parameter • Photons energy density • Neutrinos energy density • Baryons energy density • Cold Dark Matter (CDM) energy density • Dark energy (CC) energy density • Amplitude of the fluctuations • Tilt of the primordial spectrum • Reionization depth known because T~2.7K known because Nν=3 known because Everything is consistent with a six-parameter model

  24. Standard Model of Cosmology ЛCDM model is confirmed by Planck • Hubble parameter • Photons energy density • Neutrinos energy density • Baryons energy density • Cold Dark Matter (CDM) energy density • Dark energy (CC) energy density • Amplitude of the fluctuations • Tilt of the primordial spectrum • Reionization depth

  25. Puzzles The standard model, despite its impressive achievements, suffers from a number of troubling puzzles - Horizon problem - Flatness problem - Origin of the inhomogeneities in our Universe - etc … All this issues are related to the initial conditions

  26. Horizon problem time Present time Big Bang hypersurface t=0 A B space At a given time, we only see a limited part of the Universe because light propagates with finite speed

  27. Horizon problem time Present time Big Bang hypersurface t=0 A B space Of course the size of this limited part grows with time

  28. Horizon problem time B and A become causally connected Present time Big Bang hypersurface t=0 A B space We can see points A and B before they knew about each other

  29. proton electron photon CMB anisotropies But one cannot see beyond the last scattering surface At the lss, z~1100, the Universe became transparent HAtom Black body radiation T=2.7 K The lss (thanks F. Bouchet)

  30. Horizon problem time Present time lss C D Big Bang hypersurface t=0 A B space One can observe C and D on the lss even if C & D are causally disconnected

  31. Horizon problem time Present time lss C D Big Bang hypersurface t=0 A B space We expect the regions around C & D to have different temperature

  32. Horizon problem time Present time lss C D Big Bang hypersurface t=0 A B space What is the angular size of the horizon at lss viewed from Earth?

  33. Horizon problem Size of the moon!

  34. Horizon problem What we have just computed … ~ angular size of the moon hot spot cold spot Low contrast map

  35. Horizon problem What we observe … Low contrast map

  36. Inflation The horizon problem suggests that the evolution of the scale factor in the very early Universe is different from t1/2 … let us therefore consider a new epoch, prior to the radiation dominated era of the hot Big Bang model Inflation

  37. How inflation solves the horizon problem In presence of the new epoch, the angular size of the horizon becomes lss de eq end ini dark energy inflation radiation matter duration of inflation

  38. How inflation solves the horizon problem In presence of the new epoch, the angular size of the horizon becomes Hot Big Bang term

  39. How inflation solves the horizon problem In presence of the new epoch, the angular size of the horizon becomes Hot Big Bang term Inflationary correction

  40. How inflation solves the horizon problem In presence of the new epoch, the angular size of the horizon becomes Hot Big Bang term Inflationary correction - If we want the inflationary correction to play a significant role, then ie a fluid with negative pressure!

  41. How inflation solves the horizon problem In presence of the new epoch, the angular size of the horizon becomes Hot Big Bang term Inflationary correction - If we want the inflationary correction to play a significant role, then ie a fluid with negative pressure! - This implies an accelerated expansion= inflation

  42. How inflation solves the horizon problem In presence of the new epoch, the angular size of the horizon becomes Hot Big Bang term Inflationary correction 60 e-folds of inflation!

  43. Puzzles The standard model, despite its impressive achievements, suffers from a number of troubling puzzles - Horizon problem - Flatness problem - Origin of the inhomogeneities in our Universe - etc … One can show that the other puzzles are also solved if there is a phase of inflation lasting 60 e-folds

  44. Example: flatness problem Our universe The condition for our Universe to be sufficiently spatially flat is Same condition as before!

  45. Conclusion How can we realize a phase of inflation? Lecture II to be continued …

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