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Cosmic Inflation and Quantum Mechanics I: Concepts

Discover the Lambda/CDM model, cosmological fluctuations, and quantum-mechanical origins of inflationary perturbations. Learn how precision cosmology measures parameters to explain the expanding Universe and the Cosmic Microwave Background. Delve into the structure formation, CMB anisotropies, and gravitational instability in the Universe.

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Cosmic Inflation and Quantum Mechanics I: Concepts

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  1. Cosmic Inflation and Quantum Mechanics I: Concepts Jerome Martin CNRS/Institut d’Astrophysique de Paris New Frontiers in Testing Quantum Mechanics from Underground to Space Laboratori Nazionali di Frascati November 29th- December 1st, 2017

  2. The talk Outline • Modern cosmology: the Lambda/CDM model • Cosmological fluctuations of quantum-mechanical origin • Quantum Mechanics in the sky? Can we show that inflationary perturbations • are of quantum-mechanical origin? • Conclusions

  3. The talk Outline • Modern cosmology: the LambdaCDM model • Cosmological fluctuations of quantum-mechanical origin • Quantum Mechanics in the sky? Can we show that inflationary perturbations • are of quantum-mechanical origin? • Conclusions

  4. Lambda CDM model 1- Cosmology has now a well-tested standard model: the Lambda/CDM model. It is a six parameter model. It is based on GR since Gravity shapes the Universe

  5. Lambda CDM model 1- Cosmology has now a well-tested standard model: the Lambda/CDM model. It is a six parameter model. It is based on GR since Gravity shapes the Universe 2- The parameters are determined at the % level: era of precision cosmology.

  6. Lambda CDM model 1- Cosmology has now a well-tested standard model: the Lambda/CDM model. It is a six parameter model. It is based on GR since Gravity shapes the Universe 2- The parameters are determined at the % level: era of precision cosmology. 3- This model is compatible with thousands of different measurements and has a great explanatory power:

  7. Lambda CDM model 1- Cosmology has now a well-tested standard model: the Lambda/CDM model. It is a six parameter model. It is based on GR since Gravity shapes the Universe 2- The parameters are determined at the % level: era of precision cosmology. 3- This model is compatible with thousands of different measurements and has a great explanatory power: - it explains (or predicts) that the Universe is expanding

  8. FLRW metric time Scale factor

  9. Lambda/CDM=Four epochs Scale factor: a(t)/a(tini) Dark energy dominated era Radiation dominated era Matter dominated era Realized with a scalar field: the “inflaton” Ordinary fluids

  10. CMB 1- Cosmology has now a well-tested standard model: the Lambda/CDM model. It is a six parameter model. It is based on GR since Gravity shapes the Universe 2- The parameters are determined at the % level: era of precision cosmology. 3- This model is compatible with thousands of different measurements and has a great explanatory power: - it explains (or predicts) that the Universe is expanding - the Cosmic Microwave background (CMB)

  11. CMB Scale factor: a(t)/a(tini) Dark energy dominated era Radiation dominated era Matter dominated era

  12. CMB Scale factor: a(t)/a(tini) Last scattering surface Dark energy dominated era Radiation dominated era Matter dominated era

  13. CMB T~2.7 K time CMB is the most accurate black body ever produced in Nature

  14. The talk Outline • Modern cosmology: the LambdaCDM model • Cosmological fluctuations of quantum-mechanical origin • Quantum Mechanics in the sky? Can we show that inflationary perturbations • are of quantum-mechanical origin? • Conclusions

  15. Perturbations of quantum-mechanical origin 1- Cosmology has now a well-tested standard model: the Lambda/CDM model. It is a six parameter model. It is based on GR since Gravity shapes the Universe 2- The parameters are determined at the % level: era of precision cosmology. 3- This model is compatible with thousands of different measurements and has a great explanatory power: - it explains (or predicts) that the Universe is expanding - the Cosmic Microwave background (CMB) - Structure formation: origin of the galaxies and of CMB anisotropies

  16. CMB anisotropies • It is found that the temperature of the CMB is not exactly the same in all • direction, δT/T~ 1/100000

  17. CMB anisotropies • It is found that the temperature of the CMB is not exactly the same in all • direction, δT/T~ 1/100000 • This is has been measured with increasing precision along the years COBE (1992) WMAP (2003) This is a proof that the Universe was inhomogeneous at the LSS time Planck (2013 & 2015)

  18. CMB anisotropies • It is found that the temperature of the CMB is not exactly the same in all • direction, δT/T~ 1/100000 • This is has been measured with increasing precision along the years • Today we know that the Universe is even more inhomogeneous … The amplitude of the fluctuations is now longer small

  19. Structure formation In order to have a convincing scenario for structure formation, we need to answer two questions

  20. Structure formation In order to have a convincing scenario for structure formation, we need to answer two questions How do they grow?

  21. Structure formation In order to have a convincing scenario for structure formation, we need to answer two questions How do they grow? Gravitational instability

  22. Structure formation In order to have a convincing scenario for structure formation, we need to answer two questions What is their origin?

  23. Structure formation In order to have a convincing scenario for structure formation, we need to answer two questions What is their origin? Quantum fluctuations during inflation According to inflation, this is the quantum spacetime which is at the origin of CMB anisotropies and large scale structures For a review, see J. Martin, Lect. Notes Phys. 669 (2005), 199, hep-th/040611

  24. CMB Scale factor: a(t)/a(tini) Last scattering surface Dark energy dominated era Radiation dominated era Matter dominated era

  25. Perturbations of quantum-mechanical origin Scale factor: a(t)/a(tini) Last scattering surface Dark energy dominated era Radiation dominated era Matter dominated era Initial fluctuations

  26. Lambda/CDM=Four epochs Scale factor: a(t)/a(tini) Last scattering surface Dark energy dominated era Radiation dominated era Matter dominated era Initial fluctuations amplification

  27. Perturbations of quantum-mechanical origin Scale factor: a(t)/a(tini) Last scattering surface Dark energy dominated era Radiation dominated era Matter dominated era Initial fluctuations amplification

  28. Perturbations of quantum-mechanical origin How to calculate the evolution of the quantum cosmological fluctuations? Geometry=Matter time

  29. Perturbations of quantum-mechanical origin How to calculate the evolution of the quantum cosmological fluctuations? 1- Use Einstein equations of GR! Geometry=Matter time

  30. Perturbations of quantum-mechanical origin How to calculate the evolution of the quantum cosmological fluctuations? 1- Use Einstein equations of GR! Geometry=Matter 2- Use perturbations theory since the fluctuations are small time

  31. Perturbations of quantum-mechanical origin How to calculate the evolution of the quantum cosmological fluctuations? 1- Use Einstein equations of GR! Geometry=Matter 2- Use perturbations theory since the fluctuations are small time 3- Quantize the system

  32. Perturbations of quantum-mechanical origin - The Hamiltonian controlling the evolution of the fluctuation is Corresponds to creation of pair of particles The pump source vanishes if space-time is not dynamical, a’=0 k -k

  33. Perturbations of quantum-mechanical origin - The Hamiltonian controlling the evolution of the fluctuation is - Schroedinger evolution gives Corresponds to creation of pair of particles The pump source vanishes if space-time is not dynamical, a’=0 k -k Two mode squeezed states -”Classical” coherent state: equal dispersion on x and p - Squeezed state: not the same dispersion (rsqueezing parameter)

  34. Perturbations of quantum-mechanical origin - The Hamiltonian controlling the evolution of the fluctuation is - Schroedinger evolution gives - The strongest squeezed state ever produced in Nature! Corresponds to creation of pair of particles The pump source vanishes if space-time is not dynamical, a’=0 k -k Two mode squeezed states

  35. Perturbations of quantum-mechanical origin - The Hamiltonian controlling the evolution of the fluctuation is - Schroedinger evolution gives - The strongest squeezed state ever produced in Nature! - It is an entangled state. In fact a two mode squeezed state with r going to infinity is an EPR state. Corresponds to creation of pair of particles The pump source vanishes if space-time is not dynamical, a’=0 k -k Two mode squeezed states

  36. Planck data Computed with the Lambda CDM model (hence with inflation): it works!!!

  37. The talk Outline • Modern cosmology: the LambdaCDM model • Cosmological fluctuations of quantum-mechanical origin • Quantum Mechanics in the sky? Can we show that inflationary perturbations • are of quantum-mechanical origin? • Conclusions

  38. Open issues The fact that the state of the perturbations is “very quantum” raises some issues and hopes with regards to the quantum-mechanical nature of spacetime • Quantum to classical transition of the perturbations • What is the importance of decoherence? (D.Polarski, A Starobinsky, CQG 13 1996) • Reduction of the wave packet: should we go beyond Copenhagen? • Unambiguous observational signature of the quantum origin of the galaxies? Can we see quantum correlations in the sky? (J. Maldacena, Fortsch. Phys. 64 2016; J. Martin & V.Vennin, PRD96 2017 063501, PRA94 2016 052135) time

  39. The talk Outline • Modern cosmology: the LambdaCDM model • Cosmological fluctuations of quantum-mechanical origin • Quantum Mechanics in the sky? Can we show that inflationary perturbations • are of quantum-mechanical origin? • Conclusions

  40. Conclusions Recap • According to cosmic inflation, the CMB fluctuations are placed in a strongly two- mode squeezed state which is an entangled state • Inflation is the only situation in Physics where GR & QM are used and where, at the same time, we have high accuracy data • Inflation pushes QM in unexplored regimes, eg high energies, large scales, • QM without observers etc … • Take away message: inflation is not only a successful scenario of the early Universe, it is also a very interesting playground for foundational issues of quantum mechanics See Vincent Vennin’s talk …

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