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. Modern cosmology: the Lambda/CDM model
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. Modern cosmology: the LambdaCDM model
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. a great explanatory power:
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. a great explanatory power:
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)
Radiation
dominated
era
Matter
dominated
era
Dark energy
dominated
era
Realized with
a scalar field:
the “inflaton”
Ordinary fluids

10. a great explanatory power:
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. Scale factor: a(t)/a(tini)
CMB
Scale factor: a(t)/a(tini)
Radiation
dominated
era
Matter
dominated
era
Dark energy
dominated
era

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

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

14. Modern cosmology: the LambdaCDM model
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. This is has been measured with increasing precision along the years
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. This is has been measured with increasing precision along the years
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. Gravitational instability
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. Quantum fluctuations during
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. Scale factor: a(t)/a(tini) Last scattering surface
CMB
Scale factor: a(t)/a(tini)
Last scattering surface
Radiation
dominated
era
Matter
dominated
era
Dark energy
dominated
era

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

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

27. Perturbations of quantum-mechanical origin
Scale factor: a(t)/a(tini)
Last scattering surface
Radiation
dominated
era
Matter
dominated
era
Dark energy
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
3- Quantize the system
time

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

37. Modern cosmology: the LambdaCDM model
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. Quantum to classical transition of the perturbations
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 )
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, PRD , PRA )
time

39. Modern cosmology: the LambdaCDM model
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. QM without observers etc …
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 …