1. Quantum Spacetime and Cosmic Inflation
Jerome Martin
CNRS/Institut d’Astrophysique de Paris
Probing Quantum Spacetime with Astrophysical Sources: the CTA era and beyond
LPNHE, 29 and 30 November 2017

2. The theory of cosmic inflation in brief: basic principles
The talk
Outline
The theory of cosmic inflation in brief: basic principles
Cosmological fluctuations of quantum-mechanical origin
Quantum Mechanics in the sky? Opens issues
Conclusions

3. The theory of cosmic inflation in brief: basic principles
The talk
Outline
The theory of cosmic inflation in brief: basic principles
Cosmological fluctuations of quantum-mechanical origin
Quantum Mechanics in the sky? Opens issues
Conclusions

4. Lambda/CDM=Four epochs
Inflation is a phase of accelerated expansion taking place in the very early Universe. It solves the fine tuning puzzles of the standard model of cosmology
Radiation
dominated
era
Matter
dominated
era
Dark energy
dominated
era
Scale factor: a(t)/a(tini)

5. Inflation is (usually) realized with one (or many) scalar field(s)
Inflation in brief
Inflation is (usually) realized with one (or many) scalar field(s)
If the scalar field moves slowly (the potential is flat), then pressure is negative
which, in the context of GR, means accelerated expansion and, hence, inflation takes place.

6. minimum of the potential
Inflation in brief
Inflation (usually) stops when the field reaches a part of the potential which
is no longer flat enough to support inflation; this happens in the vicinity of the
minimum of the potential
The field oscillates, decays and the decay products thermalize …Then the radiation dominated era starts …

7. The theory of cosmic inflation in brief: basic principles
The talk
Outline
The theory of cosmic inflation in brief: basic principles
Cosmological fluctuations of quantum-mechanical origin
Quantum Mechanics in the sky? Opens issues
Conclusions

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

9. 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

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

11. 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

12. Perturbations of quantum-mechanical origin
If inflation is correct …
… These are probes of quantum spacetime

13. Perturbations of quantum-mechanical origin
1- In the early Universe, the fluctuations are small and, hence, a linear approach is possible

14. Perturbations of quantum-mechanical origin
1- In the early Universe, the fluctuations are small and, hence, a linear approach is possible
2- The small fluctuations on top of an expanding spacetime are of two types:
a- scalar characterized by curvature perturbations v(t,x) and b- tensor (or primordial gravitational waves)

15. Perturbations of quantum-mechanical origin
1- In the early Universe, the fluctuations are small and, hence, a linear approach is possible
2- The small fluctuations on top of an expanding spacetime are of two types:
a- scalar characterized by curvature perturbations v(t,x) and b- tensor (or primordial gravitational waves)
3- The evolution of the quantum perturbations is controlled by the Hamiltonian

16. Perturbations of quantum-mechanical origin
1- In the early Universe, the fluctuations are small and, hence, a linear approach is possible
2- The small fluctuations on top of an expanding spacetime are of two types:
a- scalar characterized by curvature perturbations v(t,x) and b- tensor (or primordial gravitational waves)
3- The evolution of the quantum perturbations is controlled by the Hamiltonian
Free term

17. Perturbations of quantum-mechanical origin
1- In the early Universe, the fluctuations are small and, hence, a linear approach is possible
2- The small fluctuations on top of an expanding spacetime are of two types:
a- scalar characterized by curvature perturbations v(t,x) and b- tensor (or primordial gravitational waves)
3- The evolution of the quantum perturbations is controlled by the Hamiltonian
Free term
Interaction term between the
quantum fluctuations and the
classical background

18. Perturbations of quantum-mechanical origin
1- In the early Universe, the fluctuations are small and, hence, a linear approach is possible
2- The small fluctuations on top of an expanding spacetime are of two types:
a- scalar characterized by curvature perturbations v(t,x) and b- tensor (or primordial gravitational waves)
3- The evolution of the quantum perturbations is controlled by the Hamiltonian
Free term
Interaction term between the
quantum fluctuations and the
classical background
1- Pump field ~ time dependent coupling constant.
2- Only depends on the scale factor and its derivatives.
3- Vanishes if a’=0

19. Perturbations of quantum-mechanical origin
1- In the early Universe, the fluctuations are small and, hence, a linear approach is possible
2- The small fluctuations on top of an expanding spacetime are of two types:
a- scalar characterized by curvature perturbations v(t,x) and b- tensor (or primordial gravitational waves)
3- The evolution of the quantum perturbations is controlled by the Hamiltonian
Free term
Interaction term between the
quantum fluctuations and the
classical background
Corresponds to creation of pair of particles k -k

20. with a classical source
Perturbations of quantum-mechanical origin
This is similar to the Schwinger effect: interaction of a quantum field
with a classical source
J. Martin, Lect. Notes Phys. 738 (2008), 195
arXiv:
Schwinger effect
Inflationary cosmological perturbations
- Electron and positron fields
- Inhomogeneous gravity field
- Classical electric field
- Background gravitational field: scale factor
Amplitude of the effect controlled
by E
Amplitude controlled by the Hubble
parameter H
See also dynamical Schwinger effect, dynamical Casimir effect etc …

21. Perturbations of quantum-mechanical origin
Under the previous Hamiltonian, Schroedinger evolution gives
Two mode squeezed states

22. Perturbations of quantum-mechanical origin
Under the previous Hamiltonian, Schroedinger evolution gives
Two mode squeezed states
- Squeezed states are very well-known in other field of Physics, e.g. Quantum Optics
-”Classical” coherent state:
equal dispersion on x and p
- Squeezed state: not the
same dispersion (r squeezing
parameter)

23. Perturbations of quantum-mechanical origin
Under the previous Hamiltonian, Schroedinger evolution gives
Two mode squeezed states
- Squeezed states are very well-known in other field of Physics, e.g. Quantum Optics
- This is the strongest squeezed state ever produced in nature, r=O(100)!

24. Perturbations of quantum-mechanical origin
Under the previous Hamiltonian, Schroedinger evolution gives
Two mode squeezed states
- Squeezed states are very well-known in other field of Physics, e.g. Quantum
Optics
- This is the strongest squeezed state ever produced in nature, r=O(100)!
- A squeezed state is an entangled state. In the limit of very strong squeezing,
it is equivalent to an Einstein Podolsky Rosen (EPR) state (~ r → ∞)

25. The theory of cosmic inflation in brief: basic principles
The talk
Outline
The theory of cosmic inflation in brief: basic principles
Cosmological fluctuations of quantum-mechanical origin
Quantum Mechanics in the sky? Opens issues
Conclusions

26. 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

27. The theory of cosmic inflation in brief: basic principles
The talk
Outline
The theory of cosmic inflation in brief: basic principles
Cosmological fluctuations of quantum-mechanical origin
Quantum Mechanics in the sky? Opens issues
Conclusions

28. a result of quantum spacetime. Planck data is a way to probe quantum
Conclusions
Recap
According to cosmic inflation, the CMB anisotropies and the galaxies are
a result of quantum spacetime. Planck data is a way to probe quantum
spacetime!
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, very large
length 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 and (maybe) quantum gravity