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

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

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

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)

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.

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 …

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

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

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

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 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

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

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

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)

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

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

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

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

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

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:0704.3540 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 …

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

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)

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)!

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 → ∞)

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

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 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

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

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