Thesis

Entanglement in Quantum Field Theory in Inertial and Non-Inertial Frames and Applications to Cosmology

• Call:

  IDPASC Portugal - PHD Programme 2016

• Academic Year:

  2016 / 2017

• Domains:

  Theoretical Particle Physics | Cosmology

• Supervisor:

  Brigitte Hiller

• Co-Supervisor:

  Marcos Rodrigues-Sampaio

• Institution:

  Universidade de Coimbra

• Host Institution:

  Universidade de Coimbra

• Abstract:

  Quantum fields in non-Minkowskian spacetimes present peculiar effects as compared with quantum fields in flat spacetime. Of particular physical interest are dynamical spacetimes with or without horizons preventing observers from having access to the full quantum state of a field [1]. Generally, neither the particle content nor the structure of vacuum fluctuations remain covariant: the Unruh effect and the Hawking black hole radiation and entropy are good examples. Such a fusion between statistical physics, relativity and quantum mechanics set a landmark in the search for a quantum theory of gravity. Quantum entanglement serves as a tool to study experimental and theoretical cosmology. In the early universe, the energy content was largely dominated by a highly entangled quantum field background [1]. Even though experimental evidence shows that primordial perturbations have undergone quantum-to-classical transitions by decoherence mechanisms, some quantum correlations could in principle linger, particularly in the case of weakly interacting fields, and encode information about the evolution of the universe [2]. The theoretical framework to study such phenomena is quantum field theory in curved backgrounds [3]. The propagation of quantum fields in expanding spacetimes leads to spontaneous creation of pair of particles with opposite momenta building up nonlocal quantum correlations. In [4], the entanglement of quantum field modes of opposite momenta was shown to contain information about the cosmic parameters characterizing the spacetime expansion. The research proposal involves the following considerations. - Entanglement of Interacting Fields in Expanding Spacetimes. We intend to study how interactions affect quantum correlations in two scenarios. Firstly for self interactions of scalar fields both in the interaction picture and in the Schroedinger picture. Whilst the former allows for a straightforward perturbative evaluation, the latter can be solved in a scheme which does not rely on the smallness of the coupling constant. Secondly, for the case of fermion fields we intend to model a gauge interaction with a vector field which we shall consider as an environment in order to study how the correlations between fermionic particles of opposite momenta are affected by decoherence and thus evaluate the deleterious effects on the cosmological parameters encoded in the quantum correlations. - Cosmological Consequences of Initial State Entanglement The effect of an initial entangled state of the inflaton with another spectator scalar field on cosmological observables in the power spectrum was studied in [5]. We intend to calculate the power spectrum based on an initially interacting Lagrangian which will inevitably entangle the fields and change the equations for the mode functions whose solutions serve as an input to evaluate field correlations and thus the power spectrum. References: [1] E. Martin-Martinez and N. C. Menicucci, Class. Quant. Grav. 31 (2014) 214001. [2] Y. Nambu, Phys. Rev. D78 (2008) 044023. [3] G. Souza, K. M. Fonseca-Romero, Marcos Sampaio and M. C. Nemes, Phys. Rev. D90 (2014) 125039; H. Alexander, Marcos Sampaio, Paul Mansfield and G. Souza, Eur. Lett. 111 (2015) 60001. [4] J. L. Ball, I. Fuentes and F. P. Schuller, Phys. Lett. A359 (2006) 550. [5] A. Albretch et al., JHEP 1411 (2014) 093.