Thesis

Loop quantum cosmology: a sight into the early Universe

• Call:

  IDPASC Portugal - PHD Programme 2017

• Academic Year:

  2017 / 2018

• Domains:

  General Relativity | Cosmology

• Supervisor:

  Mercedes Martin Benito

• Co-Supervisor:

  Javier A Olmedo Nieto

• Institution:

  Faculdade de Ciências - Universidade de Lisboa

• Host Institution:

  Faculdade de Ciências - Universidade de Lisboa

• Abstract:

  Loop quantum cosmology (LQC) is a serious proposal that connects quantum gravity effects and the physics of the early Universe. The extension of LQC to inhomogeneous cosmologies provides master equations for the dynamics of cosmological perturbations that encode quantum geometry effects. Unlike in the standard cosmological model, where cosmological perturbations propagate on a classical (low-curvature) background, in LQC the quantum geometry is described via the expectation values of geometrical operators on suitable quantum states. With this framework at hand, lots of effort is put these days to understand the extension of traditional inflation into the deep Planck regime, and compute predictions of the primordial power spectra rooted in LQC that can be confronted with present observations of the CMB. However the analyses done so far are partial inasmuch as 1) they ignore quantum fluctuations since only expectation values of geometrical operators contribute to the effective semiclassical evolution, and 2) they ignore the backreaction of the perturbations on the quantum homogeneous geometry. The goal of this project is to improve the analysis going beyond these approximations. We will work out analytical and numerical methods in order to integrate the quantum dynamics of the quantum background, with the aim of retaining quantum geometry effects as much as possible and analyzing their physical consequences. Moreover, we will consider the quantum backreaction of the perturbations on the background geometry. In this way, we can gain insight into the interplay between the homogeneous sector and the inhomogeneities since it might have been important in the deep quantum regime of LQC prior to inflation. Our aim is then to recover the backreaction terms and study regimes where this backreaction, even if small, is non-negligible. This type of effects might be responsible, fully or partially, of anomalies observed in the CMB, as small non-Gaussianitites. Going even beyond, the plan is also to study more general states than those so far considered in LQC, so that the interaction between the quantum background and the perturbations becomes physically richer.