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Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/211121
Towards a non-perturbative description of cosmological inflation
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[eng] From the observation of the cosmic microwave background radiation (CMBR) we know that the universe is isotropic on scales larger than ∼ 75 Megaparsec to at least one part in 100000. The leading paradigm for explaining this observational data is a period of accelerated expansion in the earliest stages of the universe, called cosmological inflation.
Inflation also provides a causal mechanism for generating anisotropies on cosmological scales. These anisotropies result from the amplification of the unavoidable vacuum quantum excitations of the gravitational and matter fields due to the accelerated expansion. In particular, it is possible to explain the almost scale invariant power spectrum of the CMBR temperature map with a very simple inflationary regime called Slow Roll (SR) inflation.
Quantum fluctuations are usually assumed to be small enough such that they are well described with cosmological perturbation theory. However rare large quantum fluctuations can also be randomly generated during inflation. These large inhomogeneities can lead to the formation of Primordial Black Holes (PBH) and the probability of its generation is related with the amplitude of the power spectrum.
Both the amplitude of the power spectrum and the non-gaussianities measured at the CMBR are too small to generate a relevant amount of large fluctuations. To form enough PBH we need to exponentially enhance the amplitude of the power spectrum on scales which are not probed by the CMBR, for which a violation of SR is needed.
Although the growth of the power spectrum can be described at leading order in perturbation theory, the description of the tail of the Probability Distribution Function (PDF), where the large inhomogeneities are located, must be done in a non-perturbative way. We study two main approaches that aim to describe inflation in a non-perturbative way, the δN formalism and the stochastic approach.
Both approaches are based on gradient expansion, which assumes that the effect of quantum fluctuations whose characteristic wavelength is much larger than the Hubble radius is well described by an ensemble of locally homogeneous and isotropic patches, where spatial gradients are negligible, this approach is valid for any amplitude of local over-densities. In this thesis we show that spatial gradients and the momentum constraint of general relativity play an essential role when we use global coordinates, which are necessary to describe the statistical properties of the inhomogeneities by comparing different patches.
The δN formalism and the stochastic inflation represent consistent ways of providing initial conditions to gradient expansion. In the δN formalism, initial conditions on the field fluctuations are perturbatively given. The idea of stochastic inflation is fully non-perturbative. In this approach, the long-wavelength part of the field follows the evolution dictated by gradient expansion and the short-wavelength part act as a random noise continuously changing local trajectories such that the cumulative behaviour of small random kicks can induce non-perturbative effects in the local patch.
During this thesis we formulate for the first time a stochastic approach to inflation which includes spatial gradients and the momentum constraint and hence it is in principle able to describe the correct long-wavelength dynamics of inflationary inhomogeneities in a non-perturbative way. To test our results, we show that for any inflationary regime, the stochastic inflation so formulated, precisely reproduces the results of perturbative correlators in all regimes in which perturbation theory is supposed to work.
We also elucidate that, in order to take into account the whole non-perturbative dynamics of the local patches via stochastic inflation, the noises must be computed over the stochastically corrected local background rather than over the fiducial deterministic global background, as it is typically done in the literature.
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CRUCES MATEO, Diego. Towards a non-perturbative description of cosmological inflation. [consulta: 2 de desembre de 2025]. [Disponible a: https://hdl.handle.net/2445/211121]