Abordagem efetiva em gravitação quântica com aplicação em cosmologia primordial

Abstract

In this thesis, we explore various semiclassical and quantum aspects of the gravitational interaction via the anomaly-induced effective action. Considering the importance of the conformal symmetry in the semiclassical contributions, we address the conformal generalization of the gauge vector field to the case of an arbitrary dimension and construct four versions of the theory with conformal symmetry in 𝑑−dimensions. We formulate the induced action with a metric-scalar background in two standard covariant forms and extend the study on ambiguities in the total derivative terms of the anomaly using Pauli-Villars regularization. Our analysis of induced action at low energies reveals existing connection to the renormalization group and effective potential. Subsequently, we investigate the decoupling of massive ghost mode in the four-dimensional theory of the conformal factor of the metric. The analysis of the derived one-loop nonlocal form factors includes their asymptotic behavior in the ultraviolet (UV) and infrared (IR) limits. In the UV domain, our results reproduce the Minimal Subtraction scheme-based beta functions. In the IR, the diagrams with massive ghost internal lines collapse into snail-type graphs and become irrelevant. On the other hand, those structures that contribute to the running of parameters of the full action, and survive in the IR, are well-correlated with the divergent part coming from the effective low-energy theory of the conformal factor. Finally, we discuss whether these results may shed light on the possible running of the cosmological constant at low energies. Next, as an additional application, we explore the possibility of avoiding cosmological singularity with a bounce solution in the early Universe. The main finding is that simple and well-known semiclassical correction, which describes the mixing of radiation and gravity in the effective action, may provide an analytic solution with a bounce. This solution requires a positive beta function for the total radiation term and the contraction of the Universe at the initial instant. The numerical estimate shows that the bounce may occur in an acceptable range of energies, but only under strong assumptions about the particle physics beyond the Standard Model.