Dark energy in quantum field theory: Implications on modern cosmology

Abstract

[eng] The Cosmological Constant, Λ, has been a controversial element in theoretical physics and cosmology since its introduction by Einstein in his field equations in 1917. Despite maintaining an irregular reputation over the years, the discovery of the accelerated expansion of the Universe at the end of the 20th century confirmed Λ as a major ingredient in the cosmological puzzle and a part of the standard model of cosmology, the ΛCDM model. Although the ΛCDM model fits well with the overall cosmological data, it still faces several theoretical conundrums and observational issues that require urgent attention.

The cause of the accelerated expansion is called Dark Energy, which is mathematically modeled by Λ, but its origin is uncertain, despite the fact that it is commonly assumed to be vacuum energy. General theoretical estimates of the vacuum energy density in the context of Quantum Field Theory differ from observations by as much as 123 orders of magnitude in the most severe case. Additionally, attempts to adjust its value by collecting several contributions to the vacuum budget have been unsuccessful and drove to the well-known problem of fine-tuning. This inability to derive the correct observed value of vacuum energy density in the Universe constitutes the Cosmological Constant Problem one of the biggest mysteries that theoretical physics faces. The problem becomes even more significant when considering the fact that Dark Energy and Matter have an energy density of the same order of magnitude at present, despite the fact that Dark Energy have a constant energy density, while Matter dilutes with cosmological expansion. This is known as the Coincidence Problem.

If that were not enough, we also have additional problems from a phenomenological perspective. Specifically, there are cosmological tensions between early Universe and local observations affecting two important parameters in the cosmological model. The first one is H0 (the Hubble function or expansion rate at the current time) and the second one is σ8 (related to the structure formation in the Universe). The discrepancies can reach up to ∼ 4 − 5σ and 2 − 3σ, respectively.

Inspired by these significant challenges, the work performed under the direction of Prof. Joan Sol`a Peracaula has followed two different but closely related directions. Firstly, we focused on the renormalization and regularization of the vacuum energy density in the context of Quantum Field Theory through a new formalism based on the traditional adiabatic regularization. We obtained significant and noteworthy results regarding the dynamical behavior of the vacuum energy density, which seems to evolve smoothly with the background expansion in terms of the Hubble function, ρvac(H). These results coincide with the so-called Running Vacuum Models (RVM), which have been around for many years.

Secondly, with the cosmological tensions in mind, we tested two models related to the previous theoretical investigations against a large set of cosmological data to constrain the cosmological parameters: 1) The Brans-Dicke model consists in a modification of General relativity by promoting the Gravitational Constant to be a scalar degree of freedom. This can be reformulated as an effective picture of General Relativity possessing a dynamical vacuum component, similar to the RVM. 2) The Ricci-RVM is a variation of the more traditional model in which we replace the dependency in H by R, the Ricci scalar. This has some adventages such as not affecting the usual predictions for Big Bang Nucleosynthesis. To summarize, this thesis presents a rigorous investigation of the departure of the cosmological framework from the ΛCDM model, considering the possibility of Dark Energy being a dynamical quantity. We study this possibility from first principles in the context of Quantum Field Theory, obtaining surprising and unprecedented results in the literature. Additionally, we explore two models against different cosmological datasets and scenarios to obtain a more complete perspective. Our fits show promising results suggesting a possible deviation from the ΛCDM model.

[cat] La Constant Cosmològica, Λ, és un element controvertit des que Einstein les va introduir a les equacions de camp el 1917. Actualment, Λ és un ingredient vital del model estàndard de cosmologia, el ΛCDM. Aquest model acomoda la major part de les observacions, per`o presenta problemes de caràcter teòric i fenomenològic que necessiten atenció La causa de l’expansió accelerada s’anomena Energia Fosca, representada matemàticament amb Λ, i normalment identificada amb energia de buit. Estimacions teòriques determinen que l’energia de buit obtinguda de les observacions cosmològiques se separa molt de les prediccions de la teoria quàntica de camps. Aquesta incapacitat per derivar el resultat observacional constitueix el Problema de la Constant Cosmològica, un dels majors misteris al qual s’enfronta la física teòrica. També hi ha problemes des de l’àmbit fenomenològic. Específicament, hi ha tensions en dos paràmetres cosmològics importants entre les diferents observacions: H0 (la funció de Hubble o rati d’expansió en el present) i σ8 (relacionat amb la formació d’estructura en l’Univers). Les discrepàncies poden arribar a 4 − 5σ i 2 − 3σ, respectivament. Aquesta tesi estudia una possible desviació respecte del ΛCDM, considerant la possibilitat que la densitat d’energia de buit sigui dinàmica en el context de la teoria quàntica de camps. A través d’un nou formalisme, hem obtingut el comportament dinàmic de l’energia de buit, la qual evoluciona suaument amb l’expansió en termes de la funció de Hubble. Aquests resultats coincideixen amb els coneguts Running Vacuum Models (RVM), els quals han estat presents a la literatura des de fa uns anys, però que ara justifiquem rigorosament. Addicionalment, explorem dos models basats en aquesta dinàmica de buit contra les dades observacionals: El model de Brans-Dicke, de gravetat modificada, i el Ricci-RVM, una modificació del RVM en el qual reemplacem la dependència en H per R, l’escalar de Ricci. Els nostres fits mostren resultats prometedors envers una possible desviació respecte del tradicional model ΛCDM.