The Cosmological Constant Problem and Running Vacuum in the Expanding Universe (2203.13757v2)

Abstract: It is well-known that quantum field theory (QFT) induces a huge value of the cosmological constant, $\Lambda$, which is outrageously inconsistent with cosmological observations. We review here some aspects of this fundamental theoretical conundrum (the cosmological constant problem') and strongly argue in favor of the possibility that the cosmic vacuum density $\rho_{\rm vac}$ may be mildly evolving with the expansion rate $H$. Such arunning vacuum model' (RVM) proposal predicts an effective dynamical dark energy without postulating new ad hoc fields (quintessence and the like). Using the method of adiabatic renormalization within QFT in curved spacetime we find that $\rho_{\rm vac}(H)$ acquires a dynamical component ${\cal O}(H^2)$ caused by the quantum matter effects. There are also ${\cal O}(H^n)$ ($n=4,6,..$) contributions, some of which may trigger inflation in the early universe. Remarkably, the evolution of the adiabatically renormalized $\rho_{\rm vac}(H)$ is not affected by dangerous terms proportional to the quartic power of the masses ($\sim m^4$) of the fields. Traditionally, these terms have been the main source of trouble as they are responsible for the extreme fine tuning feature of the cosmological constant problem. In the context under study, however, the late time $\rho_{\rm vac}(H)$ around $H_0$ is given by a dominant term ($\rho_{\rm vac}^0$) plus the aforementioned mild dynamical component $\propto \nu (H^2-H_0^2)$ (with $|\nu|\ll1$), which makes the RVM to mimic quintessence. Finally, on the phenomenological side we show that the RVM may be instrumental in alleviating some of the most challenging problems (so-called tensions') afflicting nowadays the observational consistency of theconcordance' $\Lambda$CDM model, such as the $H_0$ and $\sigma_8$ tensions.

• The paper demonstrates that a running vacuum model, with vacuum energy density evolving as H², can alleviate the longstanding cosmological constant problem.
• Methodology employs adiabatic renormalization in curved spacetime to remove quartic mass divergences, linking quantum field theory to cosmic dynamics.
• Results indicate that the dynamic vacuum framework may help reconcile current tensions in H₀ and σ₈ measurements with the standard ΛCDM cosmology.

The Cosmological Constant Problem and Running Vacuum in the Expanding Universe

The paper "The Cosmological Constant Problem and Running Vacuum in the Expanding Universe" by Joan Solà Peracaula addresses longstanding theoretical challenges in cosmology, focusing on the notorious cosmological constant problem (CCP) and exploring alternative models for vacuum energy in the context of the expanding universe. The CCP involves a glaring discrepancy between the theoretical predictions of the cosmological constant $\Lambda$ in quantum field theory (QFT) and the value observed in cosmology. This paper offers an in-depth review and proposes novel insights to tackle this issue.

Summary of the Paper

The cosmological constant problem arises from the vast difference between the vacuum energy density predicted by QFT and the minuscule observed value, often referred to as the "vacuum catastrophe." The author revisits fundamental aspects of this problem, proposing that the vacuum energy density $\rho_{\rm vac}$ might exhibit a slow evolution with the universe's expansion rate $H$. This hypothesis leads to the concept of a "running vacuum model" (RVM), which introduces dynamical dark energy without necessitating new fields, such as quintessence, traditionally invoked to account for cosmic acceleration.

The study employs a framework of adiabatic renormalization within QFT in curved spacetime to derive that $\rho_{\rm vac}(H)$ includes a dynamical component proportional to $H^2$, stemming from quantum matter effects. Other contributions proportional to higher powers of $H^n$ ($n=4,6,...$) might have implications for inflationary epochs. Crucially, the adiabatically renormalized vacuum energy density is shown to be free from problematic terms proportional to the quartic power of field masses ($\sim m^4$), which are typically associated with fine-tuning issues in $\Lambda$CCP.

The author theoretically underpins the possibility of a mild evolution in the vacuum dynamics, helping alleviate conflicts such as the $H_0$ and $\sigma_8$ tensions observed in $\Lambda$CDM cosmology. These tensions refer to discrepancies between different methods of measuring the Hubble constant $H_0$ and the amplitude of fluctuations on scales of 8 Mpc, respectively.

Implications and Future Developments

The paper posits that the running vacuum model could serve as a viable alternative to the standard cosmological model, providing theoretical foundations to tackle observational inconsistencies in $\Lambda$CDM. The RVM serves as a bridge between QFT calculations and cosmological observations, offering a framework that naturally incorporates a mild form of dynamical dark energy evolution without deviating significantly from the trusted $\Lambda$CDM model predictions.

The implications of the research extend to both theoretical and practical realms. Theoretically, the paper suggests that embracing a dynamical vacuum energy model could offer a resolution to the cosmological constant problem that is deeply rooted in quantum theoretical calculations. Practically, the approach may guide the development of future astronomical observations and experiments aimed at validating the existence of evolving vacuum dynamics.

The paper also highlights ongoing tension between observational data points, such as those from the Planck Collaboration, and other local measurements, suggesting that the RVM could provide crucial insights into addressing these discrepancies. Additionally, the author speculates on future developments in AI and its potential role in analyzing vast cosmological datasets to further scrutinize model predictions and constraints.

In conclusion, Solà Peracaula's work contributes significantly to the dialogue surrounding one of the major challenges in modern cosmology, offering a fresh angle to approach and potentially resolve the cosmological constant problem through the running vacuum model. The paper underscores the importance of linking quantum field theory insights with cosmological observations, fostering a more holistic understanding of the universe's accelerating expansion.