On the possible running of the cosmological "constant" (0910.4925v1)

Abstract: Despite the many outstanding cosmological observations leading to a strong evidence for a nonvanishing cosmological constant (CC) term in the gravitational field equations, the theoretical status of this quantity seems to be lagging well behind the observational successes. It thus seems timely to revisit some fundamental aspects of the CC term in Quantum Field Theory (QFT). We emphasize that, in curved space-time, nothing a priori prevents this term from potentially having a mild running behavior associated to quantum effects. Remarkably, this could be the very origin of the dynamical nature of the Dark Energy, in contrast to many other popular options considered in the literature. In discussing this possibility, we also address some recent criticisms concerning the possibility of such running. Our conclusion is that, while there is no comprehensive proof of the CC running, there is no proof of the non-running either. The problem can be solved only through a deeper understanding of the vacuum contributions of massive quantum fields on a curved spacetime background. We suggest that such investigations are at the heart of one of the most important endeavors of fundamental theoretical cosmology in the years to come.

• The paper shows that the cosmological constant may run dynamically under quantum corrections in curved space-time.
• It applies renormalization group techniques to extend quantum field theory methods to a cosmologically relevant framework.
• The study outlines key theoretical challenges and suggests future research to bridge quantum mechanics with cosmological observations.

On the Possible Running of the Cosmological "Constant"

The paper explores the intriguing possibility that the cosmological constant (CC), denoted as $\Lambda$, may exhibit a running behavior within the framework of quantum effects in curved space-time. While the observational evidence for a non-vanishing cosmological constant is robust, its theoretical underpinning remains a subject of intense discussion within cosmological research. This paper examines the theoretical possibility that the CC is subject to running akin to other physical parameters in quantum field theory (QFT), thereby proposing a dynamic nature for dark energy.

Theoretical Context and Scientific Discussions

The authors discuss several approaches addressing the cosmological constant problem, mainly through the lens of the renormalization group (RG) running within QFT and quantum gravity (QG) contexts. Of particular interest is the proposition that the CC could manifest as a mild running quantity within perturbative QFT in curved space-time. This scenario diverges from the traditional consideration of a static CC, which has posed significant theoretical challenges, especially regarding the so-called "old" and "coincidence" problems.

The "old" CC problem refers to the discrepancies between theoretical predictions of vacuum energy density from QFT and its observed value in cosmological measurements. Meanwhile, the "coincidence problem" seeks to understand why the present-day vacuum energy density is comparable to the matter energy density. Both issues motivate the investigation into a dynamical CC.

Implications of CC Running

Operationalizing the concept of a running cosmological constant would entail framing its evolution as an inherent dynamic feature of dark energy, potentially linked to quantum fluctuations and interactions within the universe's expanding fabric. The RG techniques, conventionally employed in particle physics to understand the scale dependence of physical parameters, are extended to the cosmological setting. However, these extensions require overcoming significant challenges due to the unique nature of gravitational interactions in a curved space-time fabric. The authors stress that such an analysis necessitates identifying an appropriate scale to replace the unphysical $\mu$ scale of the minimal subtraction scheme with a cosmologically relevant parameter, such as the Hubble function, $H$.

Exploring Quantum Effects

This paper explores the functional consequences of vacuum energy and its quantum corrections, highlighting the similarity between processes in curved space-time and the Nambu-Jona-Lasinio model. The vacuum energy density $\rho_{\Lambda}$ becomes subject to running, encapsulated in a proposed differential equation akin to the standard beta-function treatments in QFT. The authors argue that a non-zero $\beta_{\Lambda}$ function could emerge from interactions in curved space-time, suggesting a potential link between the cosmological behavior of $\Lambda$ and physical parameters of an expanding universe.

Challenges and Theoretical Speculations

Several hurdles are outlined that currently preclude rigorous proof of CC running, not least of which is the complexity of a consistent QFT framework in curved space. While the authors acknowledge critiques proposing the theoretical impossibility of CC running, they effectively counter these claims by highlighting gaps in existing arguments, particularly concerning the misinterpretation of renormalization ambiguities.

Conclusion and Future Directions

The investigation concludes without definitive evidence either for or against the running of the cosmological constant. Nonetheless, the discussion underscores the critical importance of further research in this area, advocating for continued theoretical exploration alongside observational studies. The authors suggest that a deeper understanding of the CC's behavior may pave avenues for linking particle physics more closely with cosmological phenomena, offering potentially new insights into the universe's fate and the nature of dark energy.

In summary, while the theoretical status of a dynamic cosmological constant remains nascent, this paper lays groundwork for continued inquiry into its feasibility, thus representing an intriguing direction for theoretical and computational cosmology.