Cosmology with a decaying vacuum (1304.2796v1)

Abstract: Properties of unstable false vacuum states are analyzed from the point of view of the quantum theory of unstable states. Some of false vacuum states survive up to times when their survival probability has a non-exponential form. At times much latter than the transition time, when contributions to the survival probability of its exponential and non-exponential parts are comparable, the survival probability as a function of time t has an inverse power-like form. We show that at this time region the instantaneous energy of the false vacuum states tends to the energy of the true vacuum state as $1/t^{2}$ for $t \to \infty$.

• The paper demonstrates that unstable false vacuum states exhibit non-exponential decay at long timescales, following an inverse power-law rather than the traditional exponential.
• It applies this non-exponential decay concept to a Flat Robertson-Walker cosmological model, suggesting a time-dependent dark energy component.
• The analysis uses quantum theory to show that the false vacuum's energy approaches the true vacuum energy as 1/t over time.

Decaying Vacuum and Its Cosmological Implications

K. Urbanowski and M. Szydłowski present a detailed investigation into the properties of unstable false vacuum states from the perspective of quantum theory. This paper explores the dynamics of decaying vacuum states, emphasizing their non-exponential decay characteristics over extended timescales and exploring the implications of such behavior for cosmology.

Overview of Key Concepts

The paper revisits the concept of false vacuum decay, initially pioneered by Coleman and Callan, where a system's state is not at the absolute minimum of energy density and is instead separated by a potential barrier. Such states are prone to transition to the true vacuum state, potentially through quantum tunneling, even if thermal transitions are not feasible due to low temperatures.

A central point of discussion is the long-time behavior of these false vacuum states. The paper highlights the limitations of the exponential decay law, demonstrating that at times significantly longer than the characteristic decay time, the survival probability follows an inverse power-law pattern. The paper finds that the instantaneous energy of false vacuum states approaches that of the true vacuum state, scaling as $1/t$ as $t$ approaches infinity.

Quantitative Findings

Urbanowski and Szydłowski rigorously analyze the decay process, showcasing that the survival amplitude $A(t)$ at large times deviates from an exponential form:

$A(t) \propto t^{-(l+1)}e^{-iE_{\text{min}}t}$

where $l$ is a parameter related to the energy distribution. This indicates a non-exponential decay pattern in the survival probability, pointing towards a time-dependent cosmological constant scenario.

The authors derive an effective Hamiltonian for the one-dimensional subspace of states, leading to expressions for instantaneous energy and decay rate that underline the non-stationary nature of vacuum decay in cosmological settings.

Cosmological Applications

In the context of cosmology, the results suggest that certain false vacuum regions could persist significantly beyond the decay time "T", affecting cosmological models, particularly those associated with dark energy. The theoretical framework is applied to a Flat Robertson-Walker (FRW) universe model. In this model, the energy density of the dark sector includes both a constant component and a time-dependent term.

The paper's dynamical systems analysis results in critical points linked to classical cosmological scenarios such as the Einstein-de Sitter universe and the de Sitter universe, with varying stability and dynamical behaviors based on the parameter $a$.

Implications and Speculation on Future Developments

The findings contribute to our understanding of the decay dynamics in the context of the universe's evolution. The paper opens avenues for considering decay processes in string cosmology landscapes, where multiple vacua are prevalent. Furthermore, the implications for dark energy models in the FRW universe suggest adjustments could be necessary for accurate cosmological predictions.

Looking forward, this research could prompt further examination of false vacuum states in quantum field theory and their integration into large-scale cosmological models. Such extensions could potentially refine our grasp of the universe's fate, particularly concerning hypotheses around metastable dark energy states.

In conclusion, this paper provides a systematic examination of decaying vacuum cosmology, shedding light on the intricate dynamics that challenge traditional decay laws. This could pave the way for novel interpretations and applications within both quantum mechanics and cosmology research.