A stringy perspective on the coincidence problem

Abstract: We argue that, for generic string compactifications, dark energy is likely to signal the beginning of the end of our universe, perhaps even through decompactification, with possible implications for the cosmological coincidence problem. Thanks to the scarcity (absence?) of stable de Sitter vacua, dark energy in string theory is assumed to take the form of a quintessence field in slow roll. As it rolls, a tower of heavy states will generically descend, triggering an apocalyptic phase transition in the low energy cosmological dynamics after at most a few hundred Hubble times. As a result, dark energy domination cannot continue indefinitely and there is at least a percentage chance that we find ourselves in the first Hubble epoch. We use a toy model of quintessence coupled to a tower of heavy states to explicitly demonstrate the breakdown in the cosmological dynamics as the tower becomes light. This occurs through a large number of corresponding particles being produced after a certain time, overwhelming quintessence. We also discuss some implications for early universe inflation.

• The paper proposes that the scarcity of stable de Sitter vacua under swampland constraints implies dark energy behaves as a short-lived quintessence field rather than a cosmological constant.
• It develops a toy model where a quintessence field coupled with a tower of heavy states becomes light during field evolution, triggering a calculable phase transition.
• The study reinforces string theory's swampland program by quantifying dark energy's limited temporal epoch, thereby offering a potential resolution to the cosmological coincidence problem.

A Stringy Perspective on the Coincidence Problem

The paper "A Stringy Perspective on the Coincidence Problem," authored by Francesc Cunillera and Antonio Padilla, offers a thorough exploration of the cosmological coincidence problem through the lens of string theory and its constraints. It confronts the enigmatic observation that the current energy densities of matter and dark energy in the universe are of roughly the same order, despite evolving at vastly different rates over the universe's history. Within the framework of string theory, this study scrutinizes the implications of the swampland conjectures for the nature of dark energy and its potential responses to this cosmological puzzle.

Key Thesis and Findings

The authors propose that for string compactifications broadly consistent with swampland constraints, dark energy serves as a signal for profound changes in the universe, perhaps even leading to its decompactification. At the heart of this proposal is the assertion that there is a scarcity or even absence of stable de Sitter vacua in string theory. This implies dark energy should be characterized as a quintessence field in slow roll, rather than a cosmological constant, and is bound to a finite temporal epoch.

By positioning the field on a potential that satisfies either of the criteria from the refined de Sitter conjecture—a gradient condition or a Hessian bound—their models suggest that dark energy domination will not extend beyond a few hundred Hubble times, thereby providing a "solution" to the coincidence problem by making the current epoch of dark energy statistically less improbable.

Methodology and Modelling

The authors develop a toy model incorporating a quintessence field coupled with a tower of heavy states that become light as the field evolves. This model demonstrates how the field's excursion leads to an accumulation of light states, potentially initiating a phase transition. Such a situation would terminate dark energy domination within a calculable period. Their analysis employs parameters from string theory's swampland conjectures, particularly the distance conjecture, to frame this cosmological transition.

Theoretical Implications

The implications of this work are multifaceted. Theoretically, it reinforces aspects of the swampland program and its restrictions on effective field theories derived from string theory. Furthermore, it suggests that the nature of dark energy as a dynamic field ubiquitously aligns with string theory's predictions, offering a coherent theoretical framework to address the coincidence problem without resorting to anthropic arguments or fine-tuning.

Speculation on Future Developments

Future developments may include deeper investigations into other possible field configurations and their cosmological impacts within string theory. The study suggests that further theoretical work could explore connections between string theory's constraints and late-time cosmology, possibly predicting observable phenomena or constraining models of early universe inflation in line with swampland considerations.

Conclusion

While this paper does not settle the cosmological coincidence problem, it leverages string theory’s frameworks to present a compelling model where the temporally limited nature of dark energy alleviates the "why now?" question. It encourages continued exploration of cosmological models within the broader structure of theoretical physics, particularly those informed by the rich landscape and constraints of string theory. Future research in this context could yield insights not only into the fate of the universe but also into the fundamental constructs of theoretical physics and cosmology.