Bounds on Slow Roll and the de Sitter Swampland (1807.05193v2)

Abstract: The recently introduced swampland criterion for de Sitter (arXiv:1806.08362) can be viewed as a (hierarchically large) bound on the smallness of the slow roll parameter $\epsilon_V$. This leads us to consider the other slow roll parameter $\eta_V$ more closely, and we are lead to conjecture that the bound is not necessarily on $\epsilon_V$, but on slow roll itself. A natural refinement of the de Sitter swampland conjecture is therefore that slow roll is violated at ${\cal O}(1)$ in Planck units in any UV complete theory. A corollary is that $\epsilon_V$ need not necessarily be ${\cal O}(1)$, if $\eta_V \lesssim -{\cal O}(1)$ holds. We consider various tachyonic tree level constructions of de Sitter in IIA/IIB string theory (as well as closely related models of inflation), which superficially violate arXiv:1806.08362, and show that they are consistent with this refined version of the bound. The phrasing in terms of slow roll makes it plausible why both versions of the conjecture run into trouble when the number of e-folds during inflation is high. We speculate that one way to evade the bound could be to have a large number of fields, like in $N$-flation.

• The paper demonstrates that slow roll conditions are bounded at an O(1) level, posing challenges to the existence of de Sitter vacua in quantum gravity.
• It analyzes tachyonic instabilities in Type II string theory to reconcile perceived swampland violations with refined slow roll parameters.
• The study critically assesses multi-field inflation scenarios, suggesting that viable inflation models must overcome these tight theoretical constraints.

Analysis of "Bounds on Slow Roll and the de Sitter Swampland"

The paper by Garg and Krishnan addresses significant questions in the field of string theory, particularly focusing on the existence of de Sitter vacua within this framework. The authors build upon the swampland conjecture, which suggests that certain conditions or states—like de Sitter vacua—are not feasible in consistent theories of quantum gravity. The concept of the swampland places de Sitter solutions as problematic, and this paper explores the nature of these challenges by examining slow-roll parameters.

Summary of Core Contributions

1. Slow-Roll Boundaries: A pivotal element of the paper is the discussion around the slow roll parameters, $\epsilon_V$ and $\eta_V$. They posit that a true bound exists not merely on $\epsilon_V$ but on slow roll as a whole. The conjecture leads to asserting that slow roll conditions are violated at a significant order (i.e., $\mathcal{O}(1)$) in any UV-complete theory of quantum gravity. This presents a shift from the perspective that bounds the individual $\epsilon_V$ to considering broader slow-roll dynamics.
2. Analysis of Tachyonic Directions: Through a detailed assessment of tachyonic tree-level constructions in Type II string theory, including integrations over various fluxes and orientifold planes, the authors argue that examples which superficially violate the swampland conjecture can actually be reconciled within their refined bound. They focus on tachyonic instabilities often yielding directions that imply $\eta_V$ values far removed from zero, suggesting these continuously violate slow-roll conditions.
3. Impact on Inflating Models: Examining scenarios such as N-flation, the paper considers scenarios under which the swampland criteria may be circumvented by engaging with multiple fields. The discussion hinges on whether large numbers of fields inherently adjust the swampland boundaries—crucial for models needing substantial e-folds during inflation.

Implications and Theoretical Speculations

The content of this paper, while rooted in string theory cosmology, extends broader implications about the plausible structures of our universe. The suggestion that slow roll is fundamentally incompatible with a UV-complete quantum gravity echo concerns about the traditional understanding of cosmological inflation. In light of this, the research underscores potential limitations of single-field inflationary models within string theory, emphasizing that reconciling high e-fold numbers with swampland assertions demands creative theoretical innovations, potentially involving multiple fields or radical theoretical shifts.

Furthermore, from a theoretical physics standpoint, these explorations provoke deeper examination into why current observational data pointing toward a universe with a small cosmological constant seems inconsistent with string theoretic principles as interpreted through swampland conjecture. Thus, future trajectories in theoretical physics research shall likely scrutinize methods for either reconciling observational data within these constraints or reshaping foundational principles.

Future Directions in AI and Quantum Theories

The methodologies of bounding and analyzing theoretical constructs like those in this paper could be further enhanced by utilizing AI tools adept at managing complex data pools and simulating quantum scenarios over large parameter spaces. As AI models evolve, they may offer new insights into string theory landscapes, potentially revealing patterns and constraints that manual analytic approaches might overlook or delineate slowly.

In conclusion, Garg and Krishnan's work provides critical insights while strategically bridging hypothetical string landscapes with known empirical constraints, perpetuating both skepticism and hope towards comprehending whether true de Sitter vacua can exist within quantum gravitational frameworks. Their insights potentially guide the future of theoretical physics, while keeping the scientific community vigilant and reflective about the assumptions underlying quantum cosmology.