From swampland to cosmos: A journey through swampland conjectures via supergravity and string inflation

Abstract

In this dissertation, we have combined insights from distinct yet interrelated areas of research to obtain a more thorough understanding of the de Sitter swampland conjectures, the trans-Planckian Censorship Conjecture, and the EFT for inflation with spontaneously broken supersymmetry. By integrating these diverse aspects of the research, we aim to provide a unified, in-depth overview of the theoretical frameworks of inflation, the swampland program, and string cosmology, as well as their connections, interdependencies, and implications for one another. Chapter 1 situates this dissertation within the current scientific landscape by providing a concise overview of various key topics, such as Inflation, Standard Model, Supersymmetry, Supergravity, String Inflation, and Swampland Conjectures. It also introduces the essential theoretical background, methodologies, and notation utilized throughout the study. The remaining chapters of the dissertation present a combination of my published research and ongoing work in the field. The research explores the interplay between single-field inflationary models and de Sitter swampland conjectures, seeking to provide a deeper understanding of the possibility of their mutual compatibility. By incorporating nilpotent superfields and examining the Trans-Planckian censorship conjecture, the scope of the research is broadened, addressing crucial aspects of supergravity and effective field theories. Chapter 2 was published in Atli and Guleryuz (2021), and investigates de Sitter swampland conjectures and their implications for single-field inflationary models with a generic potential. It revisits the de Sitter swampland conjectures by distinguishing the effective potential and inflationary potential from superconformal embedding of the superconformal action. It introduces the bounded de Sitter conjecture, which provides insight into the relationship between single-field inflationary models and de Sitter swampland conjectures. In that chapter, we showed that the stabilization of the inflaton field required the concave inflation potential and that the bounded de Sitter conjecture can be satisfied for any concave inflation potential as long as the related inflation parameter fulfills the condition $0 \lesssim -\eta \leq c' \approx \mathcal{O}(1)$. This finding offers valuable insights into the relationship between single-field inflationary models and the de Sitter swampland conjectures, providing a modest step towards understanding their possible mutual compatibility. Chapter 3 was published in Guleryuz (2021), where we focused on the trans-Planckian Censorship Conjecture (TCC) and examined its implications for non-minimal coupling terms in both Einstein and Jordan frames. It demonstrates the robustness of the TCC and the strong interplay between non-minimal coupling terms and inflationary dynamics. In that chapter, we demonstrated a general embedding of the generic non-minimal coupling term to the TCC for both frames and presented an example for the generalized non-minimal coupling case. In this example, we showed that the upper bound on the inflationary parameter $r$ becomes independent of the Jordan frame potential in the strong coupling limit of the generalized non-minimal coupling case. Moreover, the upper bound on the Jordan frame potential $V_J(\phi)$ can be eased in the strong coupling limit. These findings not only highlight the robustness of the TCC but also shows that the TCC bound might become less constraining in certain circumstances, allowing for a wider range of inflationary potentials that satisfy the conjecture. Thus, open up new avenues for future research on the compatibility of various inflationary models with the TCC, as well as the implications of non-minimal coupling terms for our understanding of the early universe's dynamics. Chapter 4 was published in Guleryuz (2023). In that chapter, we built an effective field theory for inflation with spontaneously broken supersymmetry without generating any supersymmetric AdS vacua by combining the tools offered by the nilpotent supergravity and the universal attractor mechanism. We showed that various Kähler potentials could produce the same kinetic term in flat directions without disrupting the scalar potential up to a Kähler transformation, and linearly coupled nilpotent superfields in the Kähler potential plays a crucial role in inflation, spontaneous SUSY breaking, and obtaining a de Sitter vacuum at the minimum of the potential. We also showed that one can promote an arbitrary parameter, such as in the $\alpha$-attractor models, as an overall multiplier to the total Kähler potential, capturing a unified region of the inflationary attractors, allowing us to obtain de Sitter and Minkowski vacua while avoiding AdS vacua. Additionally, we embedded the nilpotent superfields into the de Sitter swampland conjecture in an $\mathcal{N}=1$, $D=4$ SUGRA background, and expanded the consistent EFT space for the dSC. We showed that the bound on the parameter $c\sim \mathcal{O}(1)$ of the de Sitter swampland conjecture might undergo dynamic evolution during the inflationary epoch in case nilpotent superfields are incorporated into the potential gradient. The most stringent bound seems to emerge in the asymptotic limit with $4.61 \gtrsim c$. This result reveals a possible intricate interplay between the swampland conjecture and the underlying structure of the effective field theory space. Hence, the (super)universal attractors in the presence of nilpotent superfields offer a potential way out of the single-field inflation and swampland conflict by drawing an elegant picture for the swampland, which could contribute to a deeper understanding of the interrelations between string theory and cosmology. In conclusion, this study has provided a comprehensive analysis of the de Sitter swampland conjectures, the trans-Planckian Censorship Conjecture, and the effective field theory for inflation with spontaneously broken supersymmetry. Our findings offer a solid foundation for further research into the compatibility of various inflationary models with the TCC and the de Sitter swampland conjectures, as well as the implications of non-minimal coupling terms. Moreover, our results suggest that there is still much to be explored, and the insights gained from these investigations may prove instrumental in shaping our future understanding of the universe's underlying principles and the ultimate nature of reality.