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In this paper, we study the inflationary scenario in the realm of k-essence model and swampland conjectures. Taking into account three models of Chaplygin gas, such as generalized, modified, and generalized cosmic Chaplygin gas models, we discuss the equation of state (EoS) parameter ω, slow roll parameters (ϵ(ϕ),η(ϕ)), curvature perturbation (Ps), tensor to scalar ratio (r), and scalar spectral index (ns). As regards the k-essence model, the coupling function as a function of scalar field L(ϕ) is used. We investigate the swampland conjecture and then find the value of ζ(ϕ), i.e., bound of second conjecture for these three models by unifying swampland conjecture and k-essence. We plot the EoS parameter ω, inflationary parameters plane r−ns and bound of swampland conjecture ζ(ϕ)−ϕ, which determine that the values of &omega

This dissertation consists of five chapters. The first broadly and briefly orients the reader through an introduction to inflationary cosmology, and why we might expect multi-field inflation to take place. The next four chapters correspond to distinct lines of research conducted during my time as a graduate student. Chapter two is based on work conducted with my advisor Sonia Paban, studying the landscape of possible multi-field inflationary models through a random-matrix generated potential [1]. Chapter three is based on work with Diederik Roest and Perseas Christodoulidis, studying universality and prior dependence in multi-field inflation [2]. Chapters four and five are based on work with Sonia Paban and Vikas Aragam, studying inflation in potentials compatible with quantum gravity and rapidly turning trajectories [3, 4].

This paper reviews the theoretical and phenomenological implications of the swampland conjectures from the perspective of inflationary cosmology, focusing on warm inflation. We demonstrate how the swampland conjectures appear to favor the strong dissipative regime, giving warm inflation a competitive edge over standard inflation. Additionally, we ponder the possible deeper implications of dissipation for constructing successful inflation models from string theory.

We investigate the consequences of combining swampland conjectures with the requirement of asymptotic safety. To this end, we explore the infrared regime of asymptotically safe gravity in the quadratic one-loop approximation, and we identify the hypersurface spanned by the endpoints of asymptotically safe renormalization group trajectories. These comprise the allowed values of higher-derivative couplings as well as standard logarithmic form factors. We determine the intersection of this hypersurface with the regions of parameter space allowed by the weak-gravity conjecture, the swampland de Sitter conjecture, and the trans-Planckian censorship conjecture. The latter two depend on some order-one constants, for generic values of which we show that the overlap region is a proper subspace of the asymptotically safe hypersurface. Moreover, the latter lies inside the region allowed by the weak gravity conjecture assuming electromagnetic duality. Our results suggest a non-trivial interplay between the consistency conditions stemming from ultraviolet completeness of the RG flow, black hole physics, and cosmology., Comment: 33 pages, 8 figures. Invited contribution to the special issue "Asymptotic Safety in Quantum Gravity" in Universe. V2: figures added, typos fixed. Matches published version

We present model independent reconstructions of quintessence and the Swampland conjectures (SC) using both Machine Learning (ML) and cosmography. In particular, we demonstrate how the synergies between theoretical analyses and ML can provide key insights on the nature of dark energy and modified gravity. Using the Hubble parameter $H(z)$ data from the cosmic chronometers we find that the ML and cosmography reconstructions of the SC are compatible with observations at low redshifts. Finally, including the growth rate data $f\sigma_8(z)$ we perform a model independent test of modified gravity cosmologies through two phase diagrams, namely $H-f\sigma_8$ and $\eta-f\sigma_8$, where the anisotropic stress parameter $\eta$ is obtained via the $E_g$ statistics, which is related to gravitational lensing data. While the first diagram is consistent within the errors with the $\Lambda$CDM model, the second one has a $\sim 2\sigma$ deviation of the anisotropic stress from unity at $z\sim 0.3$ and a $\sim 4\sigma$ deviation at $z\sim 0.9$, thus pointing toward mild deviations from General Relativity, which could be further tested with upcoming large-scale structure surveys., Comment: 13 pages, 6 figures, 4 tables. Changes match published version