Multi-feature universe: large parameter space cosmology and the swampland

Under the belief that the universe should be multi-feature and informative, we employ a model-by-model comparison method to explore the possibly largest upper bound on the swampland constant $c$. Considering the interacting quintessence dark energy as the comparison model, we constrain the large parameter space interacting dark energy model, a 12-parameter extension to the $Λ$CDM cosmology, in light of current observations. We obtain the largest $2σ$ ($3σ$) bound so far, $c\lesssim1.62$ $(1.94)$, which would allow the existences of a number of string theory models of dark energy such as 11-dimensional supergravity with double-exponential potential, $O(16)\times O(16)$ heterotic string and some Type II string compactifications. For inflationary models with concave potential, we find the $2σ$ ($3σ$) bound $c\lesssim0.13$ $(0.14)$, which is still in strong tension with the string-based expectation $c \sim \mathcal{O}(1)$. However, combining Planck primordial non-Gaussianity with inflation constraints, it is interesting that the Dirac-Born-Infeld inflation with concave potential gives the $2σ$ ($3σ$) bound $c\lesssim0.53$ $(0.58)$, which is now in a modest tension with the swampland conjecture. Using the Bayesian evidence as the model selection tool, it is very surprising that our 18-parameter multi-feature cosmology is extremely strongly favored over the $Λ$CDM model.

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