Abstract
We present a proposal to relate the de Sitter conjecture (dSC) with the time dependence of fluxes via the covariant entropy bound (CEB). By assuming an early phase of accelerated expansion where the CEB is satisfied, we take into account a contribution from time-dependent flux compactification to the four-dimensional entropy which establishes a bound on the usual slow-roll parameters ηH and ϵH. We also show an explicit calculation of entropy from a toroidal flux compactification, from a transition amplitude of time-dependent fluxes which allows us to determine the conditions on which the bounds on the slow-roll parameters are in agreement to the dSC.
Highlights
The Swampland program has reached great advances in the last few years in its pursuit of characterize those features distinguishing effective theories that can be consistently completed into a quantum gravity theory (Landscape) from those which do not (Swampland) [1,2,3,4]
We shall show that a time dependence of entropy leads to the presence of bounds on η H and e H
We have proposed a relation between the de Sitter conjecture with the time dependence of fluxes through the covariant entropy bound (CEB)
Summary
The Swampland program has reached great advances in the last few years in its pursuit of characterize those features distinguishing effective theories that can be consistently completed into a quantum gravity theory (Landscape) from those which do not (Swampland) [1,2,3,4]. Some of them are based on solid grounds, such as the distance conjecture and the weak gravity conjecture, while others, as the de Sitter conjectures, were initially motivated by some empirical evidence based on string models [5,6], and appropriately refined into its final form in order to be compatible with some well known effective scenarios such as the Higgs potential [7] among others. As stochastic effects become relevant, it is found by thermodynamic arguments that slow-roll conditions either violate the second law or the swampland dSC [25,26]. We are interested in studying the implications of the CEB [42,43,44,45] on the inflationary slow-roll parameters.
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