Inflationary Implications of the Covariant Entropy Bound and the Swampland de Sitter Conjectures

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.

Nonlinear dynamics of flux compactification

We study the nonlinear evolution of unstable flux compactifications, applying numerical relativity techniques to solve the Einstein equations in D dimensions coupled to a q-form field and positive cosmological constant. We show that initially homogeneous flux compactifications are unstable to dynamically forming warped compactifications. In some cases, we find that the warping process can serve as a toy-model of slow-roll inflation, while in other instances, we find solutions that eventually evolve to a singular state. Analogous to dynamical black hole horizons, we use the geometric properties of marginally trapped surfaces to characterize the lower dimensional vacua in the inhomogeneous and dynamical settings we consider. We find that lower-dimensional vacua with a lower expansion rate are dynamically favoured, and in some cases find spacetimes that undergo a period of accelerated expansion followed by contraction.

Extranatural flux inflation

We propose a new inflation scenario in flux compactification, where a zero mode scalar field of extra components of the higher dimensional gauge field is identified with an inflaton. The scalar field is a pseudo Nambu-Goldstone boson of spontaneously broken translational symmetry in compactified spaces. The inflaton potential is non-local and finite, which is protected against the higher dimensional non-derivative local operators by quantum gravity corrections thanks to the gauge symmetry in higher dimensions and the shift symmetry originated from the translation in extra spaces. We give an explicit inflation model in a six dimensional scalar QED, which is shown to be consistent with Planck 2018 data.

Nonvanishing finite scalar mass in flux compactification

We study possibilities to realize a nonvanishing finite Wilson line (WL) scalar mass in flux compactification. Generalizing loop integrals in the quantum correction to WL mass at one-loop, we derive the conditions for the loop integrals and mode sums in one-loop corrections to WL scalar mass to be finite. We further guess and classify the four-point and three-point interaction terms satisfying these conditions. As an illustration, the nonvanishing finite WL scalar mass is explicitly shown in a six dimensional scalar QED by diagrammatic computation and effective potential analysis. This is the first example of finite WL scalar mass in flux compactification.

The layered phase of anisotropic gauge theories: A model for topological insulators

Topological insulators are materials where current does not flow through the bulk, but along the boundaries, only. They are of particular practical importance, since it is considerably more difficult, by “conventional” means, to affect their transport properties, than for the case of conventional materials. They are, thus, particularly robust to perturbations. One way to accomplish such changes is by engineering defects. The defects that have been the most studied are domain walls; however flux compactifications can also work. We recall the domain wall construction and compare it to the construction from flux compactification. A particular way of engineering the presence of such defects is by introducing anisotropic couplings for the gauge fields. In this case, a new phase appears, where matter is confined along layers and local degrees of freedom cannot propagate through the bulk. It is also possible to take into account the “backreaction” of the dynamics of the gauge fields on the defects and find that a new phase, the layered phase, where, while transport of local degrees of freedom is confined to surfaces, the topological properties can propagate through the bulk, constituting an example of anomaly flow. The anisotropy itself can be understood as emerging from a particular Maxwell-dilaton coupling.

Modified Gravity in Higher Dimensions, Flux Compactification, and Cosmological Inflation

We review a possible origin of cosmological inflation from higher ( D ) spacetime dimensions in the context of modified gravity theory. It is demonstrated that it requires a spontaneous warped compactification of higher ( D ) spacetime dimensions together with the stabilization of extra ( D − 4 ) dimensions by Freund–Rubin mechanism. The relevant tools include an extra gauge ( D / 2 − 1 ) -form field with a non-vanishing flux in compact dimensions and a positive cosmological constant in D dimensions. Those features are illustrated on the specific example in eight spacetime dimensions compactified on a four-sphere with a warped factor and a flux, which leads to a viable Starobinsky-like inflationary model in four (non-compact) spacetime dimensions.