Comment on Coleman-DeLuccia instantons

We complete an old argument that causal diamonds in the crunching region of the Lorentzian continuation of a Coleman-Deluccia instanton for transitions out of de Sitter space have finite area, and provide quantum models consistent with the principle of detailed balance, which can mimic the instanton transition probabilities for the cases where this diamond is larger or smaller than the causal patch of de Sitter space. We review arguments that potentials which do not have a positive energy theorem when the lowest de Sitter minimum is shifted to zero, may not correspond to real models of quantum gravity.

The inflationary wavefunction from analyticity and factorization

We study the analytic properties of tree-level wavefunction coefficients in quasi-de Sitter space. We focus on theories which spontaneously break dS boost symmetries and can produce significant non-Gaussianities. The corresponding inflationary correlators are (approximately) scale invariant, but are not invariant under the full conformal group. We derive cutting rules and dispersion formulas for the late-time wavefunction coefficients by using factorization and analyticity properties of the dS bulk-to-bulk propagator. This gives a unitarity method which is valid at tree-level for general n-point functions and for fields of arbitrary mass. Using the cutting rules and dispersion formulas, we are able to compute n-point functions by gluing together lower-point functions. As an application, we study general four-point, scalar exchange diagrams in the EFT of inflation. We show that exchange diagrams constructed from boost-breaking interactions can be written as a finite sum over residues. Finally, we explain how the dS identities used in this work are related by analytic continuation to analogous identities in Anti-de Sitter space.

A de-Sitter weak gravity conjecture

The study of de-Sitter Reissner–Nordstrøm black holes allows us to uncover a Weak Gravity Conjecture in de-Sitter space. It states that for a given mass [Formula: see text] there should be a state with a charge [Formula: see text] bigger than a minimal value [Formula: see text], depending on the mass and the de-Sitter radius [Formula: see text], in Planck units. This reproduces the well-known flat space–time result [Formula: see text] in the large radius limit (large [Formula: see text]). In the highly curved de-Sitter space, ([Formula: see text]) [Formula: see text] behaves as [Formula: see text]. Finally, we discuss the case of backgrounds from gauged R-symmetry in [Formula: see text] supergravity. This paper is based on [I. Antoniadis and K. Benakli, Fortsch. Phys. 68, 2000054 (2020), arXiv:2006.12512 [hep-th]].

De Sitter Holography: Fluctuations, Anomalous Symmetry, and Wormholes

The Goheer–Kleban–Susskind no-go theorem says that the symmetry of de Sitter space is incompatible with finite entropy. The meaning and consequences of the theorem are discussed in light of recent developments in holography and gravitational path integrals. The relation between the GKS theorem, Boltzmann fluctuations, wormholes, and exponentially suppressed non-perturbative phenomena suggests that the classical symmetry between different static patches is broken and that eternal de Sitter space—if it exists at all—is an ensemble average.

Vortical Effects for Free Fermions on Anti-De Sitter Space-Time

Here, we study a quantum fermion field in rigid rotation at finite temperature on anti-de Sitter space. We assume that the rotation rate Ω is smaller than the inverse radius of curvature ℓ−1, so that there is no speed of light surface and the static (maximally-symmetric) and rotating vacua coincide. This assumption enables us to follow a geometric approach employing a closed-form expression for the vacuum two-point function, which can then be used to compute thermal expectation values (t.e.v.s). In the high temperature regime, we find a perfect analogy with known results on Minkowski space-time, uncovering curvature effects in the form of extra terms involving the Ricci scalar R. The axial vortical effect is validated and the axial flux through two-dimensional slices is found to escape to infinity for massless fermions, while for massive fermions, it is completely converted into the pseudoscalar density −iψ¯γ5ψ. Finally, we discuss volumetric properties such as the total scalar condensate and the total energy within the space-time and show that they diverge as [1−ℓ2Ω2]−1 in the limit Ω→ℓ−1.

r-Stablity Index of r-Maximal Closed Hypersurfaces in de Sitter Spaces

It is well-known that some of minimal (or maximal) hypersurfaces are stable. However, there is growing recognition on unstable hypersurfaces by introducing the concept of index of stability for minimal ones. For instance, the index of stability for minimal hypersurefces in Euclidean n-sphere has been defined by J. Simons and followed by many people. Also, Barros and Sousa have studied a high order extention of index as the concept of r-index (i.e. index of r-stability) on r-minimal hypersurfaces of n-sphere. They gave low bonds for r-stability index of r-minimal hypersurfaces in Euclidean sphere. In this paper, we low bounds for the r-stability index of r-maximal closed spacelike hypersurfaces in the de Sitter space.