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Register a new userConstraints on Dark Energy from Inflation and the Swampland Conjectures
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Authors
Jacob M. Leedom
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We discuss the prospects of measuring deviations of the dark energy equation of state from w=-1 by using the swampland conjectures to relate inflationary models to quintessence scenarios. This note is based on work done by the author with H. Murayama and C. Chiang arXiv:1811.01987.
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We discuss the relations between swampland conjectures and observational constraints on both inflation and dark energy. Using the requirement $| abla V|geq c V$, with $c$ as a universal constant whose value can be derived from inflation, there may be no observable distinction between constant and non-constant models of dark energy. However, the latest modification of the above conjecture, which utilizes the second derivative of the potential, opens up the opportunity for observations to determine if the dark energy equation of state deviates from that of a cosmological constant. We also comment on the observability of tensor fluctuations despite the conjecture that field excursions are smaller than the Planck scale.
Among Swampland conditions, the distance conjecture characterizes the geometry of scalar fields and the de Sitter conjecture constrains allowed potentials on it. We point out a connection between the distance conjecture and a refined version of the de Sitter conjecture in any parametrically controlled regime of string theory by using Boussos covariant entropy bound. The refined version turns out to evade all counter-examples at scalar potential maxima that have been raised. We comment on the relation of our result to the Dine-Seiberg problem.
The Swampland de Sitter conjecture in combination with upper limits on the tensor-to-scalar ratio $r$ derived from observations of the cosmic microwave background endangers the paradigm of slow-roll single field inflation. This conjecture constrains the first and the second derivatives of the inflationary potential in terms of two ${cal O} (1)$ constants $c$ and $c$. In view of these restrictions we reexamine single-field inflationary potentials with $S$-duality symmetry, which ameliorate the unlikeliness problem of the initial condition. We compute $r$ at next-to-leading order in slow-roll parameters for the most general form of $S$-dual potentials and confront model predictions to constraints imposed by the de Sitter conjecture. We find that $c sim {cal O} (10^{-1})$ and $c sim {cal O} (10^{-2})$ can accommodate the 95% CL upper limit on $r$. By imposing at least 50 $e$-folds of inflation with the effective field theory description only valid over a field displacement ${cal O} (1)$ when measured as a distance in the target space geometry, we further restrict $c sim {cal O} (10^{-2})$, while the constraint on $c$ remains unchanged. We comment on how to accommodate the required small values of $c$ and $c$.
The Swampland Distance Conjecture (SDC) constraints the dynamics emerging at infinite distances in field space of any effective field theory consistent with quantum gravity. It provides a relation between the cut-off in energies and the field range which, as we show, in the context of inflation it yields a universal upper bound on the inflaton excursion in terms of the tensor-to-scalar ratio, measured at typical CMB scales. In this note, we investigate the interplay between the SDC and the emergent inflationary physics around infinite distances singularities in string theory, with a special look at its significance for the $alpha$-attractor scenario of inflation. We show that the conjecture itself suggests that inflation may arise as an infinite distance phenomenon with the asymptotic kinetic structure typical of $alpha$-attractors. Furthermore, we argue that a proper string realisation of these cosmological models in Calabi-Yau manifolds should occur around infinite field distance singularities. However, such constructions typically imply that inflation should not take place in the limit where the inflaton kinetic term develops a pole but rather in the opposite regime. Finally, we study the constraints that the SDC poses on $alpha$-attractors and show that they still leave considerable room for compatibility with observations.
Perhaps the greatest challenge for fundamental theories based on compactification from extra dimensions is accommodating a period of accelerated cosmological expansion. Previous studies have identified constraints imposed by the existence of dark energy for two overlapping classes of compactified theories: (1) those in which the higher dimensional picture satisfies certain metric properties selected to reproduce known low energy phenomenology; or (2) those derived from string theory assuming they satisfy the Swampland conjectures. For either class, the analyses showed that dark energy is only possible if it takes the form of quintessence. In this paper, we explore the consequences for theories that belong to both classes and show that the joint constraints are highly restrictive, leaving few options.
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