Metastable De Sitter Research Articles

A new class of de Sitter vacua in type IIB large volume compactifications

We construct a new class of metastable de Sitter vacua of flux compactifications of type IIB string theory. These solutions provide a natural extension of the ‘Large Volume Scenario’ anti-de Sitter vacua, and can analogously be realised at parametrically large volume and weak string coupling, using standard mathcal{N} = 1 supergravity. For these new vacua, a positive vacuum energy is achieved from the inclusion of a small amount of flux-induced supersymmetry breaking in the complex structure and axio-dilaton sector, and no additional ‘uplift’ contribution (e.g. from anti-branes) is required. We show that the approximate no-scale structure of the effective theory strongly influences the spectrum of the stabilised moduli: one complex structure modulus remains significantly lighter than the supersymmetry breaking scale, and metastability requires only modest amounts of tuning. After discussing these general results, we provide a recipe for constructing de Sitter vacua on a given compactification manifold, and give an explicit example of a de Sitter vacuum for the compactification on the Calabi-Yau orientifold realised in mathbb{C}{mathrm{mathbb{P}}}_{11169}^4 . Finally, we note that these solutions have intriguing implications for phenomenology, predicting no csuperpartners in the spectrum below ∼50 TeV, and no WIMP dark matter.

Anti-D3 branes and moduli in non-linear supergravity

Anti-D3 branes and non-perturbative effects in flux compactifications spontaneously break supersymmetry and stabilise moduli in a metastable de Sitter vacua. The low energy 4D effective field theory description for such models would be a supergravity theory with non-linearly realised supersymmetry. Guided by string theory modular symmetry, we compute this non-linear supergravity theory, including dependence on all bulk moduli. Using either a constrained chiral superfield or a constrained vector field, the uplifting contribution to the scalar potential from the anti-D3 brane can be parameterised either as an F-term or Fayet-Iliopoulos D-term. Using again the modular symmetry, we show that 4D non-linear supergravities that descend from string theory have an enhanced protection from quantum corrections by non-renormalisation theorems. The superpotential giving rise to metastable de Sitter vacua is robust against perturbative string-loop and α′ corrections.

Linking light scalar modes with a small positive cosmological constant in string theory

Based on the studies in Type IIB string theory phenomenology, we conjecture that a good fraction of the meta-stable de Sitter vacua in the cosmic stringy landscape tend to have a very small cosmological constant Λ when compared to either the string scale MS or the Planck scale MP , i.e., Λ ≪ MS4 ≪ MP4. These low lying de Sitter vacua tend to be accompanied by very light scalar bosons/axions. Here we illustrate this phenomenon with the bosonic mass spectra in a set of Type IIB string theory flux compactification models. We conjecture that small Λ with light bosons is generic among de Sitter solutions in string theory; that is, the smallness of Λ and the existence of very light bosons (may be even the Higgs boson) are results of the statistical preference for such vacua in the landscape. We also discuss a scalar field ϕ3/ϕ4 model to illustrate how this statistical preference for a small Λ remains when quantum loop corrections are included, thus bypassing the radiative instability problem.

De Sitter Vacua from an Anomalous Gauge Symmetry.

We find a new class of metastable de Sitter solutions in compactifications of six-dimensional supergravity motivated by type IIB or heterotic string vacua. Two Fayet-Iliopoulos terms of a local U(1) symmetry are generated by magnetic flux and by the Green-Schwarz term canceling the gauge anomalies, respectively. The interplay between the induced D term, the moduli dependence of the effective gauge coupling, and a nonperturbative superpotential stabilizes the moduli and determines the size of the extra dimensions.

Single-step de Sitter vacua from nonperturbative effects with matter

A scenario of moduli stabilisation based on the interplay between closed and open string sectors is explored in a bottom-up approach. We study N=1 effective supergravities inspired by type IIB orientifold constructions that include background fluxes and non-perturbative effects. The former generate the standard flux superpotential for the axiodilaton and complex structure moduli. The latter can be induced by gaugino condensation in a non-Abelian sector of D7-branes and involve the overall Kaehler modulus of the compactification as well as matter fields. We analyse the dynamics of this coupled system and show that it is compatible with single-step moduli stabilisation in a metastable de Sitter vacuum. A novelty of the scenario is that the F-term potential suffices to generate a positive cosmological constant and to stabilise all moduli, except for a flat direction that can be either lifted by a mass term or eaten up by an anomalous U(1).

Surviving in a metastable de Sitter space-time

In a metastable de Sitter space any object has a finite life expectancy beyond which it undergoes vacuum decay. However, by spreading into different parts of the universe which will fall out of causal contact of each other in future, a civilization can increase its collective life expectancy, defined as the average time after which the last settlement disappears due to vacuum decay. We study in detail the collective life expectancy of two comoving objects in de Sitter space as a function of the initial separation, the horizon radius and the vacuum decay rate. We find that even with a modest initial separation, the collective life expectancy can reach a value close to the maximum possible value of 1.5 times that of the individual object if the decay rate is less than 1% of the expansion rate. Our analysis can be generalized to any number of objects, general trajectories not necessarily at rest in the comoving coordinates and general FRW space-time. As part of our analysis we find that in the current state of the universe dominated by matter and cosmological constant, the vacuum decay rate is increasing as a function of time due to accelerated expansion of the volume of the past light cone. Present decay rate is about 3.7 times larger than the average decay rate in the past and the final decay rate in the cosmological constant dominated epoch will be about 56 times larger than the average decay rate in the past. This considerably weakens the lower bound on the half-life of our universe based on its current age.

R2 inflation from scale invariant supergravity and anomaly free superstrings with fluxes

The scale invariant gravity theory coupled to conformally invariant matter is investigated. We show that in the non-supersymmetric case the conformally coupled scalars belong to an manifold, while in the supersymmetric case the scalar manifold becomes isomorphic to the Kählerian space =. In both cases when the underlying scale symmetry is preserved the vacuum corresponds to de Sitter space. Once the scale symmetry is broken by quantum effects, a transition to flat space becomes possible. We argue that the scale violating terms are induced by anomalies related to a symmetry. The anomaly is resolved via the gauging of a Peccei-Quinn axion shift symmetry. The theory describes an inflationary transition from de Sitter to flat Minkowski space, very similar to the Starobinsky inflationary model. The extension to metastable de Sitter superstring vacua is also investigated. The scalar manifold is extended to a much richer manifold, but it contains always as a sub-manifold. In superstrings the metastability is induced by axions that cure the anomalies in chiral (or even ) supersymmetric vacua via a Green-Schwarz/Peccei-Quinn mechanism generalized to four dimensions. We present some typical superstring models and discuss the possible stabilization of the no-scale modulus.

Dynamics of warped flux compactifications with backreacting antibranes

We revisit the effective low-energy dynamics of the volume modulus in warped flux compactifications with anti-D3-branes in order to analyze the prospects for metastable de Sitter vacua and brane inflation along the lines of KKLT/KKLMMT. At the level of the ten-dimensional supergravity solution, antibranes in flux backgrounds with opposite charge are known to source singular terms in the energy densities of the bulk fluxes, which led to a debate on the consistency of such constructions in string theory. A straightforward yet nontrivial check of the singular solution is to verify that its dimensional reduction in the large-volume limit reproduces the four-dimensional low-energy dynamics expected from known results where the antibranes are treated as a probe. Taking into account the antibrane backreaction in the effective scalar potential, we find that both the volume scaling and the coefficient of the antibrane uplift term are in exact agreement with the probe potential if the singular fluxes satisfy a certain near-brane boundary condition. This condition can be tested explicitly and may thus help to decide whether flux singularities should be interpreted as pathological or benign features of flux compactifications with antibranes. Throughout the paper, we also comment on a number of subtleties related to the proper definition of warped effective field theory with antibranes.

Gauge R-symmetry and de Sitter vacua in supergravity and string theory

A new class of metastable de Sitter vacua is presented and analyzed in N=1 supergravity and string theory with tunable (infinitesimally small) value of the cosmological constant. They are based on a gauged R-symmetry and the minimal spectrum contains a vector and a linear multiplet of the string dilaton or of a compactification modulus. In the minimum of the scalar potential supersymmetry is broken by an expectation value of both a D- and F-term.

Remarks on Positive Energy Vacua via Effective Potentials in String Theory

We study warped compactifications of string/M theory with the help of effective potentials, continuing previous work of the last two authors and Michael R. Douglas presented in (On the boundedness of effective potentials arising from string compactifications. Communications in Mathematical Physics 325(3):847–878, 2014). Under physically reasonable assumptions, we provide a mathematically rigorous proof of the existence of positive local minima of a large class of effective potentials. The dynamics of the conformal factor of the internal metric, which is responsible for instabilities in these constructions, is explored, and such instabilities are investigated in the context of de Sitter vacua. We prove existence results for the equations of motion in the case of a slowly varying warp factor, and the stability of such solutions is also addressed. These solutions are a family of meta-stable de Sitter vacua from type IIB string theory in a general non-supersymmetric setup.

Cascading gauge theory on [formula omitted] and String Theory landscape

Placing anti-D3 branes at the tip of the conifold in Klebanov–Strassler geometry provides a generic way of constructing meta-stable de Sitter (dS) vacua in String Theory. A local geometry of such vacua exhibit gravitational solutions with a D3 charge measured at the tip opposite to the asymptotic charge. We discuss a restrictive set of such geometries, where anti-D3 branes are smeared at the tip. Such geometries represent holographic dual of cascading gauge theory in dS4 with or without chiral symmetry breaking. We find that in the phase with unbroken chiral symmetry the D3 charge at the tip is always positive. Furthermore, this charge is zero in the phase with spontaneously broken chiral symmetry. We show that the effective potential of the chirally symmetric phase is lower than that in the symmetry broken phase, i.e., there is no spontaneous chiral symmetry breaking for cascading gauge theory in dS4. The positivity of the D3 brane charge in smooth de-Sitter deformed conifold geometries with fluxes presents difficulties in uplifting AdS vacua to dS ones in String Theory via smeared anti-D3 branes.

Scalar masses in general N=2 gauged supergravity theories

We readdress the question of whether any universal upper bound exists on the square mass m^2 of the lightest scalar around a supersymmetry breaking vacuum in generic N=2 gauged supergravity theories for a given gravitino mass m_3/2 and cosmological constant V. We review the known bounds which apply to theories with restricted matter content from a new perspective. We then extend these results to theories with both hyper and vector multiplets and a gauging involving only one generator, for which we show that such a bound exists for both V>0 and V<0. We finally argue that there is no bound for the same theories with a gauging involving two or more generators. These results imply that in N=2 supergravity theories metastable de Sitter vacua with V<<m^2_3/2 can only arise if at least two isometries are gauged, while those with V>>m^2_3/2 can also arise when a single isometry is gauged.

Stability, tunneling and flux changing de Sitter transitions in the large volume string scenario

We study the non-perturbative stability of the Large Volume Scenario (LVS) of IIB string compactifications, by analysing transitions mediated by the Brown-Teitelboim (BT) brane nucleations and by Coleman De Luccia tunneling (CDL). We find that, as long as the effective field theory description holds, the LVS AdS minima are stable despite being non-supersymmetric. This opens the possibility of having a CFT dual. Metastable de Sitter vacua behave differently depending on the uplifting mechanism. We find explicit expressions for the different decay rates in terms of exponentials of the volume. Among the transitions of dS to dS those with increasing volume and decreasing vacuum energy are preferred, though dS decays to AdS (big-crunch sinks) have higher probability. However, the probability of transitions via the CDL mechanism to decompactification are exponentially much larger compared to these. The BT decays correspond to flux/D3 brane transitions mediated by the nucleation of D5/NS5 branes. We compare our results with previous analysis for KKLT, type IIA, and 6D Einstein-Maxwell studies. In particular we find no indication for a bubble of nothing decay.

Metastable spontaneous breaking of [formula omitted] supersymmetry

We show that contrary to the common lore it is possible to spontaneously break N=2 supersymmetry even in simple theories without constant Fayet–Iliopoulos terms. We consider the most general N=2 supersymmetric theory with one hypermultiplet and one vector multiplet without Fayet–Iliopoulos terms, and show that metastable supersymmetry breaking vacua can arise if both the hyper-Kähler and the special-Kähler geometries are suitably curved. We then also prove that while all the scalars can be massive, the lightest one is always lighter than the vector boson. Finally, we argue that these results also directly imply that metastable de Sitter vacua can exist in N=2 supergravity theories with Abelian gaugings and no Fayet–Iliopoulos terms, again contrary to common lore, at least if the cosmological constant is sufficiently large.

Simple metastable de Sitter vacua in N=2 gauged supergravity

We construct a simple class of N=2 gauged supergravity theories that admit metastable de Sitter vacua, generalizing the recent work done in the context of rigid supersymmetry. The setup involves one hypermultiplet and one vector multiplet spanning suitably curved quaternionic-Kähler and special-Kähler geometries, with an Abelian gauging based on a single triholomorphic isometry, but neither Fayet-Iliopoulos terms nor non-Abelian gauge symmetries. We construct the most general model of this type and show that in such a situation the possibility of achieving metastable supersymmetry breaking vacua crucially depends on the value of the cosmological constant V relative to the gravitino mass squared $ m_{{{3 \left/ {2} \right.}}}^2 $ in Planck units. In particular, focusing on de Sitter vacua with positive V, we show that metastability is only possible when $ V\gtrsim 2.17m_{{{3 \left/ {2} \right.}}}^2 $ . We also derive an upper bound on the lightest scalar mass in this kind of model relative to the gravitino mass m 3/2 as a function of the cosmological constant V, and discuss its physical implications.

Emerging potentials in higher-derivative gauged chiral models coupled to $ \mathcal{N}=1 $ supergravity

We present a new method to introduce scalar potentials to gauge-invariant chiral models coupled to supergravity. The theories under consideration contain consistent higher-derivative terms which do not give rise to instabilities and ghost states. The chiral auxiliaries are not propagating and can be integrated out. Their elimination gives rise to emerging potentials even when there is not a superpotential to start with. We present the case of a single chiral multiplet with and without a superpotential and, in the gauged theory, up to two chiral multiplets coupled to supergravity with no superpotential. A general feature of the emergent potential is that it is negative defined leading to anti-de Sitter vacua. In the gauge models, competing D-terms may lift the potential leading to stable and metastable de Sitter and Minkowski vacua as well with spontaneously broken supersymmetry.

Metastable de Sitter vacua in N = 2 to N = 1 truncated supergravity

Abstract We study the possibility of achieving metastable de Sitter vacua in general N=2toN=1truncatedsupergravitieswithoutvectormultiplets,andcomparewiththe situations arising in N = 2 theories with only hypermultiplets and N = 1 theories with only chiral multiplets. In N = 2 theories based on a quaternionic manifold and a graviphoton gauging, de Sitter vacua are necessarily unstable, as a result of the peculiar properties of the geometry. In N = 1 theories based on a Kähler manifold and a superpotential, de Sitter vacua can instead be metastable provided the geometry satisfies some constraint and the superpotential can be freely adjusted. In N = 2 to N = 1 truncations, the crucial requirement is then that the tachyon of the mother theory be projected out from the daughter theory, so that the original unstable vacuum is projected to a metastable vacuum. We study the circumstances under which this may happen and derive general constraints for metastability on the geometry and the gauging. We then study in full detail the simplest case of quaternionic manifolds of dimension four with at least one isometry, for which there exists a general parametrization, and study two types of truncations defining Kähler submanifolds of dimension two. As an application, we finally discuss the case of the universal hypermultiplet of N = 2 superstrings and its truncations to the dilaton chiral multiplet of N = 1 superstrings. We argue that de Sitter vacua in such theories are necessarily unstable in weakly coupled situations, while they can in principle be metastable in strongly coupled regimes.

Building an explicit de Sitter

Abstract We construct an explicit example of a de Sitter vacuum in type IIB string theory that realizes the proposal of Kähler uplifting. As the large volume limit in this method depends on the rank of the largest condensing gauge group we carry out a scan of gauge group ranks over the Kreuzer-Skarke set of toric Calabi-Yau threefolds. We find large numbers of models with the largest gauge group factor easily exceeding a rank of one hundred. We construct a global model with Kähler uplifting on a two-parameter model on $ \mathbb{CP}_{11169}^4 $ , by an explicit analysis from both the type IIB and F-theory point of view. The explicitness of the construction lies in the realization of a D7 brane configuration, gauge flux and RR and NS flux choices, such that all known consistency conditions are met and the geometric moduli are stabilized in a metastable de Sitter vacuum with spontaneous GUT scale supersymmetry breaking driven by an F-term of the Kähler moduli.

Cosmology of axions and moduli: A dynamical systems approach

This paper is concerned with string cosmology and the dynamics of multiple scalar fields in potentials that can become negative, and their features as (early) dark energy models. Our point of departure is the ``string axiverse,'' a scenario that motivates the existence of cosmologically light axion fields as a generic consequence of string theory. We couple such an axion to its corresponding modulus. We give a detailed presentation of the rich cosmology of such a model, ranging from the setting of initial conditions on the fields during inflation, to the asymptotic future. We present some simplifying assumptions based on the fixing of the axion decay constant ${f}_{a}$, and on the effective field theory when the modulus trajectory is adiabatic, and find the conditions under which these assumptions break down. As a by-product of our analysis, we find that relaxing the assumption of fixed ${f}_{a}$ leads to the appearance of a new metastable de Sitter region for the modulus without the need for uplifting by an additional constant. A dynamical systems analysis reveals the existence of many fixed point attractors, repellers and saddle points, which we analyze in detail. We also provide geometric interpretations of the phase space. The fixed points can be used to bound the couplings in the model. A systematic scan of certain regions of parameter space reveals that the future evolution of the Universe in this model can be rich, containing multiple epochs of accelerated expansion.

FRW solutions and holography from uplifted AdS/CFT systems

Starting from concrete AdS/CFT dual pairs, one can introduce ingredients which produce cosmological solutions, including metastable de Sitter and its decay to non-accelerating FRW. We present simple FRW solutions sourced by magnetic flavor branes and analyze correlation functions and particle and brane dynamics. To obtain a holographic description, we exhibit a time-dependent warped metric on the solution and interpret the resulting redshifted region as a Lorentzian low energy effective field theory in one fewer dimension. At finite times, this theory has a finite cutoff, a propagating lower dimensional graviton and a finite covariant entropy bound, but at late times the lower dimensional Planck mass and entropy go off to infinity in a way that is dominated by contributions from the low energy effective theory. This opens up the possibility of a precise dual at late times. We reproduce the time-dependent growth of the number of degrees of freedom in the system via a count of available microscopic states in the corresponding magnetic brane construction.