Swampland Conjecture Research Articles

Theory of gravity with nonminimal matter-nonmetricity coupling and the de-Sitter swampland conjectures

In this study, we investigate swampland conjectures within the setup of matter and non-metricity nonminimal coupling theories of gravity. We examine how the inflationary solution produced by a single scalar field can be resolved with the swampland criteria in string theory regarding the formation of de Sitter solutions. The new important findings are that the inflationary scenario in our study differs from the one in general relativity because of the presence of a nonminimal coupling term, and that difference gives the correction to general relativity. In addition, we observe that the slow-roll conditions and the swampland conjectures are incompatible with each other for a single scalar field within the framework of nonminimally coupled alternative gravity theories. We predict that these results will hold for a wide range of inflationary scenarios in the context of nonminimal coupling gravitational theories.

Dark dimension and the effective field theory limit

In [1], we pointed out that in the Dark Dimension scenario [2] theoretical issues arise when the prediction for the vacuum energy [Formula: see text], that is obtained from swampland conjectures in string theory, is confronted with the corresponding result for [Formula: see text] in the effective field theory (EFT) limit. One of the problems concerns the widely spread belief that in higher dimensional EFTs with compact dimensions the vacuum energy is automatically finite. On the contrary, our analysis shows that [Formula: see text] contains (previously missed) UV-sensitive terms. Our work was challenged in [3]. Here we show why in our opinion the claims in [3] are flawed, and provide further support to our findings. We conclude presenting ideas on the physical mechanism that should dispose of the large UV contributions to [Formula: see text].

Stabilization of a twisted modulus on a mirror of rigid Calabi-Yau manifold

We study the stabilization of a twisted modulus in Type IIB flux compactifications on a mirror of the rigid Calabi-Yau threefold. By analyzing the effective action of twisted and untwisted moduli, we find that three-form fluxes satisfying the tadpole cancellation conditions lead to supersymmetric AdS vacua. We also investigate swampland conjectures on this non-geometric background.

On (A)dS solutions from Scherk-Schwarz orbifolds

We investigate the existence of dS vacua in supersymmetry-breaking Scherk-Schwarz toroidal compactifications of type II string theory, using the well-understood ingredients of curvature, fluxes and 1-loop Casimir energy. Starting from the 10d equations, we derive a series of no-go theorems and existence conditions for dS, and present two explicit, fully-backreacted, solutions: a dS one, which turns out to be not under control, and an AdS one, which can be chosen at arbitrarily weak coupling and large volume by dialling the unbounded fluxes. We then use a lower-dimensional EFT description to show that any dS solution has a universal tachyon and no parametric control. The simplest AdS solutions are also perturbatively unstable. We extend the no-go theorems to slow-roll acceleration and test various swampland conjectures in our non-supersymmetric string setup. The question of numerically controlled, unstable dS is left open.

Analyzing inflationary parameters and swampland conjectures of modified cosmology according to various entropies

This paper investigates the inflationary phase of the FRW universe within the context of generalized Chaplygin gas. We explore modified cosmological scenarios incorporating two entropy corrections, namely Tsallis and Barrow. These proposed entropies lead to modifications in the Friedmann equations. By incorporating the generalized Chaplygin gas into these equations, we determine various parameters including the slow roll parameters, number of e-folds, curvature perturbation, tensor-to-scalar ratio, and spectral index. We observe variations in the values of the tensor-to-scalar ratio r and the scalar spectral index ns with respect to the Tsallis and Barrow parameters. Additionally, we plot the r−ns plane. For the Tsallis entropy, we obtain r≤0.012, r≤0.027, and r≤0.008, with ns lying between (0.961,0.964), (0.957,0.966), and (0.956,0.964), respectively. In Barrow cosmology, we find r≤0.0037, r≤0.12, and r≤0.010, while ns falls within (0.92,0.97), (0.855,0.995), and (0.960,0.966) for the chaotic, SFI, and exponential potentials, respectively. These graphical analyses demonstrate the compatibility of our models with the latest Planck data. Moreover, by considering these entropy corrections, we determine the bounds of the Swampland de Sitter conjecture for generalized Chaplygin gas. In all cases, this bound remains less than unity, satisfying the required condition for the Swampland de Sitter conjecture.

Supersymmetric Hybrid Inflation in Light of CMB Experiments and Swampland Conjectures

Abstract In this study, we revisited supersymmetric (SUSY) hybrid inflation considering the latest observations from CMB experiments and the swampland conjectures. We demonstrated that when incorporating radiative, soft mass, and SUGRA corrections to the scalar potential, SUSY hybrid inflation remains consistent with Planck 2018 data. It is commonly perceived that SUSY hybrid inflation with a minimal K"ahler potential results in a gauge symmetry breaking scale $M$ of ${\cal O}(10^{15})$ GeV, leading to issues with the proton decay rate. Our analysis introduces a new parameter space where the proton decay problem is mitigated by achieving $M \sim 10^{16}$ GeV with $M_{S}^{2}<0$ and $am_{3/2}>0$. This scenario necessitates a soft SUSY breaking scale $|M_{S}| \gtrsim 10^{6}$ GeV. Furthermore, we found that the tensor-to-scalar ratio $r$ spans from $10^{-16}$ to $10^{-6}$, indicating a very small value. This small ratio allows the modified swampland criteria to hold, although satisfying the trans-Planckian censorship conjecture remains challenging. To address this, we also explored non-minimal K"ahler potentials. By fixing the spectral index at $n_{S}=0.9665$, consistent with the central value of Planck 2018 data, and setting $M=2\times 10^{16}$ GeV, we presented our calculations. We showed that the canonical measure of primordial gravitational waves, $r$, for $M_{S}=$ 1 TeV, $m_{3/2}=$ 1 TeV, $\kappa_{S}<0$ for $\cal{N}=$1 and $\cal{N}=$2, ranges from $10^{-5}$ to $0.01$, making it detectable by Planck and upcoming experiments such as LiteBIRD, Simons Observatory, PRISM, PIXIE, CORE, CMB-S4, and CMB-HD. Additionally, we outlined the parametric space and provided benchmark points for the non-minimal case, ensuring compatibility with both the modified swampland and trans-Planckian censorship conjectures. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd

Stable vacua with realistic phenomenology and cosmology in heterotic M-theory satisfying Swampland conjectures

We recently described a protocol for computing the potential energy in heterotic M-theory for the dilaton, complex structure and Kähler moduli. This included the leading order non-perturbative contributions to the complex structure, gaugino condensation and worldsheet instantons assuming a hidden sector that contains an anomalous U(1) structure group embedded in E8. In this paper, we elucidate, in detail, the mathematical and computational methods required to utilize this protocol. These methods are then applied to a realistic heterotic M-theory model, the B − L MSSM, whose observable sector is consistent with all particle physics requirements. Within this context, it is shown that the dilaton and universal moduli can be completely stabilized at values compatible with every phenomenological and mathematical constraint — as well as with ΛCDM cosmology. We also show that the heterotic M-theory vacua are consistent with all well-supported Swampland conjectures based on considerations of string theory and quantum gravity, and we discuss the implications of dark energy theorems for compactified theories.

Constant-roll inflation with tachyon field in the holographic braneworld

Abstract We study inflation driven by the tachyon field in the holographic braneworld by assuming the second slow-roll parameter η is constant. The parameter η can be either defined by the tachyon scalar field and the Hubble parameter or by the Hubble parameter only. By assuming a constant η, we derive and numerically solve a differential equation for the Hubble expansion rate. We calculate numerically the scalar spectral index and the tensor-to-scalar ratio. We confront the results with the observational data and find some constraints on the free model parameters. The swampland conjectures are discussed in the context of the constant-roll inflation, with some accent on the holographic model.

The de Sitter Swampland Conjectures in the Context of Chaplygin-Inspired Inflation

In this work, we discuss the de Sitter swampland conjectures in the context of the generalized Chaplygin-inspired inflationary model. We demonstrate that these conjectures can be satisfied, but only in the region of the parameter space far away from the General Relativity limit. The cosmic microwave background data had already been found to restrict the allowed inflationary potentials of this model. Our results impose a further limitation on the possible potentials.

On classical de Sitter solutions and parametric control

Finding string backgrounds with de Sitter spacetime, where all approximations and corrections are controlled, is an open problem. We revisit the search for de Sitter solutions in the classical regime for specific type IIB supergravity compactifications on group manifolds, an under-explored corner of the landscape that offers an interesting testing ground for swampland conjectures. While the supergravity de Sitter solutions we obtain numerically are ambiguous in terms of their classicality, we find an analytic scaling that makes four out of six compactification radii, as well as the overall volume, arbitrarily large. This potentially provides parametric control over corrections. If we could show that these solutions, or others to be found, are fully classical, they would constitute a counterexample to conjectures stating that asymptotic de Sitter solutions do not exist. We discuss this point in great detail.

Moduli axions, stabilizing moduli, and the large field swampland conjecture in heterotic M-theory

We compute the F- and D-term potential energy for the dilaton, complex structure, and Kähler moduli of realistic vacua of heterotic M-theory compactified on Calabi-Yau threefolds where, for simplicity, we choose h1,1=h2,1=1. However, the formalism is immediately applicable to the “universal” moduli of Calabi-Yau threefolds with h1,1=h1,2>1 as well. The F-term potential is computed using the nonperturbative complex structure, gaugino condensate and “world sheet instanton” superpotentials in theories in which the hidden sector contains an anomalous U(1) structure group. The Green-Schwarz anomaly cancellation induces inhomogeneous “axion” transformations for the imaginary components of the dilaton and Kähler modulus—which then produce a D-term potential. VD is a function of the real components of the dilaton and Kähler modulus (s and t) that is minimized and precisely vanishes along a unique line in the s−t plane. Excitations transverse to this line have a mass manom which is an explicit function of t. The F-term potential energy is then evaluated along the VD=0 line. For values of t small enough that manom≳MU—where MU is the compactification scale—we plot VF for a realistic choice of coefficients as a function of the Pfaffian parameter p. We find values of p for which VF has a global minimum at negative or zero vacuum density or a metastable minimum with positive vacuum density. In all three cases, the s, t, and associated “axion” moduli are completely stabilized. Finally, we show that, for any of these vacua, the large t behavior of the potential energy satisfies the “large scalar field” Swampland conjecture. Published by the American Physical Society 2024

Chaplygin gas inspired warm inflation and swampland conjectures through various scalar potentials

In this paper, we analyze inflationary parameters and swampland conjectures in the presence of a scalar field and Chaplygin models. We examine inflationary parameters, such as slow-roll parameters, scalar and tensor power spectra, spectral index, and tensor-to-scalar ratio, in the presence of a scalar field and Chaplygin gas models. We also discuss recently proposed swampland conjectures. We assume that the inflationary expansion is driven by a standard scalar field with a decay ratio Γ that has a generic power-law dependence on the scalar field ϕ and that the temperature of the thermal bath T is given by , where is a dimensionless parameter and a is the inflation decay rate. In a scenario where our model operates within a robust dissipative environment , we analyze both fundamental and perturbative dynamics to extract key inflationary parameters. These include the scalar power spectrum , dissipative ratio R, scalar spectral index , tensor-to-scalar ratio r, running of the scalar spectral index , and generalized ratio of the swampland de-Sitter conjecture for three different potentials.

The complete Kaluza-Klein spectra of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 and N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 0 M-theory on AdS4× (squashed S7)

The squashed seven-sphere operator spectrum is completed by deriving the spectrum of the spin-3/2 operator. The implications of the results for the AdS4N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supermultiplets obtained from compactification of eleven-dimensional supergravity are analysed. The weak G2 holonomy plays an important role when solving the eigenvalue equations on the squashed sphere. Here, a novel and more universal algebraic approach to the whole eigenvalue problem on coset manifolds is provided. Having obtained full control of all the operator spectra, we can finally determine the irreps D(E0, s) for all supermultiplets in the left-squashed vacuum. This includes an analysis of possible boundary conditions. By performing an orientation flip on the seven-sphere, we also obtain the full spectrum for the non-supersymmetric right-squashed compactification which is of interest in the swampland context and in particular for the AdS swampland conjecture. Here, a number of boundary condition ambiguities arise making the analysis of dual marginal operators somewhat involved. This work is a direct continuation of [1] and [2].

Dark dimension and the standard model landscape

We study the landscape of lower-dimensional vacua of the standard model (SM) coupled to gravity in the presence of the so-called “dark dimension” of size R⊥ in the micron range, focusing on the validity of the swampland conjecture forbidding the presence of nonsupersymmetric anti–de Sitter (AdS) vacua in a consistent quantum gravity theory. We first adopt the working assumption that right-handed neutrinos propagate in the bulk, so that neutrino Yukawa couplings become tiny due to a volume suppression, leading to naturally light Dirac neutrinos. We show that the neutrino Kaluza-Klein (KK) towers compensate for the graviton tower to maintain stable de Sitter (dS) vacua found in the past, but neutrino oscillation data set restrictive bounds on R⊥ and therefore the first KK neutrino mode is too heavy to alter the shape of the radion potential or the required maximum mass for the lightest neutrino to carry dS rather than AdS vacua found in the absence of the dark dimension, m1,max≲7.63 meV. We also show that a very light gravitino (with mass in the meV range) could help relax the neutrino mass constraint m1,max≲50 meV. The differences for the predicted total neutrino mass ∑mν among these two scenarios are within reach of next-generation cosmological probes that may measure the total neutrino mass with an uncertainty σ(∑mν)=0.014 eV. We also demonstrate that the KK tower of a very light gravitino can compensate for the graviton tower to sustain stable dS vacua and thus right-handed neutrinos can (in principle) be locked on the brane. For this scenario, Majorana neutrinos could develop dS vacua, which is not possible in the SM coupled to gravity. Finally, we investigate the effects of bulk neutrino masses in suppressing oscillations of the zero modes into the first KK modes to relax the oscillation bound on R⊥. Published by the American Physical Society 2024

A small Universe

Many cosmological models assume or imply that the total size of the universe is very large, perhaps even infinite. Here we argue instead that the universe might be comparatively small, in fact not much larger than the currently observed size. A concrete implementation of this idea is provided by the no-boundary proposal, in combination with a plateau-shaped inflationary potential. In this model, opposing effects of the weighting of the wave function and of the criterion of allowability of the geometries conspire to favour small universes. We point out that a small size of the universe also fits well with swampland conjectures, and we comment on the relation with the dark dimension scenario.

Derivative corrections to extremal black holes with moduli

We derive formulas for the leading mass, entropy, and long-range self-force corrections to extremal black holes due to higher-derivative operators. These formulas hold for black holes with arbitrary couplings to gauge fields and moduli, provided that the leading-order solutions are static, spherically-symmetric, extremal, and have nonzero horizon area. To use these formulas, both the leading-order black hole solution and the higher-derivative effective action must be known, but there is no need to solve the derivative-corrected equations of motion. We demonstrate that the mass, entropy and self-force corrections involve linearly-independent combinations of the higher-derivative couplings at any given point in the moduli space, and comment on their relations to various swampland conjectures.

Dark dimension gravitons as dark matter

We consider cosmological aspects of the Dark Dimension (a mesoscopic dimension of micron scale), which has recently been proposed as the unique corner of the quantum gravity landscape consistent with both the Swampland criteria and observations. In particular we show how this leads, by the universal coupling of the Standard Model sector to bulk gravitons, to massive spin 2 KK excitations of the graviton in the dark dimension (the “dark gravitons”) as an unavoidable dark matter candidate. Assuming a lifetime for the current de Sitter phase of our universe of order Hubble, which follows from both the dS Swampland Conjecture and TCC, we show that generic features of the dark dimension cosmology can naturally lead to the correct dark matter density and a resolution of the cosmological coincidence problem, where the matter/radiation equality temperature (T ~ 1 eV) coincides with the temperature where the dark energy begins to dominate. Thus one does not need to appeal to Weinberg’s anthropic argument to explain this coincidence. The dark gravitons are produced at T ~ 4 GeV, and their composition changes as they mainly decay to lighter gravitons, without losing much total mass density. The mass of dark gravitons is mDM ∼ 1 − 100 keV today.

Hořava–Lifshitz F(R) Theories and the Swampland

The compatibility between the de Sitter Swampland conjecture and Hořava–Lifshitz F(R¯) theories with a flat FLRW metric is studied. We first study the standard f(R) theories and show that the only way in which the dS conjecture can be made independent of R is by considering a power law of the form f(R)∼Rγ. The conjecture and the consistency of the theory puts restrictions on γ to be greater but close to one. For F(R¯) theories described by its two parameters λ and μ, we use the equations of motion to construct the function starting with an ansatz for the scale factor in the Jordan frame of the power law form. By performing a conformal transformation on the three metric to the Einstein frame, we can obtain an action of gravity plus a scalar field by relating the parameters of the theory. The non-projectable and projectable cases are studied and the differences are outlined. The obtained F(R¯) function consists of terms of the form R¯γ with the possibility of having negative power terms. The dS conjecture leads to inequalities for the λ parameter; in both versions, it becomes restricted to be greater but close to 1/3. We can also study the general case in which μ and λ are considered as independent. The obtained F function has the same form as before. The consistency of the theory and the dS conjecture lead to a set of inequalities on both parameters that are studied numerically. In all cases, λ is restricted by μ around 1/3, and we obtain λ→1/3 if μ→0. We consider the f(R) limit μ,λ→1 and we obtain consistent results. Finally, we study the case of a constant Hubble parameter. The dS conjecture can be fulfilled by restricting the parameters of the theory; however, the constraint makes this compatibility exclusive to these kinds of theories.

Trans-Planckian censorship constraints on properties and cosmological applications of axion-like fields

We use the Trans-Planckian Censorship Conjecture (TCC) to constrain the decay constants f characterizing a set of N identical axion-like fields with cosine potentials, improving upon the precision of other Swampland conjectures and existing string-theoretic arguments. We find that consistency with the TCC requires any such set of axion-like fields to satisfy fN≲0.6Mpl, where Mpl is the reduced Planck mass. We show that this bound makes models of axion-driven inflation incapable of simultaneously producing the required number of e-foldings and the observed scalar spectral tilt. In contrast, we find that models of axion quintessence can be simultaneously compatible with the TCC and observational data, provided that the axions' initial field values are set near the maxima of their potentials to within roughly ±π5f.

Species entropy and thermodynamics

We analyse particle species and the species scale in quantum gravity from a thermodynamic perspective. In close analogy to black hole thermodynamics, we propose that particle species have an entropy and a temperature, which is determined by the species scale. This is identical to the Bekenstein-Hawking entropy of a corresponding minimal black hole and agrees with the number of species in a given tower of states. Through the species entropy, we find that certain entropy bounds are connected to recent swampland constraints. Moreover, the concept of species entropy and temperature allow us to formulate the laws of species thermodynamics, which are argued to govern the variations of moduli in string theory. They can be viewed as general rules that imply certain swampland conjectures, and vice versa.