Swampland Criteria Research Articles

Creating spatial flatness by combining string gas cosmology and power law inflation

We show that it is possible to combine an early phase of String Gas Cosmology which can explain the origin of the observed structures on cosmological scales with a short later period of power law inflation which creates spatial flatness. The resulting model is consistent with the ``swampland criteria'' and the constraints coming from the {\it Trans-Planckian Censorship Conjecture}. Such a construction is not possible using only canonical slow-roll inflation, but it can emerge in the warm inflation scenario or in cold inflation with an exponential potential. The resulting cosmology is non-singular. We discuss the spectrum of cosmological perturbations resulting in our scenario. On large scales (scales which remain larger than the Hubble radius after the initial string gas phase) the spectrum is determined by the thermal string gas fluctuations set up in the primordial phase, and it is almost scale-invariant with a slight red tilt. On small scales, the perturbations produced during the inflationary phase dominate. On these scales, the spectrum is once again nearly scale-invariant. There is an intermediate range (scales which enter the Hubble radius during the period of inflation) where the string gas fluctuations are damped but continue to dominate over those produced during the period of inflation. On these scales the spectrum has a sharp red spectral index of $n_s - 1 \sim -2$.

Weak equivalence principle, swampland and H0 tension with fast single radio bursts FRB 180924 and FRB 190523

Two new fast single radio bursts FRB 180924 and FRB 190523 well localized to massive galaxies have opened a new window to probe and characterize how cosmic baryons are allocated between galaxies, their surroundings and intergalactic medium. We are motivated by testing Einstein's weak equivalence principle with these two cosmic transients which have accurate redshifts. Using photons with different energies emitted by FRB 180924, we obtain, so far, the most stringent bound $\Delta\gamma<2.16\times10^{-10}$ for non-repeating FRBs with accurate redshifts when only considering the gravitational potential of the Milk Way. If using the gravitational potential of the Laniakea supercluster instead of the Milk Way one, we also obtain the strictest bound $\Delta\gamma<1.06\times10^{-14}$ to date. In light of rapid progress of FRB cosmology, towards the next two decades, we give an universal limitation $\Delta\gamma<8.24\times10^{-22}$ from photons with different energies emitted by single FRBs with accurate redshifts. Moreover, we analyze detailedly the effects of various astrophysical parameters on the precision of weak equivalence principle. We also estimate the abilities of single FRBs with known redshifts to test the validity of swampland criterion, and to distinguish which value of $H_0$ is preferred.

Swampland implications of GW170817-compatible Einstein-Gauss-Bonnet gravity

We revisit the Einstein-Gauss-Bonnet theory in view of the GW170817 event, which compels that the gravitational wave speed is equal to cT2=1 in natural units. We use an alternative approach compared to one previous work of ours, which enables us to express all the slow-roll indices and the observational indices as functions of the scalar field. Using our formalism we investigate if the Swampland criteria are satisfied for the Einstein-Gauss-Bonnet theory and as we demonstrate, the Swampland criteria are satisfied for quite general forms of the potential and the Gauss-Bonnet coupling function ξ(ϕ), if the slow-roll conditions are assumed to hold true.

Distance conjecture and de-Sitter quantum gravity

Motivated by the early discovery of the gigantic landscape of string theory vacua, in recent years people switched direction to try to find constraints on low energy effective field theories from UV-complete descriptions for example quantum gravity or string theory. Those constraints are called swampland criteria. Among the proposed swampland criteria the distance conjecture is the most well-motivated one from the universal behavior of string theory compactifications. It claims that for a type of scalar fields, called moduli, the effective field theory description will break down if it moves a large distance in field (moduli) space. In this work, we will show that in one proposal for a complete theory of quantum gravity including positive vacuum energy, the so called DS/dS correspondence, there is a strong signal of the validity of the distance conjecture.

Pole dark energy

Theories with a pole in the kinetic term have been used to great effect in studying inflation, owing to their quantum stability and attractor properties. We explore the use of such pole kinetic terms in dark energy theories, finding an interesting link between thawing and freezing models, and the possibility of enhanced plateaus with ``superattractor''-like behavior. We assess the observational viability of pole dark energy, showing that simple models can give dark energy equation of state evolution with $w(z)<-0.9$ even for potentials that could not normally achieve this easily. The kinetic term pole also offers an interesting perspective with respect to the swampland criteria for such observationally viable dark energy models.

Bounds on slow roll and the de Sitter Swampland

The recently introduced swampland criterion for de Sitter [17] can be viewed as a (hierarchically large) bound on the smallness of the slow roll parameter \U0001d716V. This leads us to consider the other slow roll parameter ηV more closely, and we are lead to conjecture that the bound is not necessarily on \U0001d716V, but on slow roll itself. A natural refinement of the de Sitter swampland conjecture is therefore that slow roll is violated at mathcal{O} (1) in Planck units in any UV complete theory. A corollary is that \U0001d716V need not necesarily be mathcal{O} (1), if {eta}_Vlesssim -mathcal{O}(1) holds. We consider various tachyonic tree level constructions of de Sitter in IIA/IIB string theory (as well as closely related models of inflation), which superficially violate [17], and show that they are consistent with this refined version of the bound. The phrasing in terms of slow roll makes it plausible why both versions of the conjecture run into trouble when the number of e-folds during inflation is high. We speculate that one way to evade the bound could be to have a large number of fields, like in N -flation.

Axion hilltops, Kahler modulus quintessence and the swampland criteria

We study the interplay among extrema of axion potentials, Kahler moduli stabilization and the swampland criteria. We argue that moving away from the minima of nonperturbatively generated axion potentials can lead to a runaway behavior of moduli that govern the couplings in the effective field theory. The proper inclusion of these degrees of freedom resolves the conflict between periodic axion potentials and the gradient de Sitter criterion, without the need to invoke the refined de Sitter criterion. We investigate the possibility of including this runaway direction as a model of quintessence that satisfies the swampland criteria. Using a single nonperturbative effect, the maximum along the axion direction provides such a runaway direction, which is unstable in the axion directions, sensitive to initial conditions and too steep to allow for a Hubble time of expansion without violating the field excursion criterion. Adding a second nonperturbative effect generates a saddle point in the potential satisfying the refined de Sitter criterion, which solves the steepness problem and improves the initial conditions problem although some fine-tuning remains required.

Swampland conjecture in f(R) gravity by the Noether symmetry approach

Swampland conjecture has been recently proposed to connect early time cosmological models with the string landscape, and then to understand if related scalar fields and potentials can come from some fundamental theory in the high energy regime. In this paper, we discuss swampland criteria for $f(R)$ gravity considering models where duality symmetry is present. In this perspective, specific $f(R)$ models can naturally belong to the string landscape. In particular, it is possible to show that duality is a Noether symmetry emerging from dynamics. The selected $f(R)$ models, satisfying the swampland conjecture, are consistent, in principle, with both early and late-time cosmological behaviors.

Emergent dark universe and the swampland criteria

We study a model of the emergent dark universe, which lives on the time-like hypersurface in a five-dimensional bulk spacetime. The holographic fluid on the hypersurface is assumed to play the role of the dark sector, mainly including the dark energy and apparent dark matter. Based on the modified Friedmann equations, we present a Markov-Chain-Monte-Carlo analysis with the observational data, including type Ia Supernova and the direct measurement of the Hubble constant. We obtain a good fitting result and the matter component turns out to be small enough, which matches well with our theoretical assumption that only the normal matter is required. After considering the fitting parameters, an effective potential of the model with a dynamical scalar field is reconstructed. The parameters in the swampland criteria are extracted, and they satisfy the criteria at the present epoch but are in tension with the criteria if the potential is extended to the future direction. The method to reconstruct the potential is helpful to study the swampland criteria of other models without an explicit scalar field.

Gauss–Bonnet Inflation and the String Swampland

The swampland criteria are generically in tension with single-field slow-roll inflation because the first swampland criterion requires small tensor-to-scalar ratio while the second swampland criterion requires either large tensor-to-scalar ratio or large scalar spectral tilt. The challenge to single-field slow-roll inflation imposed by the swampland criteria can be avoided by modifying the relationship between the tensor-to-scalar ratio and the slow-roll parameter. We show that the Gauss–Bonnet inflation with the coupling function inversely proportional to the potential overcomes the challenge by adding a constant factor in the relationship between the tensor-to-scalar ratio and the slow-roll parameter. For the Gauss–Bonnet inflation, while the swampland criteria are satisfied, the slow-roll conditions are also fulfilled, so the scalar spectral tilt and the tensor-to-scalar ratio are consistent with the observations. We use the potentials for chaotic inflation and the E-model as examples to show that the models pass all the constraints. The Gauss–Bonnet coupling seems a way out of the swampland issue for single-field inflationary models.

Inflationary Cosmology with Quantum Gravitational Effects and Swampland Conjectures**Supported by National Natural Science Foundation of China under Grant No. 11675143 and the Fundamental Research for the Provincial Universities of Zhejiang in China under Grant No. RF-A2019015

Recently proposed two swampland criteria that arising from string theory landscape leads to the important challenge of the realization of single-field inflationary models. Especially one of swampland criteria which implies a large tensor-to-scalar ratio is strongly in tension with recent observational results. In this paper, we explore the possibility the swampland conjectures could be compatible with single-field inflationary scenarios if the effects due to the quantum theory of gravity are considered. We show that the quantum gravitational effects due to the nonlinear dispersion relation provides significant modifications on the amplitude of both the scalar and tensor perturbation spectra. Such modifications could be either raise or reduce the perturbation spectra depending on the values of the parameters in the nonlinear terms of the dispersion relations. Therefore, these effects can reduce the tensor-to-scalar ratio to a smaller value, which helps to relax the tension between the swampland conjecture and observational data.

Conditions for (no) eternal inflation

We construct analytic and numerical solutions of the Fokker-Planck equation that arises in the context of stochastic inflation. We use these solutions to derive necessary conditions for eternal inflation on the higher derivatives of the scalar field potential and examine the prospects for eternal inflation in a variety of popular models. We note similarities between the conditions needed to avoid eternal inflation and several recently-proposed Swampland criteria, which leads us to speculate on the possibility that the de Sitter Swampland conjectures should be viewed as approximate consequences of a No Eternal Inflation principle.

Chaotic inflation on the brane and the swampland criteria

In this paper, we show that single-field chaotic inflation on the brane with the potential $V=a \phi^p$ is compatible with the Swampland criteria. The spectral index and the running spectral index are within experimental bounds for $0<p \leq 2$. The tensor to scalar ratio is within observational bounds if $p \lesssim \mathcal{O}(1)$.

Swampland criteria in the slotheon field dark energy

We explore in this work whether Slotheon model of Dark Energy obeys the Swampland criteria of string theory. Since de Sitter vacuum is very difficult to construct in string theory the cosmological constant as an explanation of Dark Energy is almost ruled out in string theory since it involves a scalar potential $V$ with positive local minimum that ends up to a stable (or meta stable) de Sitter (ds) vacuum. In quintessence model however if the derivative of the scalar potential $V$ ($\nabla V$) is small and $\frac{|\nabla V|}{V} \sim {\cal {O}}(1)$ then in this situation the potential $V$ can be positive but the scalar field may not be at the minimum. For a consistent quantum theory of gravity the theory should not have any ds or meta stable ds vacua. In this regard the Swampland criterion is proposed which any low energy theory should obey to be consistent with quantum theory of gravity. This criterion is written as $|\nabla V|/V > c \sim {\cal {O}}(1)$. In this work we consider a scalar field model for Dark Energy namely the Slotheon Dark Energy model inspired by the theories of extra dimensions and show that this Dark Energy model agrees better with the Swampland criteria than the quintessence Dark Energy model.

Nonsingular bounces catalyzed by dark energy

We investigate classically non-singular bounces caused by dark energy. In the presence of positive spatial curvature, vacuum energy, either in the form of a cosmological constant or a scalar field potential, allows for an open set of initial conditions leading to non-singular bounces, without any violation of the null energy condition. We study anisotropic Bianchi IX cosmologies, and demonstrate that they can even have multiple bounces, accompanied by intricate evolutions of the anisotropies that provide a non-singular analogue of mixmaster crunches. The relation of these solutions to more complete cosmological models, as well as to the recently proposed swampland criteria, are briefly discussed.

Horndeski gravity in the swampland

We investigate the implications of string Swampland criteria for alternative theories of gravity. Even though this has not rigorously been proven, there is some evidence that exact de-Sitter solutions with a positive cosmological constant cannot be successfully embedded into string theory, and that the low energy effective field theories containing a scalar field $\pi$ with a potential $V$ in the habitable landscape should satisfy the Swampland criteria $|V'|/V\ge c\sim\mathcal{O}(1)$. As a paradigmatic class of modified gravity theories for inflation and dark energy, we consider the extensively studied family of Horndeski Lagrangians in view of cosmological observations. Apart from a possible potential term, they contain derivative self-interactions as the Galileon and non-minimal couplings to the gravity sector. Hence, our conclusions on the Galileon sector can be also applied to many other alternative theories with scalar helicity modes containing derivative interactions such as massive gravity and generalized Proca. In the presence of such derivative terms, the dynamics of the scalar mode is substantially modified, and imposing the cosmological evolution constrained by observations places tight constraints on $c$ within the Swampland conjecture.

Dark energy beyond quintessence: constraints from the swampland

The string theory swampland proposes that there is no UV-completion for an effective field theory with an exact (metastable) de Sitter vacua, thereby ruling out standard ΛCDM cosmology if the conjecture is taken seriously. The swampland criteria have also been shown to be in sharp tension with quintessence models under current and forthcoming observational bounds. As a logical next step, we introduce higher derivative self-interactions in the low-energy effective Lagrangian and show that one can satisfy observational constraints as well as the swampland criteria for some specific models. In particular, the cubic Galileon term, in the presence of an exponential potential, is examined to demonstrate that parts of the Horndeski parameter space survives the swampland and leads to viable cosmological histories.

Swampland criteria for a dark energy dominated universe ensuing from Gaussian processes and H(z) data analysis

Implications of the string Swampland criteria for a dark energy dominated universe, obtained by using Gaussian processes and $H(z)$ data analysis, are discussed. In particular, the Swampland criteria for a scalar-field dark energy, without assuming any specific form for the potential. By allowing the Gaussian process to reconstruct the form of the potential from $H(z)$ data, upper bounds on the second Swampland criterion (involving $|V^{\prime}|/V$) for two different kernel functions (the squared exponential and Matern~($\nu = 9/2$) kernels) are estimated . The approach here differs from previous studies, since the upper bound of the second Swampland criterion is derived in a thoroughly model-independent way, without resorting to a model-to-model comparison strategy. The analysis is performed using the latest values of $H_{0}$ reported by the Planck and Hubble missions. Results for the estimation of the constant of $SC2$ hint towards the possibility of getting upper bounds well behind the estimations for the dark energy dominated universe as reported in previous studies, which involved model-to-model comparison. Estimations from this new approach turn to be quite sensitive and just depend on the quality of the data and on the kernel employed. This study is a first attempt towards the exploitation of the Swampland criteria in a model-independent way and may be extended to involve other datasets and, also, in trying to understand what is the impact of higher-redshift data on the upper bounds. In the analysis, $40$-point $H(z)$ data have been used, consisting of a $30$-point sample deduced from a differential age method and an additional $10$-point sample obtained from the radial BAO method. Hints towards the possibility of eventually disproving the Swampland conjecture are noted.

Warm inflation within a supersymmetric distributed mass model

We study the dynamics and observational predictions of warm inflation within a supersymmetric distributed mass model. This dissipative mechanism is well described by the interactions between the inflaton and a tower of chiral multiplets with a mass gap, such that different bosonic and fermionic fields become light as the inflaton scans the tower during inflation. We examine inflation for various mass distributions, analyzing in detail the dynamics and observational predictions. We show, in particular, that warm inflation can be consistently realized in this scenario for a broad parametric range and in excellent agreement with the Planck legacy data. Distributed mass models can be viewed as realizations of the landscape property of string theory, with the mass distributions coming from the underlying spectra of the theory, which themselves would be affected by the vacuum of the theory. We discuss the recently proposed swampland criteria for inflation models on the landscape and analyze the conditions under which they can be met within the distributed mass warm inflation scenario. We demonstrate mass distribution models with a range of consistency with the swampland criteria including cases in excellent consistency.

Note on single-field inflation and the swampland criteria

The recently proposed Swampland Criteria aim to evade any (meta-)stable de Sitter constructions within String landscapes, making it difficult to accommodate accelerating phases, like dark energy domination and inflationary epoch, in cosmology. In this note, we analyse the status of various models of single field slow-roll inflation given the old as well as the refined Swampland conjectures, which constrain the form of scalar potentials in any low energy effective field theory residing in the landscapes. In particular, we note that Warm Inflation turns out to be the most befitting scenario as long as lifting the tensions with Swampland Criteria are concerned.