Luis A. Anchordoqui, Ignatios Antoniadis, Dieter Lust, Jorge F. Soriano
备注：
Extensive discussion on the ambiguity of the definition of slow-roll-parameters in relation to how this uncertainty may help ameliorate the tension between single-field inflationary models and the de Sitter Swampland conjecture. Accepted for publication in Phys. Rev. D
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 $c'$.
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.
In this paper, I show that type I hilltop inflation under the current observational constaints could have $M_P^2 \frac{V^{\prime\prime}}{V} \sim -\mathcal{O}(10^{-2})$ in the parameter space which is in tension with the refined swampland criteria. On the other hand, $M_P^2 \frac{V^{\prime\prime}}{V} \sim -\mathcal{O}(1)$ can be achieved if type I hilltop inflation on the brane is considered.
In this paper, we show that single-field chaotic inflation on the brane with the potential $V=a ϕ^p$ 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 $p \lesssim \mathcal{O}(1)$.
Warm Inflation seems to be the most befitting single-field slow-roll inflation scenario in the context of the recently proposed Swampland Criteria. We investigate the constraints these Swampland Criteria impose on Warm Inflation parameters and show that Warm Inflation is in accordance with both the current cosmological observations and the proposed Swampland Criteria in both weak and strong dissipative regimes depending on the value of the parameter $c$ which limits the slope of the inflaton potential according to the criteria.
Inflation is the currently accepted paradigm for the beginnings of the Universe. To explain the observed almost scale invariant spectrum of density perturbations with only a slight spectral tilt, inflation must have been "slow roll", that is with a potential with sufficiently small slope. While the origin of inflationary structure is intrinsically quantum mechanical, gravity gets treated semiclassically within inflationary models. Recent work, in terms of the so called de-Sitter swampland conjecture, has called into question whether slow roll inflation is consistent with a complete theory of q…
Warm inflation has been noted previously as a possible way to implement inflationary models compatible with the dS swampland bounds. But often in these discussions the heat bath dynamics is kept largely unspecified. We point out that the recently introduced Minimal Warm Inflation of arXiv:1910.07525, where an axionic coupling of the inflaton leads to an explicit model for the thermal bath, yields models of inflation that can easily fit cosmological observations while satisfying de Sitter swampland bounds, as well as the swampland distance bound and trans-Planckian censorship.
We study the de Sitter (dS) swampland conjecture in the Dirac-Born-Infeld (DBI) inflation model. We obtain the dS swampland bound for the relativistic regime using Bousso's entropy bound argument and proper distance. It restricts $m_{\rm Pl}\nabla V/V$ by some positive constant depending on warping and the field range. In the specific case of the DBI model driven by the quadratic potential, the model-dependent backreaction argument is interpreted as a natural bound for the slow-roll parameter. This shows that quasi-dS spacetime in the DBI model is a result of tuning.
I investigate whether eternal inflation is possible when the inflaton originally travels upslope the scalar potential and inevitably reaches a turn-around point where its classical kinetic energy momentarily vanishes. This behaviour occurs regardless of the steepness of the potential slope. Such steep eternal inflation, if achieved, would satisfy the recent swampland conjecture and allow eternal inflation in the string landscape.
We consider thermal, trapped and chromo-natural inflation in light of the swampland criteria and the Trans-Planckian Censorship Conjecture (TCC). Since thermal inflation occurs at energies low compared to those of Grand Unification, it is consistent with the TCC, and it is also consistent with the refined swampland conditions. Trapped and chromo-natural inflation are candidates for primordial (high energy scale) inflation. Since in both of these scenarios there are effective damping terms in the scalar field equation of motion, the models can easily be consistent with the swampland criteria. T…
We provide some comments about the constraints on the inflationary models inferred from the two Swampland criteria which have been recently proposed. In particular we argue that, in the absence of any knowledge about the origin of the adiabatic curvature perturbations, within the slow-roll single field models of inflation there is no tension between the swampland criteria and the current lower bound on the tensor-to-scalar ratio.
We discuss the relations between swampland conjectures and observational constraints on both inflation and dark energy. Using the requirement $|\nabla V|\geq c V$, 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 comm…
The swampland criteria put significant constraints on inflation models. In this paper, I show that hilltop inflation on the brane may provide an initial condition for hilltop inflation and produce topological eternal inflation without violating the swampland distance and refined de Sitter criteria. This shows a way that string theory may not be incompatible with eternal inflation.
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 l…
We discuss how dissipative effects and the presence of a thermal radiation bath, which are inherent characteristics of the warm inflation dynamics, can evade the recently proposed Swampland conjectures. Different forms of dissipation terms, motivated by both microphysical quantum field theory and phenomenological models, are discussed and their viability to overcome the assumed Swampland constraints is analyzed.
The runaway potentials, which do not possess any critical points, are viable potentials which befit the recently proposed de Sitter swampland conjecture very well. In this work, we embed such potentials in the warm inflation scenario motivated by quantum field theory models generating a dissipation coefficient with a dependence cubic in the temperature. It is demonstrated that such models are able to remain in tune with the present observations and they can also satisfy all the three Swampland conjectures, namely the Swampland Distance conjecture, the de Sitter conjecture and the Transplackian…
It has been suggested that low energy effective field theories should satisfy given conditions in order to be successfully embedded into string theory. In the case of a single canonically normalized scalar field this translates into conditions on its potential and the derivatives thereof. In this Letter we revisit stochastic models of small field inflation and study the compatibility of the swampland constraints with entropy considerations. We show that stochastic inflation either violates entropy bounds or the swampland criterium on the slope of the scalar field potential. Furthermore, we ill…
The refined de Sitter (dS) conjecture provides two consistency conditions for an effective theory potential of a quantum gravity theory. Any inflationary model can be checked by these conditions and minimal gauge inflation is not an exception. We develop a generic method to analyze a monotonically growing potential with an inflection point on the way to the plateau near the top such as the potential in minimal gauge inflation model and the Higgs inflation. Taking the latest observational data into account, we find the fully consistent parameter space where the model resides in the Landscape ra…
The implications of the recently proposed Trans-Planckian censorship conjecture (TCC) are analyzed in the context of warm inflation. It is found that for a single-stage accelerated expansion the constraints imposed by the censorship are roughly the same as for cold inflation. Next, we study how a two-stage inflationary expansion with an intermediate radiation-dominated era can alleviate the bounds imposed by the censorship. For a demonstrative toy model we found $r<10^{-23}$, but can be $r<10^{-5}$ for a weaker form of TCC for the later stages of expansion, while still satisfying the other swa…
The swampland conjectures from string theory have had some really interesting implications on cosmology, in particular on inflationary models. Some models of inflation have been shown to be incompatible with these criterion while some have been shown to be severely fine tuned, with most of these problems arising in single field inflationary models in a General relativistic cosmology. Recent works have although optimistically shown that single field models in more general cosmologies can be consistent with these conjectures and hence there is an optimism that not all such models lie in the swam…
The "de Sitter constraint" on the space of effective scalar field theories consistent with superstring theory provides a lower bound on the slope of the potential of a scalar field which dominates the evolution of the Universe, e.g., a hypothetical inflaton field. Whereas models of single scalar field inflation with a canonically normalized field do not obey this constraint, it has been claimed recently in the literature that models of warm inflation can be made compatible with it in the case of large dissipation. The de Sitter constraint is known to be derived from entropy considerations. Sin…
I apply recently proposed "Swampland" conjectures to eternal inflation in single-scalar field theories. Eternal inflation is a phase of infinite self-reproduction of a quasi-de Sitter universe which has been argued to be a generic consequence of cosmological inflation. The originally proposed de Sitter swampland conjectures were shown by Matsui and Takahashi and by Dimopoulos to be generically incompatible with eternal inflation. However, the more recently proposed "refined" swampland conjecture imposes a slightly weaker criterion on the scalar field potential in inflation, and is consistent w…
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 lo…
We study if eternal inflation is realized while satisfying the recently proposed string Swampland criteria concerning the range of scalar field excursion, $|Δϕ| < \mathcal{D} \cdot M_{\rm P}$, and the potential gradient, $|\nabla V| > c \cdot V/M_{\rm P}$, where $\mathcal{D}$ and $c$ are constants of order unity, and $M_{\rm P}$ is the reduced Planck mass. We find that only the eternal inflation of chaotic type is possible for $c \sim {\cal O}(0.01)$ and $1/\mathcal{D} \sim {\cal O}(0.01)$, and that the Hubble parameter during the eternal inflation is parametrically close to the Planck scale, …
Recently researchers have been studying various conditions as swampland criteria in cosmological implications. They have studied many inflation models with different swampland conditions. Occasionally these conjectures are modified and lead to fascinating points. The swampland conjecture is in contradiction with the slow-roll single-field inflation model. So in this paper, we will briefly describe resolving this contradiction with the special method; we consider a small parameter λ with respect to a coupling function in inflation and resolve this important antithesis. Then we will discuss a ne…
The difficulty of building metastable vacua in string theory has led some to conjecture that, in the string theory landscape, potentials satisfy $\left|\nabla V/V\right|\geq c\sim \mathcal{O}(1)$. This condition, which is supported by different explicit constructions, suggests that the EFTs which lead to metastable de-Sitter vacua belong to what is dubbed as swampland. This condition endangers the paradigm of single field inflation. In this paper, we show how scalar excited initial states cannot rescue single field inflation from the swampland, as they produce large local scalar non-gaussianit…
The trans-Planckian censorship conjecture implies that single-field models of inflation require an extreme fine-tuning of the initial conditions due to the very low-scale of inflation. In this work, we show how a quantum cosmological proposal -- namely the tunneling wavefunction -- naturally provides the necessary initial conditions without requiring such fine-tunings. More generally, we show how the tunneling wavefunction can provide suitable initial conditions for hilltop inflation models, the latter being typically preferred by the swampland constraints.
We study the effects of particle production on the evolution of the inflaton field in an axion monodromy model with the goal of discovering in which situations the resulting dynamics will be consistent with the {\it swampland constraints}. In the presence of a modulated potential the evolving background field (solution of the inflaton homogeneous in space) induces the production of long wavelength inflaton fluctuation modes. However, this either has a negligible effect on the inflaton dynamics (if the field spacing between local minima of the modulated potential is large), or else it traps the…
We study the implications on inflation of an infinite tower of higher-spin states with masses falling exponentially at large field distances, as dictated by the Swampland Distance Conjecture. We show that the Higuchi lower bound on the mass of the tower automatically translates into an upper bound on the inflaton excursion. Strikingly, the mere existence of all spins in the tower forbids any scalar displacement whatsoever, at arbitrarily small Hubble scales, and it turns out therefore incompatible with inflation. A certain field excursion is allowed only if the tower has a cut-off in spin. Fin…
We discuss under which conditions multi-field cold and warm inflationary models with canonical kinetic energy terms are compatible with the swampland conjectures about the emergence of de Sitter solutions in string theory. We find that under quite general conditions the slow-roll conditions for multi-field cold inflation are at odds with the swampland conjectures for an arbitrary number of scalar fields driving inflation. However, slow-roll conditions can be reconciled with the swampland conjectures in the strong dissipative regime of warm inflation.
We show how the inclusion of non-perturbative, {\em dynamical} quantum effects on the evolution of the inflaton can allow for an inflationary phase that is both consistent with cosmological constraints {\em and} avoids the problems associated with the so-called swampland conditions. In particular, for concave potentials such as those preferred by the Planck data, spinodal instabilities associated with tachyonic masses for long wavelength modes induce a second round of inflation, which in essence decouples the tree-level potential from the inflationary phase. We illustrate these points using na…
The "swampland conjectures" have been recently suggested as a set of criteria to assess if effective field theories (EFTs) are consistent with a quantum gravity embedding. Such criteria, which restrict the behavior of scalar fields in the theory, have strong implications for cosmology in the early universe. As we demonstrate, they will also have direct consequences for formation of primordial black holes (PBHs) and dark matter (DM).
In this work we shall study a class of $f(R,ϕ)$ gravity models which during the inflationary era, which is the large curvature regime, result to an effective inflationary Lagrangian that contains a rescaled Einstein-Hilbert term $αR$ in the presence of a canonical minimally coupled scalar field. The dimensionless parameter $α$ is chosen to take values in the range $0<α<1$ and the main motivation for studying these rescaled Einstein-Hilbert $f(R,ϕ)$ gravities, is the fact that the rescaled action may render an otherwise incompatible canonical scalar field theory with the Swampland criteria, to …
On the one hand, David Andriot and Christoph Roupec proposed an alternative refined de Sitter conjecture, which gives a natural condition on a combination of the first and second derivatives of the scalar potential. On the other hand, in our previous article, we have found that Palatini Higgs inflation model is in strong tension with the refined de Sitter swampland conjecture. Therefore, following our previous research, in this article we examine if Higgs inflation model and its two variations: Palatini Higgs inflation and Higgs-Dilaton model can satisfy the further refining de Sitter swamplan…
We consider single-field inflation in light of string-motivated "swampland" conjectures suggesting that effective scalar field theories with a consistent UV completion must have field excursion $Δϕ\lesssim M_{\rm Pl}$, in combination with a sufficiently steep potential, $M_{\rm Pl} V_ϕ/V \gtrsim {\cal O}(1)$. Here, we show that the swampland conjectures are inconsistent with existing observational constraints on single-field inflation. Focusing on the observationally favoured class of concave potentials, we map the allowed swampland region onto the $n_S$-$r$ "zoo plot" of inflationary models, …
In String Gas Cosmology, the simplest shape modulus fields are naturally stabilized by taking into account the presence of string winding and momentum modes. We determine the resulting effective potential for these fields and show that it obeys the de Sitter conjecture, one of the swampland criteria for effective field theories to be consistent with superstring theory.
It has very recently been realized that coupling branes to higher dimensional quantum gravity theories and considering the consistency of what lives on the branes, one is able to understand whether such theories can belong either to the swampland or to the landscape. In this regard, in the present work, we study a warm inflation model embedded in the Randall-Sundrum braneworld scenario. It is explicitly shown that this model belongs to the landscape by supporting a strong dissipative regime with an inflaton steep exponential potential. The presence of extra dimension effects from the braneworl…
The methods of supergravity allow us to derive a multi-field F-term potential. Using this, we denote a generic and non-positive single-field F-term potential. We insert our theory into the scalar-gravity part of the $SU(2,1|1)$ invariant superconformal action. That action leads us to a de Sitter solution at the inflationary trajectory. One can denote stabilization of fields in terms of the Kähler kinetic terms and single-field slow-roll inflation parameters. We combine these with the de Sitter swampland conjecture to generate a bounded conjecture. This approach allowed us to show that the sing…
One class of single-field inflationary models compatible with the recently-conjectured Swampland criteria would be those in which a Hubble slow-roll parameter $ε_\text{H}$ is not the same as $ε_\text{V} \sim (V'/V)^2$. However, a roadblock for these models (with a convex potential) lie in the unacceptably high tensor-to-scalar ratio, $r$, generically predicted by them. In this work, illustrating through an explicit example, we point out that having a non-Bunch-Davies component to the initial state of cosmological perturbations makes the value of $r$ compatible with observations. In this way, w…
The swampland conjectures from String theory have had very interesting implications for cosmology and particularly for Inflation. It has been shown that the single field inflationary models in a GR based cosmology are in unavoidable tensions with these conjectures, while these single field models can still be consistent in certain non-trivial inflationary regimes. So it becomes interesting to see whether there is a way to overcome the issues of the swampland and single field inflation in an essentially GR based cosmology. We show that this can indeed be the case and for this, we consider a cer…
We provide an overview of the string landscape and the Swampland program. Our review of the string landscape covers the worldsheet and spacetime perspectives, including vacua and string dualities. We then review and motivate the Swampland program from the lessons learned from the string landscape. These lecture notes are aimed to be self-contained and thus can serve as a starting point for researchers interested in exploring these ideas. These notes are an expanded version of two courses "The String Landscape and the Swampland" taught by C.~Vafa at Harvard University in 2018 with a focus on th…
Swampland Conjectures have attracted quite some interest in the Cosmological Community. They have been shown to have wide ranging implications , like Constraints on Inflationary Models, Primordial Black Holes etc. to name a few. A particularly revealing insight on dark energy also shows that one can have the dark energy equation of state for a quintessence scenario to be signficantly different than -1 after one takes into account the refined dS conjecture. Another interesting issue with the swampland conjectures is that they have been shown to be incompatible with single field inflationary mod…
Attempts to construct string derived effective field theory models realizing large field inflation are plagued by control issues. Targeted at a broader audience, in this article we review recent progress in isolating the underlying conceptual reasons for this failure. Special emphasis is given to models of axion monodromy inflation and their relation to the Swampland Distance Conjecture. This discriminates effective actions that admit a UV completion, the landscape, from those that do not, the swampland. Since they are conceptually very similar, we also comment on implied challenges for axioni…
Recent studies show that there is tension between the de Sitter swampland conjectures proposed by Obeid, et al. and inflationary cosmology. In this paper, we consider an alternative to inflation, `tachyacoustic' cosmology, in light of swampland conjectures. In tachyacoustic models, primordial perturbations are generated by a period of superluminal sound speed instead of accelerating expansion. We show that realizations of tachyacoustic Lagrangians can be consistent with the de Sitter swampland conjectures, and therefore can in principle be consistent with a UV-complete theory. We derive a gene…
We study how both the swampland distance conjecture and the Lyth bound affect the parameter space of multi-field models of inflation. A generic feature of multi-field inflation is that the geodesic distance $\left[Δϕ\right]_\text{G}$ separating any two points laying along the inflationary trajectory differs from the non-geodesic distance $\left[Δϕ\right]_\text{NG}$ traversed by the inflaton between those points. These distances must respect a relation of the form $\left[Δϕ\right]_\text{G} = f\left(\left[Δϕ\right]_\text{NG}\right) \leq \left[Δϕ\right]_\text{NG}$, where $f$ is a function determi…
An alternative refined de Sitter conjecture giving rise to a natural combination of the first and second derivatives of the scalar potential was proposed recently by David Andriot and Christoph Roupec (Fortsch. Phys. 67 (2019) no.1-2, 1800105). In this work, we study the inflation models in a general scalar-tensor theory with exponential and hyperbolic tangent forms of potential as well as model with quantum corrected potential and examine whether these three models of inflation can satisfy this further refining de Sitter swampland conjecture or not. Regarding our analysis with proper choices …
We study cosmological inflation and its dynamics in the framework of the Randall-Sundrum II brane model. In particular, we analyze in detail four representative small-field inflationary potentials, namely Natural inflation, Hilltop inflation, Higgs-like inflation, and Exponential SUSY inflation, each characterized by two mass scales. We constrain the parameters for which a viable inflationary Universe emerges using the latest PLANCK results. Furthermore, we investigate whether or not those models in brane cosmology are consistent with the recently proposed Swampland Criteria, and give predicti…
In this paper, we studied the phenomenological consequences of recently proposed swampland conjecture on the inflationary models though constraints on reheating. If dark matter is assumed to be produced during reheating, the conjecture will provide further constraints on the dark matter parameter space through its current relic abundance. As has been pointed out already and also analyzed in our present paper any successful inflationary scenario is in clear tension with the aforementioned conjecture in its current form. However considering the swampland parameters to be free and constrained by …
In this paper we study the implications of the generalized Higuchi bound on massive spin-two fields for the derivative of the scalar potential within bimetric theory. In contrast to the recent de Sitter swampland conjecture, an upper bound on the derivate of the scalar potential follows from the generalized Higuchi bound. In combination, this leaves a window for the derivate of the scalar potential. We discuss this bound in several representative bimetric models and parameter regions.
The quantum gravity conjectures that aim to separate the landscape from the swampland among the low energy theories were originally formulated in the context of scalar field spaces spanned by moduli. Because these conjectures have implications for cosmology they have recently been considered in a more general context for scalar field theories with potentials, in particular inflation. From an effective field theory perspective the presence of a potential induces a natural metric that makes the distance measure $D_V$ along scalar field trajectories dependent on the potential. The present paper p…
We discuss phenomenological consequences of the recently-introduced refinements of the de Sitter swampland conjecture. The conjecture constraints the first and the second derivatives of the scalar potential in terms of two $O(1)$ constants $c$ and $c'$, leading to interesting constraints on particle phenomenology, especially inflationary model building. Our work can also be regarded as bottom-up constraints on the values of $c$ and $c'$.
It was recently pointed out that the existence of dark energy imposes highly restrictive constraints on effective field theories that satisfy the Swampland conjectures. We provide a critical confrontation of these constraints with the cosmological framework emerging from the Salam-Sezgin model and its string realization by Cvetic, Gibbons, and Pope. We also discuss the implication of the constraints for string model building.
We study the general embedding of a $ P(X, φ) $ inflationary theory into a two-field theory with curved field space metric, which was proposed as a possible way to examine the relation between de Sitter Swampland conjecture and \textit{k}-inflation. We show that this embedding method fits into the special type of two-field model in which the heavy field can be integrated out at the full action level. However, this embedding is not exact due to the upper bound of the effective mass of the heavy field. We quantify the deviation between the speed of sound calculated via the $ P(X, φ) $ theory and…
In negatively curved field spaces, inflation can be realised even in steep potentials. Hyperinflation invokes the `centrifugal force' of a field orbiting the hyperbolic plane to sustain inflation. We generalise hyperinflation by showing that it can be realised in models with any number of fields ($N_f\geq2$), and in broad classes of potentials that, in particular, don't need to be rotationally symmetric. For example, hyperinflation can follow a period of radial slow-roll inflation that undergoes geometric destabilisation, yet this inflationary phase is not identical to the recently proposed sc…
