Two-field axion inflation and the swampland constraint in the flux-scaling scenario
Cesar Damian, Oscar Loaiza-Brito
备注：
24 pages, 6 figures. (v2): Typos corrected, References added. (v3) Some comments, one figure and references added. Version accepted for publication in Fortschritte der Physik
Based on the flux-scaling scenario we study a model consisting on Type IIB string theory compactified on a Calabi-Yau manifold with a frozen complex structure in the presence of generic fluxes. The model contains (meta)stable Minkowski and de Sitter vacua as well as inflationary directions driven by two independent linear combination of axions. Due to a numerical control by fluxes, we show that cosmological parameters as the spectral index, tensor-to-scalar ratio and non-Gaussianities can be kept within observed bounds while preserving the desired hierarchies on physical scales. Moreover we compute the deviation of the inflationary trajectories from geodesics on field space in terms of the fluxes showing that for some regions, they fulfill the recent proposed swampland criterion for multi-field scenarios.
We study the interplay between extrema of axion potentials, Kahler moduli stabilization and the swampland criteria. We argue that moving away from the minima of non-perturbatively 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 quintessenc…
We continue the investigation of F-term axion monodromy inflation in string theory, while seriously taking the issue of moduli stabilization into account. For a number of closed and open string models, we show that they suffer from serious control issues once one is trying to realize trans-Planckian field excursions. More precisely, the flux tuning required to delay the logarithmic scaling of the field distance to a trans-Planckian value cannot be done without leaving the regime where the employed effective supergravity theory is under control. Our findings are consistent with the axionic exte…
Axion monodromy models can always be described in terms of an axion coupled to 3-form gauge fields with non-canonical kinetic terms. The presence of the saxions parametrising the kinetic metrics of the 3-form fields leads to backreaction effects in the inflationary dynamics. We review the case in which saxions backreact on the Kähler metric of the inflaton leading to a logarithmic scaling of the proper field distance at large field. This behaviour is universal in Type II string flux compactifications and consistent with a refinement of the Swampland Conjecture. The critical point at which this…
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…
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…
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 …
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…
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 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 point out that the swampland conjectures, forbidding the presence of global symmetries and (meta-)stable de Sitter vacua within quantum gravity, pick up a dynamical axion for the electroweak SU(2) gauge theory as a natural candidate for the quintessence field. The potential energy of the electroweak axion provides an attractive candidate for the dark energy. We discuss constraints from the weak gravity conjecture, from the conjecture of no global symmetry, and from observations, which can be satisfied elegantly in a supersymmetric extension of the standard model.
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.
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 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…
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 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…
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.
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…
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.
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…
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.
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…
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.
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.
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…
In this paper, we study a constant-roll inflationary model in the presence of a noncommutative parameter with a homogeneous scalar field minimally coupled to gravity. The specific noncommutative inflation conditions proposed new consequences. On the other hand, we use anisotropic conditions and find new anisotropic constant-roll solutions with respect to noncommutative parameter. Also, we will plot some figures with respect to the specific values of the corresponding parameter and the swampland criteria which is raised from the exact potential obtained from the constant-roll condition. Finally…
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.
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 $p \lesssim \mathcal{O}(1)$.
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…
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…
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…
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 …
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.
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.
The swampland program of delineating the space of effective field theories consistent with quantum gravity appears similar to the bootstrap program of delineating the space of quantum field theories consistent with conformal symmetry. With this in mind we rewrite the effective field theory of the Large Volume Scenario in AdS space solely in terms of $R_{AdS}$, in a form suitable for holographic analysis. This rewritten EFT takes a remarkably universal (and previously unnoticed) form, which is uniquely determined in the large-volume limit up to terms suppressed by $\mathcal{O} \left( 1/\ln R_{A…
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 this note we show that models of natural inflation based on closed string axions are incompatible with the weak gravity conjecture (WGC). Specifically, we use T-duality in order to map the bounds on the charge-to-mass ratio of particles imposed by the WGC, to constraints on the ratio between instanton actions and axion decay constants. We use this connection to prove that if the WGC holds, even when multiple axions are present and mix with each other, one cannot have large axion decay constants while remaining in a regime of perturbative control. We also discuss the extension of the WGC to …
Over the past few decades, inflation models have been studied by researchers from different perspectives and conditions in order to introduce a model for the expanding universe. In this paper, we introduce a modified $f(R)$ gravitational model as ($R+γR^{p}$) in order to examine a new condition for inflation models. Given that our studies are related to a modified $f(R)$ gravitational model on the brane, therefore we will encounter modified cosmological parameters. So, we first introduce these modified cosmological parameters such as spectral index, a number of e-folds and etc. Then, we apply …
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 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 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…
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…
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…
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…
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…
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 …
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…
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, …
