We consider how the swampland criteria might be applied to models in which scalar fields have nontrivial kinetic terms, particularly in the context of $P(ϕ,X)$ theories, popularly used in approaches to inflation, to its alternatives, and to the problem of late-time cosmic acceleration. By embedding such theories in canonical multi-field models, from which the original theory emerges as a low-energy effective field theory, we derive swampland constraints, and study the circumstances under which these might be evaded while preserving cosmologically interesting phenomenology. We further demonstrate how these successes are tied to the phenomenon of turning in field space in the multi-field picture. We study both the general problem and specific examples of particular interest, such as DBI inflation.
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 …
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.
Multifield models with a curved field space have already been shown to be able to provide viable quintessence models for steep potentials that satisfy swampland bounds. The simplest dynamical systems of this type are obtained by coupling Einstein gravity to two scalar fields with a curved field space. In this paper we study the stability properties of the non-trivial fixed points of this dynamical system for a general functional dependence of the kinetic coupling function and the scalar potential. We find the existence of non-geodesic trajectories with a sharp turning rate in field space which…
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.
In this work we examine the Swampland criteria for a specific class of rescaled $f(R)$ gravitational models, that are capable of unifying the primordial era of the Universe with the late-time era with the inclusion of string corrections. In particular, we develop separately the theoretical framework of Gauss-Bonnet and Chern-Simons theories considering that, the rescale parameter is constrained to reside in the area $0<α<1$. As showcased, in the context of the aforementioned theories, a viable inflationary phenomenology consistent with the latest Planck data can be obtained for both cases for …
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…
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, …
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…
We consider a class of exponential models of $f(R)$ gravity, in the presence of a canonical scalar field, for which at early times the effective Lagrangian of the theory becomes that of a rescaled canonical scalar field with the Einstein-Hilbert term becoming $\sim αR$, with $α$ a dimensionless constant. This rescaled Einstein-Hilbert scalar field theory at early times alters the inflationary phenomenology of well-known scalar field models of inflation, but more importantly, in the context of this rescaled theory, the Swampland criteria are easily satisfied, assuming that the scalar field is s…
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…
We consider quintessence models within 4D effective descriptions of gravity coupled to two scalar fields. These theories are known to give rise to viable models of late-time cosmic acceleration without any need for flat potentials, and so they are potentially in agreement with the dS Swampland conjecture. In this paper we investigate the possibility of consistently embedding such constructions in string theory. We identify situations where the quintessence fields are either closed string universal moduli or non-universal moduli such as blow-up modes. We generically show that no trajectories co…
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 a model of two scalar fields with a hyperbolic field space and show that it reduces to a single-field Dirac-Born-Infeld (DBI) model in the limit where the field space becomes infinitely curved. We apply the de Sitter swampland conjecture to the two-field model and take the same limit. It is shown that in the limit, all quantities appearing in the swampland conjecture remain well-defined within the single-field DBI model. Based on a consistency argument, we then speculate that the condition derived in this way can be considered as the de Sitter swampland conjecture for a DBI scalar fie…
The First and Second Swampland Conjectures (FSC & SSC) are substantially modified in non-critical string cosmology, in which cosmic time is identified with the time-like Liouville mode of the supercritical string. In this scenario the Friedmann equation receives additional contributions due to the non-criticality of the string. These are potentially important when one seeks to apply the Bousso bound for the entropy of states that may become light as the dilaton takes on trans-Planckian values, as in a de Sitter phase, and restore consistency with the FSC and in at least some cases also the SSC…
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…
The evolution of the non-adiabatic pressure perturbation during inflation driven by two scalar fields is studied numerically for three different types of models. In the first model, the fields have standard kinetic terms. The other two models considered feature non-canonical kinetic terms; the first containing two fields which are coupled via their kinetic terms, and the second where one field has the standard kinetic term with the other field being a DBI field. We find that the evolution and the final amplitude of the non-adiabatic pressure perturbation depends strongly on the kinetic terms.
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 t…
We derive analytical expressions for the power spectra at the end of inflation in theories with two inflaton fields and non-canonical kinetic terms. We find that going beyond the slow-roll approximation is necessary and that the nature of the non-canonical terms have an important impact on the final power spectra at the end of inflation. We study five models numerically and find excellent agreement with our analytical results. Our results emphasise the fact that going beyond the slow-roll approximation is important in times of high-precision data coming from cosmological observations.
Oscillons are long-lived, localized, oscillatory scalar field configurations. In this work we derive a condition for the existence of small-amplitude oscillons (and provide solutions) in scalar field theories with non-canonical kinetic terms. While oscillons have been studied extensively in the canonical case, this is the first example of oscillons in scalar field theories with non-canonical kinetic terms. In particular, we demonstrate the existence of oscillons supported solely by the non-canonical kinetic terms, without any need for nonlinear terms in the potential. In the small-amplitude li…
We investigate the dynamics of homogeneous phase space for single-field models of inflation. Inflationary trajectories are formally attractors in phase space, but since in practice not all initial conditions lead to them, some degree of fine tuning is required for successful inflation. We explore how the dynamics of non-canonical inflation, which has additional kinetic terms that are powers of the kinetic energy, can play a role in ameliorating the initial conditions fine tuning problem. We present a qualitative analysis of inflationary phase space based on the dynamical behavior of the scalar…
We look for potential observational degeneracies between canonical and non-canonical models of inflation of a single field $ϕ$. Non-canonical inflationary models are characterized by higher than linear powers of the standard kinetic term $X$ in the effective Lagrangian $p(X,ϕ)$ and arise for instance in the context of the Dirac-Born-Infeld (DBI) action in string theory. An on-shell transformation is introduced that transforms non-canonical inflationary theories to theories with a canonical kinetic term. The 2-point function observables of the original non-canonical theory and its canonical tra…
We examine whether an extended scenario of a two-scalar-field model, in which a mixed kinetic term of canonical and phantom scalar fields is involved, admits the Bianchi type I metric, which is homogeneous but anisotropic spacetime, as its power-law solutions. Then we analyze the stability of the anisotropic power-law solutions to see whether these solutions respect the cosmic no-hair conjecture or not during the inflationary phase. In addition, we will also investigate a special scenario, where the pure kinetic terms of canonical and phantom fields disappear altogether in field equations, to …
We study preheating in models where the inflaton has a non-canonical kinetic term, containing powers of the usual kinetic energy. The inflaton field oscillating about its potential minimum acts as a driving force for particle production through parametric resonance. Non-canonical kinetic terms can impose a speed limit on the motion of the inflaton, modifying the oscillating inflaton profile. This has two important effects: it turns a smooth sinusoidal profile into a sharp saw-tooth, enhancing resonance, and it lengthens the period of oscillations, suppressing resonance. We show that the second…
We argue that in models of inflation with two scalar fields and non-canonical kinetic terms there is a possibility of obtaining a red tilt of the power spectrum of curvature perturbations from noncanonicality-induced interactions between the curvature and isocurvature perturbations. We describe an extremely simple model realizing this idea, study numerically its predictions for the perturbations and discuss applications in realistic scenarios of inflation. We discuss to what extent in this model the scale of the inflationary potential can be decoupled from the amplitude of the density fluctuat…
Tunneling is a fascinating aspect of quantum mechanics that renders the local minima of a potential meta-stable, with important consequences for particle physics, for the early hot stage of the universe, and more speculatively, for the behavior of the putative multiverse. While this phenomenon has been studied extensively for systems which have canonical kinetic terms, many theories of fundamental physics contain fields with non-canonical kinetic structures. It is therefore desirable to have a detailed framework for calculating tunneling rates and initial states after tunneling for these theor…
A new formulation of relativistic classical mechanics allows a revisiting of old unsolved problems in relativistic kinetic theory and in relativistic statistical mechanics. In particular a definition of the relativistic micro-canonical partition function is given strictly in terms of the Poincaré generators of an interacting N-particle system both in the inertial and non-inertial rest frames. The non-relativistic limit allows a definition of both the inertial and non-inertial micro-canonical ensemble strictly in terms of the Galilei generators. Also the one-particle relativistic distribution f…
It is shown that the one-loop coefficients of on-shell operators of standard supergravity with canonical gauge kinetic energy can be regulated by the introduction of Pauli-Villars chiral and abelian gauge multiplets, subject to a condition on the matter representations of the gauge group. Aspects of the anomaly structure of these theories under global nonlinear symmetries and an anomalous gauge symmetry are discussed.
We examine an extension of the quintom scenario of dark energy, in which a canonical scalar field and a phantom field are coupled through a kinetic interaction. We perform a phase space analysis and show that the kinetic coupling gives rise to novel cosmological behaviour. In particular, we obtain both quintessence-like and phantom-like late-time solutions, as well as solutions that cross the phantom divide during the evolution of the universe.
We investigate the effect of non-canonical kinetic terms on inflation in supergravity. We find that the biggest impact of such higher-derivative kinetic terms is due to the corrections to the potential that they induce via their effect on the auxiliary fields, which now have a cubic equation of motion. This is in contrast to the usual (non-supersymmetric) effective field theory expansion which assumes that mass-suppressed higher-derivative terms do not affect the lower-derivative terms already present. We demonstrate with several examples that such changes in the potential can significantly mo…
The appearance of inner brane structure is an interesting issue in domain wall {brane model}. Because such structure usually leads to quasilocalized modes of various kinds of bulk fields. In this paper, we construct a domain wall brane model by using a scalar field $ϕ$, which couples to its kinetic term. The inner brane structure emerges as the scalar-kinetic coupling increases. With such brane structure, we show that it is possible to obtain gravity resonant modes in both tensor and scalar sectors. The number of the resonant modes depends on the vacuum expectation value of $ϕ$ and the form of…
Theories possessing non-canonical kinetic terms are often studied for Q-ball states in an ad-hoc manner. This paper seeks to generalise their study for both thin- and thick-wall Q-balls. Specifically, we show that theories whose potential cannot house Q-balls can do so by virtue of their non-canonical kinetic terms. Furthermore, we also constrain the theories that possess an energetically stable thick-wall limit, with ramifications for their early universe phenomenology.
Dark energy models with non-canonical kinetic energy terms, k-essence, can have dynamical and sound speed properties distinct from canonical scalar fields, quintessence. Concentrating on purely kinetic term Lagrangians, which can be technically natural, we investigate limits on the equation of state dynamics and sound speed behaviors and the extent to which these models can be separated from quintessence.
We study the K-Inflation models where the inflaton field has non-canonical kinetic term. In particular, we consider the Dirac-Born-Infeld (DBI) form for the kinetic energy of the inflaton field. We consider quadratic and quartic potentials as well as the potential for the natural inflation. We use a modified version of the MODECODE (proposed by Mortonson et al.) to calculate the power spectrum of the primordial perturbations generated by the inflaton field and subsequently use the WMAP7 results to constrain the models. Interestingly with DBI type kinetic term, lesser gravity waves are produced…
We derive the first quantum gravitational corrections to the inflationary power spectra for a general single-field scalar-tensor theory which includes a non-minimal coupling to gravity, a non-standard scalar kinetic term and an arbitrary potential of the scalar field. We obtain these corrections from a semiclassical expansion of the Wheeler-DeWitt equation, which, in turn, governs the full quantum dynamics in the canonical approach to quantum gravity. We discuss the magnitude and relevance of these corrections, as well as their characteristic signature in the inflationary spectral observables.…
In this work we investigate the inflationary era in the presence of a canonical scalar field and Chern-Simons parity violating corrections. It was also assumed that a non minimal coupling between curvature and the scalar field is present. For the shake of completeness, the slow-roll and the constant-roll scenarios were examined separately. In the context of this scalar-tensor theory, inflation can be viable for both scenarios since the observational indices take acceptable values according to the most recent Planck data. Furthermore, the involvement of the Chern-Simons term has no effect on th…
We study the origin of fermion mass hierarchy and flavor mixing in the standard model, paying attention to flavor symmetries and fermion kinetic terms. There is a possibility that the hierarchical flavor structure of quarks and charged leptons originates from non-canonical types of fermion kinetic terms in the presence of flavor symmetric Yukawa interactions. A flavor symmetry can be hidden in the form of non-unitary bases in the standard model. The structure of Kähler potential can become a touchstone of new physics.
We investigate the canonical formulation of the (bosonic) E$_{6(6)}$ exceptional field theory. The explicit non-integral (not manifestly gauge invariant) topological term of E$_{6(6)}$ exceptional field theory is constructed and we consider the canonical formulation of a model theory based on the topological two-form kinetic term. Furthermore we construct the canonical momenta and the canonical Hamiltonian of the full bosonic E$_{6(6)}$ exceptional field theory. Most of the canonical gauge transformations and some parts of the canonical constraint algebra are calculated. Moreover we discuss ho…
The dynamical properties of a model of dark energy in which two scalar fields are coupled by a non-canonical kinetic term are studied. We show that overall the addition of the coupling has only minor effects on the dynamics of the two-field system for both potentials studied, even preserving many of the features of the assisted quintessence scenario. The coupling of the kinetic terms enlarges the regions of stability of the critical points. When the potential is of an additive form, we find the kinetic coupling has an interesting effect on the dynamics of the fields as they approach the inflat…
We consider warm inflation with a Dirac-Born-Infeld (DBI) kinetic term in which both the nonequilibrium dissipative particle production and the sound speed parameter slow the motion of the inflaton field. We find that a low sound speed parameter removes, or at least strongly suppresses, the growing function appearing in the scalar of curvature power spectrum of warm inflation, which appears due to the temperature dependence in the dissipation coefficient. As a consequence of that, a low sound speed helps to push warm inflation into the strong dissipation regime, which is an attractive regime f…
In the present work, we study the cosmological model with fermionic field and with the non-canonical kinetic term (f-essence). We also present some important reductions of the model as well as its some generalizations. We also found the exact solution of the model and examine the influence of such gravity-fermion interaction on the observed accelerated expansion of our universe. Several fermionic and bosonic-fermionic DBI models were constructed as some particular reductions of f-essence and g-essence, respectively and their Chaplygin gas counterparts are found. Finally, some nonlinear models …
Affine quantization, which is a parallel procedure with canonical quantization, needs to use its principal quantum operators, most simply $D=(PQ+QP)/2$ and $Q\neq0$, to represent appropriate kinetic factors, normally $P^2$, which involve only one canonical quantum operator. The need for this requirement stems from the quantization of selected problems that require affine quantization to achieve valid Monte Carlo results. This task is resolved for introductory examples as well as examples that involve scalar quantum field theories.
We present $\mathcal{N}=1$ supergravity models of mutated hilltop inflation (MHI) for both large and small field sectors. Models with canonical kinetic terms are developed based on a shift symmetric Kähler potential in inflaton superfield, and with a superpotential linear in Goldstino superfield. We also construct models with non-canonical kinetic terms for MHI by generalizing the shift symmetry. We found that a good fraction of the models can address the entire branch of MHI in a single framework.
We apply the Wigner-function approach and chiral kinetic theory to investigate the angular momentum and polarization of chiral fluids composed of Weyl fermions with background electric/magnetic fields and vorticity. It is found that the quantum corrections in Wigner functions give rise to nonzero anti-symmetric components in the canonical energy-momentum tensors, which are responsible for the spin-orbit interaction. In global equilibrium, conservation of the canonical angular momentum reveals the cancellation between the orbital component stemming from side jumps with nonzero vorticity and the…
We consider reheating after inflation in theories with a non-standard kinetic term. We show that the equation that exhibits parametric resonance is the Hill-Whittaker equation, which is a particular case of the more general Hill equation. This equation is in general more unstable than the Mathieu equation, such that narrow resonance preheating may be efficient in theories with a non-canonical kinetic term.
Non-canonical scalar fields with the Lagrangian ${\cal L} = X^α- V(ϕ)$, possess the attractive property that the speed of sound, $c_s^{2} = (2\,α- 1)^{-1}$, can be exceedingly small for large values of $α$. This allows a non-canonical field to cluster and behave like warm/cold dark matter on small scales. We demonstrate that simple potentials including $V = V_0\coth^2ϕ$ and a Starobinsky-type potential can unify dark matter and dark energy. Cascading dark energy, in which the potential cascades to lower values in a series of discrete steps, can also work as a unified model. In all of these mod…
We present the first 3+1-dimensional numerical simulations of scalar fields with non-minimal kinetic terms. As an example, we examine the existence and stability of preheating in the presence of a Dirac-Born-Infeld (DBI) inflaton coupled to a canonical matter field. The simulations represent the full non-linear theory in the presence of an expanding Universe. We show that parametric resonance in the matter field, along with self-resonance in the inflaton, repopulate the Universe with matter particles as efficiently as in traditional preheating.
We adopt a covariant formalism to derive exact evolution equations for nonlinear perturbations, in a universe dominated by two scalar fields. These scalar fields are characterized by non-canonical kinetic terms and an arbitrary field space metric, a situation typically encountered in inflationary models inspired by string theory. We decompose the nonlinear scalar perturbations into adiabatic and entropy modes, generalizing the definition adopted in the linear theory, and we derive the corresponding exact evolution equations. We also obtain a nonlinear generalization of the curvature perturbati…
We consider a general chaotic inflation model with non-canonical kinetic term, resulting in attractor solutions for the inflation of quadratic or other monomial type. In particular, the form of the kinetic term and the potential is fixed due to the requirement that the inflation model is a quadratic form in the large field values of the inflaton. We show that a large coupling in the non-canonical kinetic term allows for the slow-roll inflation with sub-Planckian field values of the inflaton and the successful predictions of the quadratic or other monomial type chaotic inflation in light of BIC…
While a scalar field with a pole in its kinetic term is often used to study the cosmological inflation, it can also play the role of dark energy, which is called the pole dark energy model. We propose a generalized model that the scalar field may have two or even multiple poles in the kinetic term and we call it the multi-pole dark energy. We find the poles can place some restrictions on the values of the original scalar field with non-canonical kinetic term. After transforming to the canonical form, we get a flat potential for the transformed new scalar field even if the original field has a …
We consider gauge vortices in symmetry breaking models with a non-canonical kinetic term. This work extends our previous study on global topological k-defects (hep-th/0608071), including a gauge field. The model consists of a scalar field with a non-canonical kinetic term, while for the gauge field the standard form of its kinetic term is preserved. Topological defects arising in such models, k-vortices, may have quite different properties as compared to ``standard'' vortices. This happens because an additional dimensional parameter enters the Lagrangian for the considered model -- a ``kinetic…
We propose a new broad class of multi-field non-canonical inflationary models as an extension of multi-field conformal cosmological attractors. This also generalizes the recently discovered class of non-canonical conformal attractors for single field inflation. Kinetic terms of this class of models are phenomenologically arising from ${\cal N}=1$ supergravity and from ${\cal N}=1$ superconformal theory, with two conformal scalar compensator fields in the latter. We show that the inflationary dynamics and predictions of this class of models are stable with respect to the significant modificatio…
Canonical quantization for effective theories with perturbations altering degrees of freedom: a covariant phase space approach
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
