Non-canonical Kinetic Term Research Articles

K-field kinks in two-dimensional dilaton gravity

In this work, kinks with non-canonical kinetic energy terms are studied in a type of two-dimensional dilaton gravity model. The linear stability issue is generally discussed for arbitrary static solutions, and the stability criteria are obtained. As an explicit example, a model with cuscuton term is studied. After rewriting the equations of motion into simpler first-order formalism and choosing a polynomial superpotential, an exact self-gravitating kink solution is obtained. The impacts of the cuscuton term are discussed.

Double-peaked inflation model: Scalar induced gravitational waves and primordial-black-hole suppression from primordial non-Gaussianity

A significant abundance of primordial black hole (PBH) dark matter can be produced by curvature perturbations with power spectrum $\Delta_\zeta^2(k_{\mathrm{peak}})\sim \mathcal{O}(10^{-2})$ at small scales, associated with the generation of observable scalar induced gravitational waves (SIGWs). However, the primordial non-Gaussianity may play a non-negligible role, which is not usually considered. We propose two inflation models that predict double peaks of order $\mathcal{O}(10^{-2})$ in the power spectrum and study the effects of primordial non-Gaussianity on PBHs and SIGWs. This model is driven by a power-law potential, and has a noncanonical kinetic term whose coupling function admits two peaks. By field-redefinition, it can be recast into a canonical inflation model with two quasi-inflection points in the potential. We find that the PBH abundance will be altered saliently if non-Gaussianity parameter satisfies $|f_{\mathrm{NL}}(k_{\text{peak}},k_{\text{peak}},k_{\text{peak}})|\gtrsim \Delta^2_{\zeta}(k_{\mathrm{peak}})/(23\delta^3_c) \sim \mathcal{O}(10^{-2})$. Whether the PBH abundance is suppressed or enhanced depends on the $f_{\mathrm{NL}}$ being positive or negative, respectively. In our model, non-Gaussianity parameter $f_{\mathrm{NL}}(k_{\mathrm{peak}},k_{\mathrm{peak}},k_{\mathrm{peak}})\sim \mathcal{O}(1)$ takes positive sign, thus PBH abundance is suppressed dramatically. On the contrary, SIGWs are insensitive to primordial non-Gaussianity and hardly affected, so they are still within the sensitivities of space-based GWs observatories and Square Kilometer Array.

Primordial black holes and secondary gravitational waves from natural inflation

The production of primordial black hole (PBH) dark matter (DM) and the generation of scalar induced secondary gravitational waves by using the enhancement mechanism with a peak function in the non-canonical kinetic term in natural inflation is discussed. We show explicitly that the power spectrum for the primordial curvature perturbation can be enhanced at 1012Mpc−1, 108Mpc−1 and 105Mpc−1 by adjusting the model parameters. With the enhanced primordial curvature perturbations, we show the production of PBH DM with peak masses around 10−13M⊙, the Earth's mass and the stellar mass, and the generation of scalar induced gravitational waves (SIGWs) with peak frequencies around mHz, 10−6Hz and nHz, respectively. The PBHs with the mass scale 10−13M⊙ can make up almost all the DM and the associated SIGWs is testable by spaced-based gravitational wave observatory.

Primordial black holes and secondary gravitational waves from chaotic inflation

Chaotic inflation is inconsistent with the observational constraint at 68% CL. Here, we show that the enhancement mechanism with a peak function in the noncanonical kinetic term not only helps the chaotic model V(ϕ) = V0ϕ1/3 satisfy the observational constraint at large scales but also enhances the primordial scalar power spectrum by seven orders of magnitude at small scales. The enhanced curvature perturbations can produce primordial black holes of different masses and secondary gravitational waves with different peak frequencies. We also show that the non-Gaussianities of curvature perturbations have little effect on the abundance of primordial black holes and energy density of the scalar-induced secondary gravitational waves.

Tachyonic preheating in Palatini R 2 inflation

We study preheating in the Palatini formalism with a quadratic inflaton potential and an added αR 2 term. In such models, the oscillating inflaton field repeatedly returns to the plateau of the Einstein frame potential, on which the tachyonic instability fragments the inflaton condensate within less than an e-fold. We find that tachyonic preheating takes place when α ≳ 1013 and that the energy density of the fragmented field grows with the rate Γ/H ≈ 0.011 × α0.31. The model extends the family of plateau models with similar preheating behaviour. Although it contains non-canonical quartic kinetic terms in the Einstein frame, we show that, in the first approximation, these can be neglected during both preheating and inflation.

Fractional dark energy

In this paper we introduce the fractional dark energy model, in which the accelerated expansion of the Universe is driven by a nonrelativistic gas (composed by either fermions or bosons) with a noncanonical kinetic term. The kinetic energy is inversely proportional to the cube of the absolute value of the momentum for a fluid with an equation of state parameter equal to minus one, and whose corresponding energy density mimics the one of the cosmological constant. In the general case, the dark energy equation of state parameter (times three) is precisely the exponent of the momentum in the kinetic term. We show that this inverse momentum operator appears in fractional quantum mechanics and it is the inverse of the Riesz fractional derivative. The observed vacuum energy can be obtained through the integral of the Fermi-Dirac (or Bose-Einstein) distribution and the lowest allowed energy of the particles. Finally, a possible thermal production and fate of fractional dark energy is investigated.

Primordial black holes and scalar-induced secondary gravitational waves from inflationary models with a noncanonical kinetic term

With the enhancement mechanism provided by a noncanonical kinetic term with a peak, the amplitude of primordial curvature perturbations can be enhanced by seven orders of magnitude at small scales while keeping to be consistent with observations at large scales. The peak function and inflationary potential are not restricted in this mechanism. We use the Higgs model and T-model as examples to show how abundant primordial black hole dark matter with different mass and scalar induced secondary gravitational waves with different peak frequency are generated. We also show that the enhanced power spectrum for the primordial curvature perturbations and the energy density of the scalar induced secondary gravitational waves can have either a sharp peak or a broad peak. The primordial black holes with the mass around $10^{-14}-10^{-12} M_{\odot}$ produced with the enhancement mechanism can make up almost all dark matter, and the scalar induced secondary gravitational waves accompanied with the production of primordial black holes can be tested by the pulsar timing arrays and spaced based gravitational wave observatory. Therefore, the mechanism can be tested by primordial black hole dark matter and gravitational wave observations.

Study on early inflationary phase using a new form of non-canonical scalar field model

We study the inflationary phase of the early universe as modeled by a non-canonical scalar field. The homogeneous scalar field equation is derived from a Lagrangian density containing a new form of non-canonical kinetic term and a general potential function. The Lie symmetry is studied and a one parameter Lie point symmetry for the homogeneous scalar field equation is found. We use Lie symmetry generator to construct the exact analytical group invariant closed-form solution of the homogeneous scalar field equation without applying any slow-roll approximation from invariant curve condition. The solution thus obtained is seen to be consistent with the Friedmann equations subject to constraint conditions on the potential parameter $$\lambda $$ . In this scenario, we obtain the values for various inflationary parameters and make useful checks on the observational constraints on the parameters from Planck data by imposing a set of bounds on the parameter $$\lambda $$ of the potential. The results for scalar spectral index ( $$n_S$$ ) and tensor-to-scalar ratio (r) presented in the $$(n_S,\,r)$$ plane in the background of Planck2015 and Planck2018 data are in good agreement with cosmological observations. We find $$r\sim 10^{-3}$$ , the targeted value of r that will be detected by the future CMB observation such as LiteBIRD. Interestingly, most significant primordial non-Gaussianity is also achieved. For theoretical completeness of our non-canonical model, we obtain the allowed parameter space in which the ghosts and Laplacian instabilities are absent. We apply the formulas for slow-roll parameter to explain exit from the inflationary phase using the general potential. We also treat the non-canonical scalar field model equation by the dynamical system theory to provide useful checks on the stability of the critical points and show that the group invariant non-canonical inflationary solution is stable attractor in the phase space.

Bouncing cosmology in a curved braneworld

We explore the possibility of a non-singular bounce in our universe from a warped braneworld scenario with dynamical branes and a non-zero brane cosmological constant. Such models naturally incorporate a scalar sector known as the radion originating from the modulus of the theory. The presence of brane cosmological constant renders the branes to be non-flat and gives rise to a potential and a non-canonical kinetic term for the radion field in the four dimensional effective action. The kinetic term exhibits a phantom-like behavior within the domain of evolution of the modulus which leads to a violation of the null-energy condition often observed in a bouncing universe. The interplay of the radion potential and kinetic term enables the evolution of the radion field from a normal to a phantom regime where the universe transits from a contracting era to an expanding epoch through a non-singular bounce. Analysis of the scalar and tensor perturbations over such background evolution reveal that the primordial observables e.g., the amplitude of scalar perturbations \U0001d49cs, tensor to scalar ratio r and the scalar spectral index ns are in agreement with the current constraints reported by the Planck satellite. The implications are discussed.

K-Inflation-corrected Einstein-Gauss-Bonnet gravity with massless primordial gravitons

In the present paper, we study the inflationary phenomenology of a k-inflation corrected Einstein-Gauss-Bonnet theory. Non-canonical kinetic terms are known for producing Jean instabilities or superluminal sound wave velocities in the aforementioned era, but we demonstrate in this work that by adding Gauss-Bonnet string corrections and assuming that the non-canonical kinetic term ωXγ is in quadratic, one can obtain a ghost free description. Demanding compatibility with the recent GW170817 event forces one to accept that the relation ξ¨=Hξ˙ for the scalar coupling function ξ(ϕ). As a result, the scalar functions of the theory are revealed to be interconnected and by assuming a specific form for one of them, specifies immediately the other. Here, we shall assume that the scalar potential is directly derivable from the equations of motion, once the Gauss-Bonnet coupling is appropriately chosen, but obviously the opposite is feasible as well. As a result, each term entering the equations of motion, can be written in terms of the scalar field and a relatively tractable phenomenology is produced. For quadratic kinetic terms, the resulting scalar potential is quite elegant functionally. Different exponents, which lead to either a more perplexed solution for the scalar potential, are still a possibility which was not further studied. We also discuss in brief the non-Gaussianities issue under the slow-roll and constant-roll conditions holding true, and we demonstrate that the predicted amount of non-Gaussianities is significantly enhanced in comparison to the k-inflation free Einstein-Gauss-Bonnet theory.

Multi-Brid DBI Inflation

It is shown that it is possible to apply $\delta \cN$ to some special non-canonic cases. We extended the multi-brid idea to the multi-field separable model with a non-canonical kinetic term, mainly the DBI model. Assuming a specific surface for the end of inflation and introducing new fields, enable us to find an explicit expression for the number of e-folds in terms of the new fields. By using $\delta$N formalism, we arrived at the cosmological parameters. We considered the DBI model for two different limits, viz., speed limit and constant sound speed.

Seeding Primordial Black Holes in Multifield Inflation.

The inflationary origin of primordial black holes (PBHs) relies on a large enhancement of the power spectrum Δ_{ζ} of the curvature fluctuation ζ at wavelengths much shorter than those of the cosmic microwave background anisotropies. This is typically achieved in models where ζ evolves without interacting significantly with additional (isocurvature) scalar degrees of freedom. However, quantum gravity inspired models are characterized by moduli spaces with highly curved geometries and a large number of scalar fields that could vigorously interact with ζ (as in the cosmological collider picture). Here we show that isocurvature fluctuations can mix with ζ inducing large enhancements of its amplitude. This occurs whenever the inflationary trajectory experiences rapid turns in the field space of the model leading to amplifications that are exponentially sensitive to the total angle swept by the turn, which induce characteristic observable signatures on Δ_{ζ}. We derive accurate analytical predictions and show that the large enhancements required for PBHs demand noncanonical kinetic terms in the action of the multifield system.

Scalar field unification of interacting viscous dark fluid from a geometrical scalar–tensor theory of gravity

We investigate, in the framework of a recently introduced new class of invariant geometrical scalar-tensor theory of gravity, the possibility that a viscous dark fluid can be described in a unified manner by a single scalar field. Thus we developed a model in which both the metric tensor and the scalar field have geometrical origin. The scalar field is characterized by a non-canonical kinetic term and the scalar viscosity of the dark fluid appears as soon the kinetic energy of the scalar field is no longer canonical. The scalar viscosity is considered as a function of the Hubble and the deceleration parameters. To illustrate the formalism we have considered two cases: a constant and a thermodynamic equation of state parameters. In the both cases we obtain analytic representations for the scalar field and their respective potentials. We delimit free parameters by comparing with some Planck 2018 results.

Multi-pole dark energy * * Supported by National Science Foundation of China (11105091, 11047138), "Chen Guang" project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation (12CG51), and Shanghai Natural Science Foundation, China (10ZR1422000)

A scalar field with a pole in its kinetic term is often used to study cosmological inflation; it can also play the role of dark energy, which is called the pole dark energy model. We propose a generalized model where 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 that the poles can place some restrictions on the values of the original scalar field with a non-canonical kinetic term. After the transformation to the canonical form, we get a flat potential for the transformed scalar field even if the original field has a steep one. The late-time evolution of the universe is obtained explicitly for the two pole model, while dynamical analysis is performed for the multiple pole model. We find that it does have a stable attractor solution, which corresponds to the universe dominated by the potential of the scalar field.

Primordial black holes and secondary gravitational waves from k and G inflation

The possibility that in the mass range around $10^{-12}\ M_\odot$ most of dark matter constitutes of primordial black holes (PBHs) is a very interesting topic. To produce PBHs with this mass, the primordial scalar power spectrum needs to be enhanced to the order of 0.01 at the scale $k\sim 10^{12}\ \text{Mpc}^{-1}$. The enhanced power spectrum also produces large secondary gravitational waves at the mHz band. A phenomenological delta function power spectrum is usually used to discuss the production of PBHs and secondary gravitational waves. Based on G and k inflations, we propose a new mechanism to enhance the power spectrum at small scales by introducing a non-canonical kinetic term $[1-2G(\phi)]X$ with the function $G(\phi)$ having a peak. Away from the peak, $G(\phi)$ is negligible and we recover the usual slow-roll inflation which is constrained by the cosmic microwave background anisotrpy observations. Around the peak, the slow-roll inflation transiently turns to ultra slow-roll inflation. The enhancement of the power spectrum can be obtained with generic potentials, and there is no need to fine tune the parameters in $G(\phi)$. The energy spectrum $\Omega_{GW}(f)$ of secondary gravitational waves have the characteristic power law behaviour $\Omega_{GW}(f)\sim f^{n}$ and is testable by pulsar timing array and space based gravitational wave detectors.

Exploring the inflation of F(R) gravity

The early-time expansion of the spacetime, namely, inflation, is introduced to solve some cosmological problems. [Formula: see text] gravity is a simple extension of the general relativity to induce the inflationary expansion. The precise observation of the Cosmic Microwave Background gives us the information to inspect the model of the inflation. [Formula: see text] gravity can be transformed to the Einstein–Hilbert term with a scalar field that plays the role of the inflaton. The inflaton potential is described as an explicit function of the inflaton field with a noncanonical kinetic term. In this paper, we obtain general formulae to derive the inflationary parameters including the models with a noncanonical kinetic term. The inflationary parameters are described as functions of the inflaton potential and its derivatives. We evaluate a well-known model, [Formula: see text], to confirm the validity of our formulae. Then, we apply the procedure to a model, [Formula: see text], in which it is not possible to represent the potential as an explicit function of the inflaton field with a canonical kinetic term.

Revisiting non-Gaussianity in multifield inflation with curved field space

Recent studies of inflation with multiple scalar fields have highlighted the importance of non-canonical kinetic terms in novel types of inflationary solutions. This motivates a thorough analysis of non-Gaussianities in this context, which we revisit here by studying the primordial bispectrum in a general two-field model. Our main result is the complete cubic action for inflationary fluctuations written in comoving gauge, i.e. in terms of the curvature perturbation and the entropic mode. Although full expressions for the cubic action have already been derived in terms of fields fluctuations in the flat gauge, their applicability is mostly restricted to numerical evaluations. Our form of the action is instead amenable to several analytical approximations, as our calculation in terms of the directly observable quantity makes manifest the scaling of every operator in terms of the slow-roll parameters, what is essentially a generalization of Maldacena’s single-field result to non-canonical two-field models. As an important application we derive the single-field effective field theory that is valid when the entropic mode is heavy and may be integrated out, underlining the observable effects that derive from a curved field space.

On preheating in alpha -attractor models of inflation

We study (p)reheating in alpha -attractor T-models of inflation, taking into account both scalar fields present in these models: the inflaton and the spectator. The two-field model has a negative field-space curvature which, at the end of inflation, may lead to geometrical destabilization of the spectator for small values of alpha {mathop {{}_sim }limits ^{<}} 10^{-3}. We perform the instability (Floquet) analysis of the linear dynamics and fully non-linear lattice computations with our numerical code, which we specifically designed for a class of two-field models with non-canonical kinetic terms. We find that the perturbations of the spectator field are much more unstable than the perturbations of the inflaton field, so the dynamics of the early stages of preheating is dominated by the evolution of the spectator perturbations. As a result, the transition from the inflationary era to radiation domination era is practically instantaneous and much faster than previously found in an effective theory including only the inflaton field.

Infrared resummation for derivative interactions in de Sitter space

In de Sitter space, scale invariant fluctuations give rise to infrared logarithmic corrections to physical quantities, which eventually spoil perturbation theories. For models without derivative interactions, it has been known that the field equation reduces to a Langevin equation with white noise in the leading logarithm approximation. The stochastic equation allows us to evaluate the infrared effects nonperturbatively. We extend the resummation formula so that it is applicable to models with derivative interactions. We first consider the nonlinear sigma model and next consider a more general model which consists of a noncanonical kinetic term and a potential term. The stochastic equations derived from the infrared resummation in these models can be understood as generalizations of the standard one to curved target spaces.

Realising mutated hilltop inflation in supergravity

We present 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 generalising the shift symmetry. We found that a good fraction of the models can address the entire branch of MHI in a single framework.