Non-canonical Scalar Field Research Articles

Exact renormalization group: a new method for blocking the action

We consider the exact renormalization group for a non-canonical scalar field theory in which the field is coupled to the external source in a special nonlinear way. The Wilsonian action and the average effective action are then simply related by a Legendre transformation up to a trivial quadratic form. An exact mapping between canonical and non-canonical theories is obtained as well as the relations between their flows. An application to the theory of liquids is sketched.

Nonlinear superhorizon perturbations of non-canonical scalar field

We develop a theory of non-linear cosmological perturbations at superhorizon scales for a scalar field with a Lagrangian of the form P(X,ϕ), where X = −∂μϕ∂μϕ and ϕ is the scalar field. We employ the ADM formalism and the spatial gradient expansion approach to obtain general solutions valid up to the second order in the gradient expansion. This formulation can be applied to, for example, DBI inflation models to investigate superhorizon evolution of non-Gaussianities. With slight modification, we also obtain general solutions valid up to the same order for a perfect fluid with a general equation of state P = P(ρ).

On the evolution of tachyonic perturbations at super-Hubble scales

In the slow-roll inflationary scenario, the amplitude of the curvature perturbationsapproaches a constant value soon after the modes leave the Hubble radius. However,relatively recently, it was shown that the amplitude of the curvature perturbations inducedby the canonical scalar field can grow at super-Hubble scales if there is either a transitionto fast roll inflation or if inflation is interrupted for some period of time. In this work, weextend the earlier analysis to the case of a non-canonical scalar field described by theDirac–Born–Infeld action. With the help of a specific example, we show thatthe amplitude of the tachyonic perturbations can be enhanced or suppressed atsuper-Hubble scales if there is a transition from slow roll to fast roll inflation. We alsoillustrate as to how the growth of the entropy perturbations during the fast rollregime proves to be responsible for the change in the amplitude of the curvatureperturbations at super-Hubble scales. Furthermore, following the earlier analysis for thecanonical scalar field, we show that the power spectrum evaluated in the longwavelength approximation matches the exact power spectrum obtained numericallyvery well. Finally, we briefly comment on an application of this phenomenon.

Cosmologies with a general non-canonical scalar field

The scalar field models with the Lagrangian L = F(X) − V(ϕ), which we call general non-canonical scalar field models, are investigated. We find that a special square potential (with a negative minimum) is needed to drive the linear field solution (ϕ = ϕ0t) in our model, while in the K-essence model (L = −V(ϕ)F(X)) the potential should be taken as an inverse square one. Hence the cosmological evolutions for these models are totally different. The linear field solutions are found to be highly degenerate, and their cosmological evolutions are equivalent to the model where the sound speed diverges. We also study the stability of the linear field solution and find the condition for stable solutions to exist. The cosmological solution in the presence of matter and radiation is further studied by numerically solving the potential and the cosmological evolution, and the results are shown to be quite different from the case of no matter or radiation. Then we analyze the case with a constant barotropic index γ and show that, unlike in the K-essence model, the detailed form of F(X) depends on the potential V(ϕ), and that this constant γ solution is stable for γ0 ⩽ 1. When the potential is taken to be a constant, we find the first integral and obtain the corresponding γ, which is similar to that in the K-essence model.

Reconstruction of hessence dark energy and the latest type Ia supernovae gold dataset

Recently, many efforts have been made to build dark energy models whose equation-of-state parameter can cross the so-called phantom divide ${w}_{\mathrm{de}}=\ensuremath{-}1$. One of them is the so-called hessence dark energy model in which the role of dark energy is played by a noncanonical complex scalar field. In this work, we develop a simple method based on Hubble parameter $H(z)$ to reconstruct the hessence dark energy. As examples, we use two familiar parametrizations for $H(z)$ and fit them to the latest 182 type Ia supernovae Gold dataset. In the reconstruction, measurement errors are fully considered.

Minimal noncanonical cosmologies

We demonstrate how much it is possible to deviate from the standard cosmological paradigm of inflation-assisted LambdaCDM, keeping within current observational constraints, and without adding to or modifying any theoretical assumptions. We show that within a minimal framework there are many new possibilities, some of them wildly different from the standard picture. We present three illustrative examples of new models, described phenomenologically by a noncanonical scalar field coupled to radiation and matter. These models have interesting implications for inflation, quintessence, reheating, electroweak baryogenesis, and the relic densities of WIMPs and other exotics.

Cosmological evolution of “hessence” dark energy and avoidance of the big rip

Recently, many dark energy models whose equation-of-state parameter can cross the phantom divide w(de)=-1 have been proposed. In a previous paper [H. Wei, R. G. Cai, and D. F. Zeng, Classical Quantum Gravity 22, 3189 (2005)], we suggest such a model named hessence, in which a noncanonical complex scalar field plays the role of dark energy. In this work, the cosmological evolution of the hessence dark energy is investigated. We consider two cases: one is the hessence field with an exponential potential, and the other is with a (inverse) power-law potential. We separately investigate the dynamical system with four different interaction forms between hessence and background perfect fluid. It is found that the big rip never appears in the hessence model, even in the most general case, beyond particular potentials and interaction forms.

Haloes of k-essence

We study gravitationally bound static and spherically symmetric configurations ofk-essence fields. In particular, we investigate whether these configurations can reproducethe properties of dark matter haloes. The classes of Lagrangians we consider leadto non-isotropic fluids with barotropic and polytropic equations of state. Thelatter include microscopic realizations of the often-considered Chaplygin gases,which we find can cluster into dark matter halo-like objects with flat rotationcurves, while exhibiting a dark energy-like negative pressure on cosmologicalscales. We complement our studies with a series of formal general results about thestability and initial value formulation of non-canonical scalar field theories, andwe also discuss a new class of de Sitter solutions with spacelike field gradients.

Hessence: a new view of quintom dark energy

Recently a lot of attention has been given to building a dark energy model in which the equation-of-state parameter w can cross the phantom divide w = −1. One of the models to realize crossing the phantom divide is called the quintom model, in which two real scalar fields appear, one is a normal scalar field and the other is a phantom-type scalar field. In this paper we propose a non-canonical complex scalar field as the dark energy, which we dub ‘hessence’, to implement crossing the phantom divide, in a similar sense as the quintom dark energy model. In the hessence model, the dark energy is described by a single field with an internal degree of freedom rather than two independent real scalar fields. However, the hessence is different from an ordinary complex scalar field, we show that the hessence can avoid the difficulty of the Q-ball formation which gives trouble to the spintessence model (an ordinary complex scalar field acts as the dark energy). Furthermore, we find that, by choosing a proper potential, the hessence could correspond to a Chaplygin gas at late times.

Functional equations and Green's functions for augmented scalar fields

Certain noncanonical self-coupled scalar quantum field theories, previously formulated by means of functional integration, are herein recast into the form of functional differential equations for the Green's functional. From these expressions the set of coupled equations relating the Green's functions is obtained. The new equations are compared with those of the conventional formulation, and are proposed as alternatives, especially for nonrenormalizable models when the conventional equations fail.