Stable small spatial hairs in a power-law k-inflation model
Tuan Q. Do
备注：
15 pages, 2 figures. Substantial revision with discussions on seminal papers of Starobinsky related to the cosmic no-hair conjecture and investigations on the corresponding tensor-to-scalar ratio. Main results and conclusions are not changed. Comments are welcome
In this paper, we extend our investigation of the validity of the cosmic no-hair conjecture within non-canonical anisotropic inflation. As a result, we are able to figure out an exact Bianchi type I solution to a power-law {\it k}-inflation model in the presence of unusual coupling between scalar and electromagnetic fields as $-f^2(ϕ)F_{μν}F^{μν}/4$. Furthermore, stability analysis based on the dynamical system method indicates that the obtained solution does admit stable and attractive hairs during an inflationary phase and therefore violates the cosmic no-hair conjecture. Finally, we show that the corresponding tensor-to-scalar ratio of this model turns out to be highly consistent with the observational data of the Planck 2018.
We will examine whether anisotropic hairs exist in a string-inspired scalar-Gauss-Bonnet gravity model with the absence of potential of scalar field during the inflationary phase. As a result, we are able to obtain the Bianchi type I power-law solution to this model under the assumption that the scalar field acts as the phantom field, whose kinetic is negative definite. However, the obtained anisotropic hair of this model turns out to be large, which is inconsistent with the observational data. We will therefore introduce a nontrivial coupling between scalar and vector fields such as $f^2(ϕ)F_…
We consider implications of the quantum extension of the inflationary no hair theorem. We show that when the quantum state of inflation is picked to ensure the validity of the EFT of fluctuations, it takes only ${\cal O}(10)$ efolds of inflation to erase the effects of the initial distortions on the inflationary observables. Thus the Bunch-Davies vacuum is a very strong quantum attractor during inflation. We also consider bouncing universes, where the initial conditions seem to linger much longer and the quantum `balding' by evolution appears to be less efficient.
We will present main results of our recent investigations on the validity of cosmic no-hair conjecture proposed by Hawking and his colleagues long time ago in the framework of an anisotropic inflationary model proposed by Kanno, Soda, and Watanabe. As a result, we will show that the cosmic no-hair conjecture seems to be generally violated in the Kanno-Soda-Watanabe model for both canonical and non-canonical scalar fields due to the existence of a non-trivial coupling term between scalar and electromagnetic fields. However, we will also show that the validity of the cosmic no-hair conjecture wi…
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 inflationary universes with an SU(3) gauge field coupled to an inflaton through a gauge kinetic function. Although the SU(3) gauge field grows at the initial stage of inflation due to the interaction with the inflaton, nonlinear self-couplings in the kinetic term of the gauge field become significant and cause nontrivial dynamics after sufficient growth. We investigate the evolution of the SU(3) gauge field numerically and reveal attractor solutions in the Bianchi type I spacetime. In general cases where all the components of the SU(3) gauge field have the same magnitude initially, th…
We study inflation with anisotropic hair induced by form fields. In four dimensions, the relevant form fields are gauge (one-form) fields and two-form fields. Assuming the exponential form of potential and gauge kinetic functions, we find new exact power-law solutions endowed with anisotropic hair. We also explore the phase space of anisotropic inflation and find fixed points corresponding to the exact power-law solutions. Moreover, we perform the stability analysis around the fixed points to reveal the structure of the phase space. It turns out that one of the fixed points becomes an attracto…
In this paper, we study a non-canonical extension of a supergravity-motivated model acting as a vivid counterexample to the cosmic no-hair conjecture due to its unusual coupling between scalar and electromagnetic fields. In particular, a canonical scalar field is replaced by the string-inspired Dirac-Born-Infeld one in this extension. As a result, exact anisotropic inflationary solutions for this Dirac-Born-Infeld model are figured out under a constant-roll condition. Furthermore, numerical calculations are performed to verify that these anisotropic constant-roll solutions are indeed attractiv…
We present stable solution of static spherically symmetric Einstein-Yang-Mills equations with the SU(2) gauge group. This solution is asymptotically flat and regular at r = 0 and with nontrivial Yang-Mills(YM) connection. With quantized values of the Arnowitt-Deser-Misner (ADM) mass, the solutions asymptotically approach the Schwarzschild solution and have zero global YM charges. Numerical evidences suggest that this solution is both linearly and nonlinearly stable and has a ring of generic curvature singularities along the horizon. An effective counterexample to the no-hair conjecture is prov…
In this paper, we extend a recent proposed model of two scalar and two vector fields to a hyperbolic inflation scenario, in which the field space of two scalar fields is a hyperbolic space instead of a flat space. In this model, one of the scalar fields is assumed to be a radial field, while the other is set as an angular field. Furthermore, both scalar fields will be coupled to two different vector fields, respectively. As a result, we are able to obtain a set of exact Bianchi type I solutions to this model. Stability analysis is also performed to show that this set of anisotropic solutions i…
We have already derived the Criteria for thermal stability of charged rotating quantum black holes, for horizon areas that are large relative to the Planck area. The derivation is done by using results of loop quantum gravity and equilibrium statistical mechanics of the Grand Canonical ensemble. It is also shown that in four dimensional spacetime, quantum ADS Kerr-Newman Black hole is thermally stable within certain range of its' parameters. In this paper, the expectation values of fluctuations and correlations among horizon area, charge and angular momentum of stable quantum ADS black hole ar…
Inspired by an interesting counterexample to the cosmic no-hair conjecture found in a supergravity-motivated model recently, we propose a multi-field extension, in which two scalar fields are allowed to non-minimally couple to two vector fields, respectively. This model is shown to admit an exact Bianchi type I power-law solution. Furthermore, stability analysis based on the dynamical system method is performed to show that this anisotropic solution is indeed stable and attractive if both scalar fields are canonical. Nevertheless, if one of the two scalar fields is phantom then the correspondi…
We point out that tensor consistency relations-i.e. the behavior of primordial correlation functions in the limit a tensor mode has a small momentum-are more universal than scalar consistency relations. They hold in the presence of multiple scalar fields and as long as anisotropies are diluted exponentially fast. When de Sitter isometries are approximately respected during inflation this is guaranteed by the Higuchi bound, which forbids the existence of light particles with spin: De Sitter space can support scalar hair but no curly hair. We discuss two indirect ways to look for the violation o…
Higher-order derivative terms are considered as replacement for the Skyrme term in an Einstein-Skyrme-like model in order to pinpoint which properties are necessary for a black hole to possess stable static scalar hair. We find two new models able to support stable black hole hair in the limit of the Skyrme term being turned off. They contain 8 and 12 derivatives, respectively, and are roughly the Skyrme-term squared and the so-called BPS-Skyrme-term squared. In the twelfth-order model we find that the lower branches, which are normally unstable, become stable in the limit where the Skyrme ter…
Can a black hole that suffers a superradiant instability evolve towards a 'hairy' configuration which is stable? We address this question in the context of Einstein-charged scalar field theory. First, we describe a family of static black hole solutions which possess charged scalar-field hair confined within a mirror-like boundary. Next, we derive a set of equations which govern the linear, spherically symmetric perturbations of these hairy solutions. We present numerical evidence which suggests that, unlike the vacuum solutions, the (single-node) hairy solutions are stable under linear perturb…
We compute the quasinormal frequencies for scalar perturbations of hairy black holes in four-dimensional Einstein-Maxwell-dilaton theory assuming a non-trivial scalar potential for the dilaton field. We investigate the impact on the spectrum of the angular degree, the overtone number, the charges of the black hole as well as the magnitude of the scalar potential. All modes are found to be stable. Our numerical results are summarized in tables, and for better visualization, we show them graphically as well.
In this paper, we demonstrate that a phenomenon described as "topological inflation" during which inflation occurs inside the core of topological defects, has a non-topological counterpart. This appears in a simple set-up containing Einstein gravity coupled minimally to an electromagnetic field as well as a self-interacting, complex valued scalar field. The U(1) symmetry of the model is unbroken and leads to the existence of globally regular solutions, so-called boson stars, that develop a horizon for sufficiently strong gravitational coupling. We also find that the same phenomenon exists for …
In shift-symmetric Horndeski theories, a static and spherically symmetric black hole can support linearly time-dependent scalar hair. However, it was shown that such a solution generically suffers from ghost or gradient instability in the vicinity of the horizon. In the present paper, we explore the possibility to avoid the instability, and present a new example of theory and its black hole solution with a linearly time-dependent scalar configuration. We also discuss the stability of solutions with static scalar hair for a special case where nonminimal derivative coupling to the Einstein tenso…
A set of power-law solutions of a conformal-violating Maxwell model with a non-standard scalar-vector coupling will be shown in this paper. In particular, we are interested in a coupling term of the form $X^{2n} F^{μν}F_{μν}$ with $X$ denoting the kinetic term of the scalar field. Stability analysis indicates that the new set of anisotropic power-law solutions is unstable during the inflationary phase. The result is consistent with the cosmic no-hair conjecture. We show, however, that a set of stable slowly expanding solutions does exist for a small range of parameters $λ$ and $n$. Hence a sma…
Recent numerical relativity simulations within the Einstein--Maxwell--(charged-)Klein-Gordon (EMcKG) system have shown that the non-linear evolution of a superradiantly unstable Reissner-Nordström black hole (BH) enclosed in a cavity, leads to the formation of a BH with scalar hair. Perturbative evidence for the stability of such hairy BHs has been independently established, confirming they are the true endpoints of the superradiant instability. The same EMcKG system admits also charged scalar soliton-type solutions, which can be either stable or unstable. Using numerical relativity techniques…
By using the Taylor series method and the solution-generating method, we construct exact black hole solutions with minimally coupled scalar field. We find that the black hole solutions can have many hairs except for the physical mass. These hairs come from the scalar potential. Unlike the mass, there is no symmetry corresponding to these hairs, thus they are not conserved and one cannot understand them as Noether charges. They arise as coupling constants. Although there are many hairs, the black hole has only one horizon. The scalar potential becomes negative for sufficient large $ϕ$ (or in th…
The present work deals with a non-equilibrium thermodynamics that is associated with the scenario of warm inflation. The premise is that an adiabatic radiation production process holds exactly i.e. the radiation dilution is exactly counterbalanced by a dissipation term. Under this hypothesis, it is found that radiation particle number, temperature, radiation energy density and pressure are all conserved -- a contradiction to the very nature of the warm inflation dynamics. However, such exact adiabatic radiation production process never happens in any realistic analysis of warm inflation. In th…
