arXiv subjects

Tuan Q. Do

Publications and source records attributed to Tuan Q. Do.

At least 19 recordsLinked to original sources

arXiv2026

Gravitational waves from oscillons in a generalized exponential plateau potential

We study oscillon formation and gravitational wave production in a generalized exponential plateau inflationary potential. Using Floquet analysis, we identify parametric instability bands consistent with oscillon formation, and solve numerically for the oscillon profile, finding quasi-breather solutions with lifetimes $τ_{\rm osc} \cdot m_{\rm eff} \sim 10^3$ --- $6\times10^4$. Applying the poltergeist mechanism, we compute the induced gravitational wave spectrum and find a peak at $f_{\rm peak} \approx 2.5\times10^{10}$~Hz with amplitude $Ω_{\rm GW,0}\,h^2 \sim 10^{-9}$--$10^{-8}$ for the benchmark parameter $β_{\rm pot} = 5\times10^{-6}$. This is far below the region forbidden by big bang nucleosynthesis. For $β_{\rm pot} = 5\times10^{-5}$ the signal exceeds the big bang nucleosynthesis bound for all considered oscillon energy fractions, constraining the parameter space of the model. The signal falls in the GHz regime, potentially accessible to future resonant cavity experiments.

astro-ph.CO↗

arXiv2026

Unstable de Sitter inflationary solution in sixth-order gravity

A sixth-order gravity, which involves not only two leading terms, $γ_1 R\Box R$ and $γ_2 R_{μν} \Box R^{μν}$, but also quadratic curvature terms along with cubic curvature ones, will be investigated in this paper to see if it admits an exact stable de Sitter solution. First, we will derive sixth-order differential field equations of this gravity under the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker background spacetime, using the effective method based on the Euler-Lagrange equations. Then, we will analytically solve these field equations to figure out an exact de Sitter solution, which turns out to be equivalent to a fixed point of the corresponding dynamical system of the studied gravity. Interestingly, two coefficients, $γ_1$ and $γ_2$, do not contribute to the value of the obtained de Sitter solution. However, they affect on the stability of the de Sitter solution. In particular, if these two coefficients obey the following inequality, $3γ_1+γ_2 <0$, then the de Sitter solution will always be unstable. Furthermore, numerical calculations will be performed to verify that the de Sitter fixed point is indeed a repeller of the dynamical system once this inequality is satisfied. All these results indicate that the sixth-order gravity is more suitable for an inflationary phase of early universe. To be complete, two special limits of the studied gravity model, in which field equations are reduced to second-order and fourth-order, respectively, will be investigated. As expected, only the second-order limit can always give raise a stable de Sitter solution, compatible with an accelerated expansion of late-time universe.

gr-qc↗

arXiv2026

Stability analysis of de Sitter solution in the Starobinsky-Grisaru-Zanon gravity using the dynamical system method

We study whether the so-called Starobinsky-Grisaru-Zanon gravity, which is a novel fourth-order gravity model involving the so-called Grisaru-Zanon term, admits a stable de Sitter solution. First, we derive the corresponding field equations of the Starobinsky-Grisaru-Zanon gravity for the spatially flat Friedmann-Lemaitre-Robertson-Walker metric by using an effective method based on the Euler-Lagrange equations. Then, we figure out an exact de Sitter solution of these field equations for the first time. Finally, we point out, through the dynamical system method, that the obtained de Sitter solution is always unstable. Interestingly, although the Starobinsky $R^2$ term does not contribute to the value of the obtained de Sitter solution, it does affect on the instability of this solution.

physics.gen-ph↗

arXiv2026

On the Elko inflation model

We argue that it is difficult to investigate the stability of de Sitter inflationary solution in an effective model of Elko fields due to the existence of third-order derivatives of fields, which are unfortunately unconstrained since the number of perturbation equations is not enough. This issue leads to an important question of whether the Elko inflation model is free from an instability or not.

physics.gen-ph↗

arXiv2026

Power-law Bianchi type I inflation with multiple vector fields

We investigate an inflationary anisotropic universe in a supergravity-motivated model with one scalar field non-minimally coupled to multiple vector fields. We restrict ourselves to the Bianchi type I metric, which describes a homogeneous but anisotropic universe. For consistency, we consider a configuration consisting of one homogeneous scalar field and three mutually orthogonal vector fields. As a result, we find four types of power-law solutions, classified according to the number of non-vanishing vector fields. Moreover, we show that all these solutions are stable under certain conditions on the model parameters, thereby defining stability regions described both quantitatively and qualitatively. Interestingly, our analysis suggests that vector fields with significantly larger coupling constants tend to persist as the universe expands, while those with significantly smaller coupling constants are eventually diluted. On the other hand, we also find that the anisotropies depend on the number of persisting vector fields. Furthermore, our claims are confirmed by numerical calculations. This work may therefore shed light on how vector fields and anisotropies evolve in an inflationary universe.

gr-qc↗

arXiv2026

Stability analysis of de Sitter solution in the Einstein-Grisaru-Zanon gravity using the dynamical system method

In this paper, we would like to investigate the stability of de Sitter solution in the Einstein-Grisaru-Zanon gravity, which is a novel fourth-order gravity model considered recently in a paper [Phys. Lett. B {\bf 855} (2024) 138811]. As a result, we are able to derive the corresponding field equations for the Einstein-Grisaru-Zanon gravity by using an effective method based on the Euler-Lagrange equations. Unfortunately, one of the obtained field equations does not coincide with that derived in the original paper of the Einstein-Grisaru-Zanon gravity due to a gap between higher-order derivative terms. However, our de Sitter solution is still identical to one solved in the original paper of the Einstein-Grisaru-Zanon gravity due to the vanishing of the gap. Furthermore, a stability analysis based on the dynamical system method is performed to indicate that the obtained de Sitter solution is always unstable, no matter it presents an inflationary phase or expanding phase of universe. This result confirms the validity of stability investigation carried out in the original paper of the Einstein-Grisaru-Zanon gravity.

hep-th↗

arXiv2026

Effect of $R^2$ on the stability of de Sitter solution of the generalized Einsteinian cubic gravity

In this paper, we would like to investigate whether a generalized Einsteinian cubic gravity, in which three possible cubic interactions ${\cal P}$, ${\cal C}$, and ${\cal C}'$ are treated on an equal footing, admits a de Sitter solution as its stable cosmological solution. As a result, we are able to confirm the existence of the corresponding de Sitter solution for this gravity by solving analytically its field equations. Remarkably, only the cubic interaction ${\cal P}$ gives rise to the existence of the de Sitter solution. Then, we convert the field equations into the corresponding dynamical system for a stability analysis purpose. A fixed point of this dynamical system is found and shown to be equivalent to the obtained de Sitter solution. However, the perturbed dynamical system turns out to be incomplete, leaving undetermined information of the stability of the fixed point (or equivalently the de Sitter solution). Fortunately, we show that this loophole can be cured once the well-known Starobinsky term $R^2$ is introduced into the action of the generalized Einsteinian cubic gravity, despite the fact that it contributes nothing to the value of the de Sitter solution.

physics.gen-ph↗

arXiv2026

Thermodynamics and phase transitions of charged-AdS black holes in dRGT massive gravity with nonlinear electrodynamics

Investigating black holes in modified theories of gravity offers fertile ground for exploring phenomena beyond the scope of general relativity. We investigate a novel class of charged anti-de Sitter (AdS) black holes within the ghost-free de Rham-Gabadadze-Tolley (dRGT) massive gravity, minimally coupled to an exponential form of nonlinear electrodynamics (NED). The NED sector is modelled by an exponential electrodynamics Lagrangian, which leads to singular black hole geometries in contrast to many regular configurations known in other NED models. In turn, we systematically investigate the thermodynamic properties and phase structure of the obtained black holes. The results show that the system has a rich thermodynamic structure. For different values of the magnetic charge $q$, the black hole can exhibit several types of phase transitions. These include van der Waals-like first-order phase transitions, second-order critical behavior, and a reentrant phase transition between small and large black holes without extending the phase space ($Λ=$constant). Our study enhances the understanding of AdS black holes in ghost-free massive gravity, providing further insights into the interplay between graviton mass and NED. The results highlight how the combined effects of graviton mass and electromagnetic nonlinearity can yield a rich and complex thermodynamic phase space, offering further insights relevant to the gauge/gravity duality and the ongoing search for observational signatures of modified gravity.

gr-qc↗

arXiv2025

On the stability of de Sitter inflationary solution in the Starobinsky-Bel-Robinson gravity

We will present the way to derive a de Sitter inflationary solution within the so-called Starobinsky-Bel-Robinson gravity. Then, we will show by using the dynamical system method whether the obtained solution is stable or not. According to the stability of the de Sitter inflationary solution, we could judge which phase of our universe, among the two early and late-time phases, is more appropriate for this solution.

gr-qc↗

arXiv2025

Anisotropic power-law inflation for the Sáez-Ballester theory non-minimally coupled to a vector field

In this paper, we would like to examine whether the Sáez-Ballester theory admits stable and attractive Bianchi type I inflationary solutions in the presence of a non-minimal coupling between scalar and vector fields such as $f^2(ϕ)F_{μν}F^{μν}$. As a result, such a solution will be shown to exist within this theory for a suitable setup of fields. Interestingly, the considered Sáez-Ballester theory can be shown to be equivalent to the standard scalar-vector theory via a suitable field redefinition. This means that the obtained solution can be reduced to that derived in an original anisotropic inflation model proposed by Kanno, Soda, and Watanabe. Consequently, the corresponding tensor-to-scalar ratio of this solution turns out to be higher than the latest observational value of the Planck satellite (Planck 2018) due to the fact that $c_s$, the corresponding speed of sound of scalar perturbations of the Sáez-Ballester theory, turns out to be one. This result indicates an important hint that the speed of sound, $c_s$, could play an important role in making the corresponding non-canonical anisotropic inflation cosmologically viable in the light of the Planck 2018 data. To be more specific, we will point out that any modifications of the Sáez-Ballester theory having $c_s \sim 0.1$ will have a great potential to be highly consistent with the Planck 2018 data. For heuristic reasons, a simple modified version of the Sáez-Ballester theory will be proposed as a specific demonstration. As a result, we will show that this modified model admits an anisotropic power-law inflationary solution as expected.

gr-qc↗

arXiv2025

A gap between two approaches of dimensional reduction for a six-dimensional Kaluza-Klein theory

Inspired by the five-dimensional Kaluza-Klein theory, we would like to study the dimensional reduction issue of six-dimensional Kaluza-Klein extension in this paper. In particular, we will examine two possible approaches of dimensional reduction from six-dimensional spacetimes to four-dimensional ones. The first one is a direct dimensional reduction, i.e., from six-dimensional spacetimes directly to four-dimensional ones, via a $T^2\equiv S^1 \times S^1$ compactification, while the second one is an indirect dimensional reduction, i.e., from six-dimensional spacetimes to five-dimensional ones then four-dimensional ones, via two separated $S^1$ compactifications. Interestingly, we show that these two approaches lead to different four-dimensional effective actions although using the same six-dimensional metric. It could therefore address an important question of which approach is more reliable than the other.

gr-qc↗

arXiv2025

A note on the area of event horizon of Kleinian black hole

We point out that the area of event horizon of Kleinian black hole is infinite due to the fact that its event horizon is not a sphere but a hyperboloid. Therefore, the usual interpretations of Schwarzschild black hole might not be applicable to the Kleinian black hole.

gr-qc↗

arXiv2024

Stability investigations of de Sitter inflationary solutions in power-law extensions of the Starobinsky model

In this paper, we would like to examine whether stable de Sitter inflationary solutions appear within power-law extensions of the Starobinsky model. In particular, we will address general constraints for the existence along with the stability of de Sitter inflationary solutions in a general case involving not only the Starobinsky $R^2$ term but also an additional power-law $R^n$ one. According to the obtained results, we will be able to identify which extension is more suitable for an early inflationary phase rather than a late-time cosmic acceleration phase. To be more specific, we will consider several values of $n$ to see whether the corresponding de Sitter inflationary solutions are stable or not.

gr-qc↗

arXiv2024

Anisotropic power-law inflation for a generalized model of two scalar and two vector fields

Cosmological implication of a generalized model of two scalar and two vector fields, in which both scalar fields are non-minimally coupled to each vector field, is studied in this paper. In particular, we will seek a set of new anisotropic power-law inflationary solutions to this model. Additionally, the stability of the obtained solutions will be examined by using the dynamical system approach. As a result, we will show that this set of solutions turns out to be stable and attractive during the inflationary phase as expected due to the existence of the unusual couplings between two scalar and two vector fields. Notably, we will point out that the existence of phantom field will lead to an instability of the corresponding anisotropic power-law inflation.

gr-qc↗

arXiv2024

Anisotropic power-law inflation for models of non-canonical scalar fields non-minimally coupled to a two-form field

In this paper, we investigate the validity of the so-called cosmic no-hair conjecture in the framework of anisotropic inflation models of non-canonical scalar fields non-minimally coupled to a two-form field. In particular, we focus on two typical {\it k}-inflation and Dirac-Born-Infeld inflation models, in which we find a set of exact anisotropic power-law inflationary solutions. Interestingly, these solutions are shown to be stable and attractive during an inflationary phase using the dynamical system analysis. The obtained results indicate that the non-minimal coupling between the scalar and two-form fields acts as a non-trivial source of generating stable spatial anisotropies during the inflationary phase and therefore violates the prediction of the cosmic no-hair conjecture, even when the scalar field is of non-canonical forms. In connection with the Planck 2018 data, tensor-to-scalar ratios of these anisotropic solutions are investigated. As a result, it appears that the tensor-to-scalar ratio of the anisotropic power-law inflationary solution of {\it k}-inflation model turns out to be more highly consistent with the Planck 2018 data than that of Dirac-Born-Infeld model.

gr-qc↗

arXiv2023

Stability investigations of isotropic and anisotropic exponential inflation in the Starobinsky-Bel-Robinson gravity

In this paper, we would like to examine whether a novel Starobinsky-Bel-Robinson gravity model admits stable exponential inflationary solutions with or without spatial anisotropies. As a result, we are able to derive an exact de Sitter inflationary to this Starobinsky-Bel-Robinson model. Furthermore, we observe that an exact Bianchi type I inflationary solution does not exist in the Starobinsky-Bel-Robinson model. However, we find that a modified Starobinsky-Bel-Robinson model, in which the sign of coefficient of $R^2$ term is flipped from positive to negative, can admit the corresponding Bianchi type I inflationary solution. Unfortunately, stability analysis using the dynamical system approach indicates that both of these inflationary solutions turn out to be unstable. Interestingly, we show that a stable de Sitter inflationary solution can be obtained in the modified Starobinsky-Bel-Robinson gravity.

gr-qc↗

arXiv2023

Magnetogenesis from Anisotropic Universe

The existence of large-scale anisotropy can not be ruled out by the cosmic microwave background (CMB) radiation. Over the years, several models have been proposed in the context of anisotropic inflation to account for CMB's cold spot and hemispheric asymmetry. However, any small-scale anisotropy, if exists during inflation, is not constrained due to its nonlinear evolution in the subsequent phase. This small-scale anisotropy during inflation can play a non-trivial role in giving rise to the cosmic magnetic field, which is the subject of our present study. Assuming a particular phenomenological form of an anisotropic inflationary universe, we have shown that it can generate a large-scale magnetic field at $1$-Mpc scale with a magnitude $\sim 4\times 10^{-20}~G$, within the observed bound. Because of the anisotropy, the conformal flatness property is lost, and the Maxwell field is generated even without explicit coupling. This immediately resolves the strong coupling problem in the standard magnetogenesis scenario. In addition, assuming very low conductivity during the reheating era, we can further observe the evolution of the electromagnetic field with the equation of state (EoS) $ω_{eff}$ and its effects on the present-day magnetic field.

astro-ph.CO↗

arXiv2022

Anisotropic constant-roll k-inflation model

In this paper, we would like to figure out whether a k-inflation model admits the Bianchi type I metric as its inflationary solution under a constant-roll condition in the presence of the supergravity motivated coupling between scalar and vector fields, $f^2(ϕ)F_{μν}F^{μν}$. As a result, some novel anisotropic inflationary solutions are shown to appear along with a power-law one in this scenario. Furthermore, these solutions are numerically confirmed to be attractive, in contrast to the prediction of the Hawking's cosmic no-hair conjecture.

gr-qc↗