Physics of the Dark Universe最新文献_第3页

Impact of perfect fluid dark matter on the appearance of rotating black hole 完美流体暗物质对旋转黑洞外观的影响

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2026-01-16 DOI: 10.1016/j.dark.2026.102225

Yu-Xiang Huang , Sen Guo , En-Wei Liang , Kai Lin

Understanding how dark matter affects the immediate environment of black holes (BHs) is crucial for interpreting horizon-scale observations. We study rotating BHs surrounded by perfect fluid dark matter (PFDM), exploring their observable features through both analytical and numerical approaches. Using the existence criterion of the innermost stable circular orbit (ISCO), we first derive joint constraints on the PFDM intensity parameter k and the spin parameter a. Within the resulting physically allowed parameter regime, we perform high-resolution, general-relativistic ray-tracing simulations of thin accretion disks at 87 GHz and 230 GHz, capturing the detailed brightness morphology and photon ring structure shaped by PFDM. By incorporating angular diameter measurements of M87* and Sgr A* from the Event Horizon Telescope (EHT), we further narrow down the viable parameter space and directly compare synthetic images with EHT observations of M87*. We find that the inclusion of PFDM improves the agreement with the observed compact shadow and asymmetric brightness distribution, suggesting that dark matter may leave observable imprints on horizon-scale images. Our results position PFDM as a physically motivated extension to the Kerr geometry and highlight a promising astrophysical pathway for probing dark matter near BHs with current and future VLBI campaigns.

了解暗物质如何影响黑洞（BHs）的直接环境对于解释视界尺度观测至关重要。我们研究了被完美流体暗物质（PFDM）包围的旋转黑洞，通过解析和数值方法探索它们的可观测特征。利用最内层稳定圆轨道（ISCO）的存在准则，我们首先推导了PFDM强度参数k和自旋参数a的联合约束。在由此得到的物理允许的参数范围内，我们对薄吸积盘在87 GHz和230 GHz下进行了高分辨率、广义相对论的射线追踪模拟，捕获了PFDM形成的详细亮度形态和光子环结构。通过结合事件视界望远镜（EHT）对M87*和Sgr A*的角直径测量，我们进一步缩小了可行的参数空间，并直接将合成图像与M87*的EHT观测结果进行了比较。我们发现PFDM的加入提高了与观测到的致密阴影和不对称亮度分布的一致性，这表明暗物质可能在水平尺度图像上留下可观测的印记。我们的研究结果将PFDM定位为Kerr几何的物理扩展，并强调了在当前和未来的VLBI运动中探测BHs附近暗物质的有前途的天体物理途径。

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引用次数: 0

Different effects of the Lorentz and Gaussian bump functions on the formation of primordial black holes and secondary gravitational waves 洛伦兹和高斯碰撞函数对原始黑洞和二次引力波形成的不同影响

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2026-01-16 DOI: 10.1016/j.dark.2026.102224

Wei Yang , Yu-Xuan Kang , Arshad Ali , Tao-Tao Sui , Chen-Hao Wu , Ya-Peng Hu

Scalar perturbations in the inflation can be amplified when the base inflation potential V_b(ϕ) incorporates a local bump f(ϕ) such as

V (ϕ) = V_{b} (ϕ) (1 + f (ϕ))

. This modification will lead to a peak in the curvature power spectrum, increasing a significant abundance of primordial black holes (PBHs). However, since there is no underlying physical reason for the choice of f(ϕ), it is essential to investigate the effects of various bump functions on PBH generation. In this paper, we choose the well-known Starobinsky potential as the base inflation potential to compare the effects produced by different bumps, specifically focusing on the Lorentz and Gaussian bumps which are widely used. To clearly illustrate the differences between these two bumps, we keep parameters in bump functions the same. We find an interesting and novel result that the Lorentz cases manifest a stronger ability to enhance the power spectrum and produce more abundance of PBHs than Gaussian cases. Moreover, we also investigate the different effects of bump functions on the scalar-induced gravitational waves (SIGWs). The results indicate that the Lorentz bump generates SIGWs with a higher energy density, which can be potentially detected in the future. Our study gives valuable insights into the choice and constraints on the bump functions, and the different effects may distinguish the two bump cases for practical purposes in future experiments.

当基本膨胀势Vb（φ）包含局部凸起f（φ）时，膨胀中的标量扰动可以被放大，例如V(φ)=Vb(φ)（1+f(φ)）。这种修正将导致曲率功率谱出现一个峰值，从而显著增加原始黑洞（pbh）的丰度。然而，由于f（φ）的选择没有潜在的物理原因，因此有必要研究各种凹凸函数对PBH生成的影响。在本文中，我们选择著名的Starobinsky势作为基本膨胀势来比较不同颠簸所产生的影响，特别关注广泛使用的洛伦兹和高斯颠簸。为了清楚地说明这两种凹凸之间的区别，我们保持凹凸函数中的参数相同。我们发现了一个有趣而新颖的结果，即洛伦兹情况比高斯情况表现出更强的功率谱增强能力和产生更多的pbh丰度。此外，我们还研究了碰撞函数对标量引力波（SIGWs）的不同影响。结果表明，洛伦兹碰撞产生的sigw具有更高的能量密度，未来可能会被探测到。我们的研究为碰撞函数的选择和约束提供了有价值的见解，并且不同的效果可以在未来的实验中区分两种碰撞情况。

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引用次数: 0

Evolution of fluctuations in horizon energy and its dependence on the degrees of freedom 视界能量波动的演化及其对自由度的依赖

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2026-01-16 DOI: 10.1016/j.dark.2026.102223

Vishnu S Namboothiri , Krishna P․B․ , Adithya P․S․ , Titus K Mathew

Taking account of the thermal nature of the Hubble horizon of the expanding universe, we analysed the evolution of relative fluctuations of horizon energy. For this analysis, we used two approaches: (i) by treating the Hubble horizon as a system in canonical ensemble, and (ii) by considering the microscopic degrees of freedom on the horizon. In both approaches, we obtained the relative fluctuations by using two different definitions of the horizon temperature; first, the Gibbons-Hawking temperature, and second, the Kodama-Hayward temperature. For a given temperature, both approaches yield the same general evolution for the fluctuations. In the asymptotic limit, the relative energy fluctuations corresponding to the Gibbons-Hawking temperature, is [ℏG/2π]H², and 2/N_sur for the first and second approaches respectively. Similarly, using the Kodama-Hayward temperature, the asymptotic fluctuations are [5ℏG/2π]H², and 10/N_sur. This implies that, the magnitude of the relative fluctuations of the horizon energy is higher in the case of Kodama-Hayward temperature. The inverse dependence of the fluctuation on N_sur, the number of degrees of freedom on the horizon, reflects a familiar behaviour in ordinary thermal systems: fluctuations decrease as the number of degrees of freedom increases. Notably, we also found that the relative energy fluctuations establish a connection between the Planck length scale L_p, characteristic length scale of the very early epoch of the universe, and

\sqrt{3 / Λ},

the length scale associated with the late-time accelerated phase. This relationship can offer valuable insights that could help in addressing the cosmological constant problem.

考虑到膨胀宇宙的哈勃视界的热性质，我们分析了视界能量相对涨落的演化。对于这一分析，我们使用了两种方法：(i)将哈勃视界视为正则系综中的系统，以及（ii）考虑视界上的微观自由度。在这两种方法中，我们使用两种不同的视界温度定义获得了相对涨落；第一个是吉本斯-霍金温度，第二个是科达马-海沃德温度。对于给定的温度，两种方法对波动产生相同的一般演化。在渐近极限下，第一种和第二种方法对应的相对能量涨落分别为[h G/2π]H2和2/Nsur。同样，使用koda - hayward温度，渐近波动为[5 G/2π]H2和10/Nsur。这意味着，在koda - hayward温度情况下，视界能量的相对波动幅度更大。波动与Nsur（视界上的自由度数）的反比关系反映了普通热系统中常见的行为：波动随着自由度数的增加而减少。值得注意的是，我们还发现相对能量波动在普朗克长度尺度Lp（宇宙早期的特征长度尺度）和3/Λ（与后期加速相相关的长度尺度）之间建立了联系。这种关系可以提供有价值的见解，有助于解决宇宙常数问题。

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引用次数: 0

Exploring cosmological constraints on galaxy formation time 探索星系形成时间的宇宙学限制

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2026-01-16 DOI: 10.1016/j.dark.2026.102226

Agripino Sousa-Neto , Maria Aldinêz Dantas , Javier E. González , Joel C. Carvalho , Jailson Alcaniz

The Universe consists of a variety of objects that formed at different epochs, leading to variations in the formation time which represents the time elapsed from the onset of structure formation until the formation of a particular object. In this work, we present two approaches to reconstruct and constrain the galaxy formation time t_f(z) using non-parametric reconstruction methods, such as Gaussian Processes (GP) and High-performance Symbolic Regression (SR). Our analysis uses age estimates of 32 old passive galaxies and the Pantheon+ type Ia supernova sample, and considers two different values of the Hubble constant H₀ from the SH0ES and Planck Collaborations. When adopting the ΛCDM model and the GP reconstructions, A direct comparison of the reconstructions shows that the GP-based implementations are mutually consistent across the redshift range considered. The SR reconstructions also show good agreement with the GP results and exhibit a compatible redshift evolution of t_f(z), with full agreement at intermediate and high redshifts and only a mild deviation at very low redshifts. The results also show significant differences in the formation time from SH0ES and Planck values, highlighting the impact of the H₀ tension on the cosmological estimates of t_f(z). Overall, this study suggests that galaxies have different evolutionary timescales and that t_f is not constant, with noticeable variations at lower redshifts (z ≲ 0.5).

宇宙由不同时期形成的各种物体组成，导致形成时间的变化，这代表了从结构形成开始到特定物体形成所经过的时间。在这项工作中，我们提出了两种方法来重建和约束星系形成时间tf(z)使用非参数重建方法，如高斯过程（GP）和高性能符号回归（SR）。我们的分析使用了32个古老被动星系和万神殿+ Ia型超新星样本的年龄估计，并考虑了来自SH0ES和普朗克合作组织的哈勃常数H0的两个不同值。当采用ΛCDM模型和GP重建时，直接比较重建结果表明，基于GP的实现在考虑的红移范围内是相互一致的。SR重建也显示出与GP结果的良好一致性，并显示出tf(z)的相容红移演化，在中高红移处完全一致，在非常低的红移处只有轻微的偏差。结果还显示了SH0ES和普朗克值在形成时间上的显著差异，突出了H0张力对tf(z)的宇宙学估计的影响。总的来说，这项研究表明，星系具有不同的演化时间尺度，并且tf不是恒定的，在较低的红移（z > 0.5）处有明显的变化。

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引用次数: 0

Parameter extraction of the stochastic gravitational wave background with peak-like templates in millihertz 以毫赫为单位的类峰模板随机引力波背景参数提取

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2026-01-14 DOI: 10.1016/j.dark.2026.102217

Heng-Sen Jiao , Hong-Bo Jin , Yun-Long Zhang

We investigate a framework for extracting parameters of stochastic gravitational wave background (SGWB) with peak-like templates in the millihertz frequency band, and we analyze transient contamination effects on parameter reconstruction. We present the spectrum and spectrogram under different conditions and provide the results of parameter reconstruction. Using templates from the early universe, we demonstrate that the peak-like templates outperform the broken power law (BPL) templates in power-law exponents recovery and peak frequency localization. The reconstruction results obtained using data from Fast Fourier Transform (FFT) are better than those obtained using data from Short-Time Fourier Transform (STFT) which is based on the spectrogram. For the single-peak(SP) template, the estimation accuracy of the exponent and peak frequency surpasses that of the BPL template by an order of magnitude, but it demonstrates less precision in amplitude estimation compared to the BPL template. Regarding the double-peak template, parameter estimation results derived from the FFT methodology consistently outperform those obtained using STFT. Nevertheless, transient signals exhibit a detrimental impact on parameter estimation precision, causing errors to increase by an order of magnitude, particularly in multi-peak scenarios. This framework provides an example of using templates to analyze data from space-based gravitational wave detectors.

研究了一种基于毫赫频带类峰模板的随机引力波背景参数提取框架，并分析了瞬态污染对参数重建的影响。给出了不同条件下的光谱和谱图，并给出了参数重建的结果。使用来自早期宇宙的模板，我们证明了类峰模板在幂律指数恢复和峰值频率定位方面优于破幂律模板。利用快速傅里叶变换（FFT）得到的重建结果优于基于谱图的短时傅里叶变换（STFT）得到的重建结果。对于单峰（SP）模板，指数和峰值频率的估计精度比BPL模板高出一个数量级，但其幅度估计精度低于BPL模板。对于双峰模板，FFT方法得到的参数估计结果始终优于STFT方法得到的结果。然而，瞬态信号对参数估计精度有不利影响，导致误差增加一个数量级，特别是在多峰情况下。该框架提供了一个使用模板分析天基引力波探测器数据的示例。

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引用次数: 0

Tracing inflationary imprints through the dark ages: Implications for early stars and galaxies formation 在黑暗时代追踪暴胀印记：对早期恒星和星系形成的启示

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2026-01-14 DOI: 10.1016/j.dark.2026.102214

K. El Bourakadi , M. Yu Khlopov , M. Krasnov , H. Chakir , M. Bennai

We explore how inflationary features shape the early stages of cosmic structure formation. Using the transfer function formalism, we trace the evolution of primordial perturbations, showing how causal physics and oscillatory signatures from inflation influence the matter power spectrum. The variance of smoothed density fields is then applied to model the collapse of overdense regions and predict dark matter halo abundances through the Press–Schechter framework. Extending to the baryonic sector, we analyze primordial gas collapse in minihalos, emphasizing molecular hydrogen cooling and the thermochemical pathways leading to Population III star formation. Finally, we examine primordial black holes as potential seeds for early galaxies, connecting their accretion-driven growth to the stellar masses and disk properties of high-redshift systems. Our results indicate that oscillatory features from inflation can leave measurable imprints on halo abundances and early galaxy properties, providing a testable link between high-energy physics and astrophysical observations with JWST.

我们探索暴胀特征如何塑造宇宙结构形成的早期阶段。使用传递函数形式，我们追踪原始扰动的演变，显示了暴胀的因果物理和振荡特征如何影响物质功率谱。然后将平滑密度场的方差应用于模拟过密区域的坍缩，并通过Press-Schechter框架预测暗物质晕丰度。扩展到重子区，我们分析了微晕中的原始气体坍缩，强调了分子氢冷却和导致III星族形成的热化学途径。最后，我们研究了原始黑洞作为早期星系的潜在种子，将它们的吸积驱动的增长与高红移系统的恒星质量和磁盘特性联系起来。我们的研究结果表明，暴胀的振荡特征可以在光晕丰度和早期星系特性上留下可测量的印记，为JWST的高能物理和天体物理观测提供了可测试的联系。

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引用次数: 0

Imprints of holographic dark energy and minimally deformed wormholes in general relativity 广义相对论中全息暗能量和最小变形虫洞的印记

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2026-01-12 DOI: 10.1016/j.dark.2026.102219

Mohammad Alshammari , M. Rizwan , Othman Abdullah Almatroud , M.Z. Bhatti , Saleh Alshammari , Z. Yousaf

In this paper, we construct and examine a new type of static, spherically symmetric wormhole geometries within the context of the minimal geometric deformation (MGD) formalism of gravitational decoupling. The seed solution is warped through an auxiliary source,

{\overset{θ}{T}}_{κ μ}

with its temporal component described by holographic dark energy, thus including a phenomenologically driven dark sector. We study the resulting spacetime using several diagnostic tools: the embedding diagram is used to plot the wormhole throat and flare–out structure; the mass function is calculated to examine gravitational energy distribution; the volume integral quantifier is evaluated to determine the total amount of exotic matter needed; and the exoticity parameter is examined to describe the violation of energy conditions. Additionally, the singularity structure is analyzed to validate the regularity of spacetime, while the anisotropy factor is investigated to analyze pressure distributions between tangential and radial directions. Total effective energy–momentum tensor conservation equation is considered with emphasis on the interaction between the seed geometry and the θ-sector. Last, we analyze complexity factors to determine matter–energy content structural organization. We find that the addition of holographic dark energy in the time component of the θ-sector permits traversable, asymptotically flat wormhole solutions with regulated exotic matter and smooth geometric structures.

在本文中，我们在引力解耦的最小几何变形（MGD）形式下构造并检验了一种新的静态球对称虫洞几何形状。种子溶液通过辅助源Tθκμ扭曲，其时间分量由全息暗能量描述，因此包括一个现象学驱动的暗扇区。我们使用了几种诊断工具来研究由此产生的时空：嵌入图用于绘制虫洞的喉部和耀斑结构；计算质量函数来检验引力能的分布；计算体积积分量词以确定所需外来物质的总量；并检验了奇异性参数来描述能量条件的违背。此外，还分析了奇异结构以验证时空的规律性，并研究了各向异性因子以分析切向和径向之间的压力分布。考虑了总有效能量-动量张量守恒方程，重点讨论了种子几何与θ扇形的相互作用。最后，分析复杂性因素，确定物能含量结构组织。我们发现，在θ-扇形的时间分量中添加全息暗能量允许具有调节的奇异物质和光滑几何结构的可穿越的渐近平坦虫洞解。

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引用次数: 0

Particle motion and epicyclic frequencies in the einstein special unitary matrices sigma model of black holes 黑洞的爱因斯坦特殊酉矩阵模型中的粒子运动和周转频率

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2026-01-09 DOI: 10.1016/j.dark.2026.102216

Abdelmalek Bouzenada , Imtiaz Khan , Asifa Ashraf , Emre Demir , Ertan Gudekli , Ikhtiyor Saidov , Farruh Atamurotov

In this study, we test the dynamics of test particles around static and spherically symmetric BHs arising in the Einstein SU(N) non-linear sigma model. By showing the influence of general relativity and the metric function topologically in the SU(N) group, the spacetime is illustrated as dependent on the internal symmetry parameter α, significantly modifying the BH geometry. In addition, we derive analytical expressions for the energy and angular momentum of circular equatorial orbits and investigate the behavior of the effective potential to determine the orbital stability. The innermost stable circular orbits (ISCOs) are computed and their sensitivity to variations in α and the cosmological constant Λ is analyzed. In addition, we calculate the effective radial force acting on the particles and show how the parameters SU(N) influence its attractive or repulsive nature. By perturbing the stable circular orbits, we derive the radial, vertical, and orbital epicyclic frequencies for both local and distant observers. In this case, our results show that the internal gauge structure inherent in the SU(N) model has a pronounced effect on the orbital dynamics and oscillatory behavior of test particles, offering potential observational signatures in strong-field astrophysics.

在本研究中，我们测试了在爱因斯坦SU(N)非线性sigma模型中产生的静态和球对称黑洞周围测试粒子的动力学。通过展示广义相对论和度量函数在SU(N)群中的拓扑影响，说明时空依赖于内部对称参数α，显著地改变了黑洞的几何形状。此外，我们推导了赤道圆形轨道的能量和角动量的解析表达式，并研究了有效势的行为，以确定轨道的稳定性。计算了最内层稳定圆轨道（ISCOs），并分析了它们对α和宇宙常数Λ变化的敏感性。此外，我们计算了作用在粒子上的有效径向力，并展示了参数SU(N)如何影响其吸引或排斥性质。通过扰动稳定的圆形轨道，我们得到了本地和远程观测者的径向、垂直和轨道周转频率。在这种情况下，我们的研究结果表明，SU(N)模型固有的内部规范结构对测试粒子的轨道动力学和振荡行为有显著影响，为强场天体物理学提供了潜在的观测特征。

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引用次数: 0

Feasible regions of GB phenomenon in extended Proca-Nuevo gravity 扩展原新重力中GB现象的可行区域

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2026-01-09 DOI: 10.1016/j.dark.2026.102211

Abdul Malik Sultan , Abdul Jawad , Hamood Ur Rehman , N. Myrzakulov , Sanjar Shaymatov

In this article, we investigate the gravitational baryogenesis mechanism in the framework of Extended Proca-Nuevo gravity, a theory where a massive vector field is non-minimally coupled to the curvature. This analysis is carried out for an early universe, encompassing three separate cosmological scenarios defined by power-law, exponential, and modified exponential scale factors. By deriving the modified field equations from the EPN action, we obtain precise solutions for each scale factor, including the influence of the vector field. We compute the baryon-to-entropy ratio using the gravitational baryogenesis formalism, where the baryon asymmetry arises from a dynamical coupling of the baryon current with the derivative of the Ricci scalar. Moreover, we discuss the stability of the assumed cosmological model in two different ways, the dynamical system analysis and squared speed of sound parameter. Our findings demonstrate that the baryon-to-entropy ratio is consistent with observational constraints in all scenarios, highlighting the potential of EPN gravity as a viable theory to explain the matter-antimatter asymmetry in the early universe. Moreover, stability analysis through dynamical system leads to a deSitter stability which is a trivial case while squared speed of sound gives that system is stable for all three scale factor models. The study further stresses the contribution of anisotropy and vector field dynamics to the cosmological evolution within modified gravity models.

在本文中，我们研究了扩展Proca-Nuevo引力理论框架下的引力重子发生机制，该理论认为质量矢量场与曲率非最小耦合。该分析是针对早期宇宙进行的，包括由幂律、指数和修正指数尺度因子定义的三种不同的宇宙情景。通过推导修正后的EPN作用场方程，得到了包括矢量场影响在内的各尺度因子的精确解。我们使用引力重子生成的形式来计算重子与熵的比值，其中重子不对称是由重子电流与里奇标量导数的动态耦合引起的。此外，我们还从动力系统分析和声速参数平方两种不同的角度讨论了假设宇宙模型的稳定性。我们的研究结果表明，重子与熵比在所有情况下都符合观测约束，突出了EPN引力作为解释早期宇宙中物质-反物质不对称的可行理论的潜力。此外，通过动力系统的稳定性分析得出deSitter稳定性，这是一个微不足道的情况，而声速的平方给出了系统对所有三种比例因子模型都是稳定的。研究进一步强调了各向异性和矢量场动力学对修正重力模型中宇宙演化的贡献。

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引用次数: 0

Wormhole spacetimes in an expanding universe: Energy conditions and future singularities 膨胀宇宙中的虫洞时空：能量条件和未来奇点

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2026-01-08 DOI: 10.1016/j.dark.2026.102213

Taishi Katsuragawa , Shin’ichi Nojiri , Sergei D. Odintsov

We study wormhole geometries embedded in an expanding universe within a four-scalar non-linear σ model, where the target-space metric is identified with the spacetime Ricci tensor. In this framework, wormholes can remain stable even when conventional energy conditions are violated. However, once cosmological expansion is included, the effective energy density and pressure are modified by the cosmological fluid, enabling the energy conditions to be satisfied. We further present intriguing geometries in which a finite future singularity appears in our universe but not in another universe connected by the wormhole. Near the throat, the hypersurface becomes timelike, allowing trajectories to traverse to the other universe before the singularity and return afterwards. We also construct wormhole solutions motivated by galactic dark-matter halo profiles, where the required non-vanishing pressure arises naturally from the four-scalar non-linear σ model.

我们在一个四标量非线性σ模型中研究了嵌入在膨胀宇宙中的虫洞几何形状，其中目标空间度量由时空里奇张量标识。在这个框架中，即使在常规能量条件被破坏的情况下，虫洞也能保持稳定。然而，一旦考虑到宇宙膨胀，有效能量密度和压力就会被宇宙流体修正，从而使能量条件得到满足。我们进一步提出了有趣的几何图形，其中一个有限的未来奇点出现在我们的宇宙中，而不是在由虫洞连接的另一个宇宙中。在喉部附近，超表面变得像时间，允许轨迹在奇点之前穿越到另一个宇宙，并在奇点之后返回。我们还构建了由星系暗物质晕轮廓驱动的虫洞解，其中所需的不消失压力自然来自四标量非线性σ模型。

引用次数: 0