从罗伯森到今天的宇宙学

爱因斯坦创立了引力的现代理论——广义相对论.这一理论将引力和宇宙学都几何化了.爱因斯坦本人曾设想过一种空间封闭的定态宇宙.弗里德曼发现(或猜想)了一种爱因斯坦场方程的非定态解.哈勃发现了遥远星系的红移,从而证实了宇宙膨胀演化的观念. 罗伯森采取了一条在逻辑上和数学上都严格的途径.在假定宇宙是严格均匀和各向同性的情况下,他找出了所有可能的“宇宙学”.他的结果和弗里德曼的猜测一致但更为可信. 罗伯森继后还探讨了这个解的所有观测性质:如天体的红移、角大小、亮度等与光从发射到接收所经历的时间的关系. 1965年发现了宇宙微…     

为什么宇宙学常数如此之小

1916年,爱因斯坦给出广义相对论场方程 其中R,g和丁分别是曲率、度规和能量-动量 张量,G是牛顿引力常数.然而,此方程不存在 静态宇宙解.在当时,宇宙的哈勃膨胀尚未被 观测到,爱因斯坦更倾向宇宙的静态模型.因 此,他在场方程左边又加上一项gμνλ,并把新引 入的未定参数L称为宇宙学常数.若λ为正,相 当于引入一等效于排斥力的项,它和引力的吸 引相抵消,使得有可能存在静态宇学解.当 星系红移测量表明宇宙并非静态之后,爱因斯 坦曾给韦尔写信说,如果字宙并非静态就去掉 宇宙学项. 可是,从现代量子场论看来,宇宙项很难去 掉.实际上,在场方程…     

哈勃参数对Robertson-McVittie时空中光线轨道的影响和雷达回波延迟修正

采用后牛顿近似计算方法讨论了哈勃参数H(t)对Robertson-McVittie时空中电磁波传播的后牛顿影响.对于光线的偏转实验,同时考虑了光源和接收点的有限距离(d1,d2)对偏转角度的影响,计算给出了哈勃参数H0对偏转角度的最大修正.对于雷达回波的延迟效应,给出了哈勃参数对时间延迟公式的最大修正.该工作利用经典引力实验考虑宇宙膨胀对电磁波传播的后牛顿影响,可为当前的高精度空间引力实验提供理论参考.     

邮票上的物理学史(68)--宇宙学

同星系天文学方面的工作相比 ,哈勃更重要的贡献是关于红移 -距离关系的哈勃定律的发现 (图1,圣文森特所属格林纳丁斯 2 0 0 0年 ,2 0世纪重大事件 ,邮票下方的英文是“192 9:哈勃和膨胀的宇宙”) .星系光谱的频移是美国天文学家斯里弗 (V .Slipher)发现的 ,他发现了绝大部分红移和个别同我们距离近的蓝移 .对光谱频移现象最现成的解释是多普勒效应 :红移表示星系离我们而去 .星系的这种退行并不是以我们为中心 ,而是整个宇宙的膨胀 ,如同一个膨胀气球的表面上的各点 ,每一点都相对于其他点退行 .个别星系的谱线蓝移表示离我们距离近的一些星团或星系的本动超过了膨胀运动 .192 9年 ,哈勃利用美国哈佛大学女天文学家勒维特 (H .S .Leavitt)发现的造父变星的周光关系确定星系的距离 ,发现了星系光谱的红移与星系离我们的距离成正比关系 .当时他掌握的资料只有 33个近距离星系的数据 ,距离测量也不准确 ,数据分布非常弥散 ,离拟合的直线很远 .但是后继研究却证明了上面的关系是正确的 .两年后 ,1931年 ,哈勃积累了更多的更远的星系的数据 ,发现这个关系仍然成立 ,而且拟合的质量好多...     

典型习题中的现代物理知识（第二讲） 黑洞,GM/c2还是2GM/c2?

 上一讲所说引力红移,即频率为v₀的光子从质量为M、半径为R的天体表面发射到无穷远,频率会变为v（v0）,引力为红移: Z=（v₀-v）/v=（1-GM/c²R）^-1-1…（1） 由此可知,一定质量的天体,其半径越小,周围的引力场越强,光的引力红移现象越显著。当R缩到R_g=GM/c²…（2）时,v将变为零（Z→∞）,这意味着光子的动能mc²=hv₀在引力场中全部耗尽（hv₀=GMm/R）;若Rg,光子的动能再也无法满足引力势能增加的需要,这时该天体的引力场就强到了连光子也不能从其表面逃逸的程度。 第五届全国中学生物理竞赛（1988年）决赛中就有一题涉及到这种天体:“有一种超高密度的天体,其巨大引力使得光子也无法逃逸出来,……,这种天体叫黑洞。     

科学家们在星系团的尺度上证实了红移效应

 检验引力现象很简单：通过二楼的窗子走出去(禁止付诸实践),看看会发生什么！但是要想检验爱因斯坦的引力理论--广义相对论,难度就要大得多。该理论的内容是：一个物体的引力会使其周围的空间和时间扭曲。尽管研究人员在太阳系的尺度上证明了广义相对论,但是在整个宇宙的尺度上验证该理论是更具挑战性的。
哥本哈根大学尼尔斯·玻尔研究所的拉德克·沃杰塔克(Radek Wojtak)带领一组研究人员着手检验广义相对论的一个经典预测：光在逃离引力场的时候会损失能量,引力场越强,光损失的能量就越多。结果,从一个星系团中心散发出来的光子应该比星系团边缘的光子损失的能量更多,因为星系团中心区的引力最强。星系团是包含了成千上万个星系的大型天体系统。因此在波长上,来自星系团中心的光比来自边缘的光更长,移向光谱的红端。这个效应被称为引力红移现象。
沃杰塔克及同事知道,测量单个星系内的引力红移会很困难,因为星系内引力红移效应非常小,而且需要将这种红移效应跟个体星系的轨道速度以及宇宙膨胀造成的红移效应分离开来。研究人员从斯隆数字巡天计划中搜集了8000 个星系团的数据,他们通过平均这些数据处理了这个问题。“这样做是希望通过研究星系团中星系之间的红移分布特点来发现引力红移效应,而不是分别查看各个星系的红移效应,”沃杰塔克解释说。
果然,研究人员发现正像广义相对论预测的那样,星系团中的光发生了红移,而且与到星系团中心的距离成比例。“我们可以测量出星系之间红移效应的微小差别,可以看得出来自星系团中心区星系的光不得不爬出那里的引力场,而来自边缘星系中的光可以较为轻松地散发出来,”沃杰塔克说。2011 年9 月28 日,这些发现发布在《自然》(Nature)杂志在线版上。
除了证实广义相对论之外,这些研究结果也有力地说明了拉姆达冷暗物质宇宙模型。这个已经流行于世的宇宙学模型表明宇宙的大部分是由不可见物质构成的,这种物质与构成恒星和行星的普通物质不发生相互作用。这项检验结果也支持暗能量的存在,暗能量是似乎正在使宇宙膨胀的一种神秘力量。     

星系哈勃红移的非多普勒效应解释

分析了多普勒效应在解释星系哈勃红移现象时,星系际光传播过程存在的能量不守恒和宇宙膨胀时空不平权两大问题;提出了＂时空物质属性＂的3个基本假设;最后阐述了星系哈勃红移的非多普勒效应解释。     

相对论性开普勒环的谱线轮廓

对于一个围绕强引力场物体(例如黑洞)作开普勒运动的环状发光物,它所发射的光线要受多普勒频移,引力红移和光线偏折等效应的作用,这种作用决定了远处观察者所看到的谱线轮廓,本文利用光子输运方程方法,求出在Schwarzschild度规中的开普勒环所发射的谱线的轮廓的精确解。 关键词：     

带有背景矢量场的标量场暗能量模型

讨论了带有背景矢量场的动力学标量场作为暗能量在闭宇宙的情形下的演化. 选取适当的标量场势函数后, 在得到的暗能量有效状态方程中, 参数w在红移z≈0.2处可以越过－1, 而且在z≈1.7处宇宙从减速膨胀的状态转变为加速膨胀状态, 这与最近的宇宙学观测相符.     

电磁场中光子-轴子的转化微分截面

运用费曼微扰方法分别计算了在磁偶极场、电偶极场和均匀静电场及静磁场中光子转化成轴子的非极化微分截面.在电偶极场中,沿光子传播方向及其反方向上的非极化微分截面为零;而在磁偶极场中,在上述方向上通常则具有非零的微分截面,但当光子传播方向平行于磁场偶极距矢量时,该微分截面为零.在均匀的静磁场和均匀静电场中,只有在光子传播方向及其反方向上具有非零的微分截面,但后者小于前者.在轴子质量趋于零的极限条件下,上述过程和光子转化为引力子的过程表现出某些非常类似的性质. 关键词： 轴子 光子 微分截面     

Bianchi Type-II Dark Energy Model in f(R,T) Gravity

The spatially homogeneous and totally anisotropic Bianchi Type-II space-time dark energy model with EoS parameter is considered in the presence of a perfect fluid source in the framework of f(R,T) gravity proposed by Harko et al. (Phys. Rev. D, 84:024020, 2011). With the help of special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B, 74:182, 1983) a dark energy cosmological model is obtained in this theory. We consider f(R,T) model and investigate the modification R+f(T) in Bianchi type-II cosmology with an appropriate choice of a function f(T)=λT. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

Kantowski-Sachs Universe Filled with Perfect Fluid in f(R,T) Theory of Gravity

The exact solutions of the field equations in respect of Kantowski-Sachs universe filled with perfect fluid in the framework of f(R,T) theory of gravity (Harko et al. in Phys. Rev. D 84:024020, 2011) is derived. A cosmological model with an appropriate choice of the function f(T) is constructed. The physical behavior of the cosmological model is studied. Some important features of astrophysical phenomena, like Hubble’s parameter H(z), luminosity distance (d _L ) and distance modulus μ(z) with red-shift are also discussed.     

Higher Dimensional Cosmological Models Filled with Perfect Fluid in f(R,T) Theory of Gravity

The new class of higher dimensional cosmological model of the early universe filled with perfect fluid source in the framework of f(R,T) theory of gravity (Harko et al. in Phys. Rev. D 84, 024020, 2011) is considered. A cosmological model with an appropriate choice of the function f(T) has been constructed. The physical behavior of the model is studied. The well known astrophysical phenomena, namely the Hubble parameter H(z), luminosity distance (d _L ) and distance modulus μ(z) with redshift are discussed.     

Five Dimensional Cosmological Models in General Relativity

A five dimensional Kaluza-Klein space-time is considered in the presence of a perfect fluid source with variable G and Λ. An expanding universe is found by using a relation between the metric potential and an equation of state. The gravitational constant is found to decrease with time as G∼t ^−(1−ω) whereas the variation for the cosmological constant follows as Λ∼t ⁻², L ~ ([(R)\dot]/R)²\Lambda \sim (\dot{R}/R)^{2} and L ~ [(R)\ddot]/R\Lambda \sim \ddot{R}/R where ω is the equation of state parameter and R is the scale factor.     

Is the Pioneer Anomaly a Counter Example to the Dark Matter Hypothesis?

The Hubble law is extended to massive particles based on the de Broglie wavelength. Due to the expansion of the universe the wavelength of an unbound particle would increase according to its cosmological redshift. Based on the navigation anomalies of the Pioneer 10 & 11 spacecraft it is postulated that an unbound massive particle has a cosmological redshift z=(c/v ₀)H ₀ t, where c is the speed of light in vacuum, v ₀ is the initial velocity of the particle, H ₀ is Hubble’s constant and t is the duration of time that the particle has been unbound. The increase in wavelength of the particle corresponds to a decrease in its speed by Δv=−cH ₀ t. Furthermore, it is hypothesized that the solar system has escaped the gravity of the Galaxy as evidenced by its orbital speed and radial distance and by the visible mass within the solar system radius. This means that spacecraft which become unbound to the solar system would also be galactically unbound and subject to the Hubble law. This hypothesis and the extended Hubble law may explain the anomalous acceleration found to be acting upon the unbound Pioneer 10 & 11 spacecraft. Thus, the Pioneer anomaly may be a counter example to the dark matter hypothesis. Because photons have a speed which make them unbound to the Galaxy, it is predicted that the navigation beam in open space would undergo a cosmological redshift in its frequency which would be detectable with modern clocks.     

Running coupling: does the coupling between dark energy and dark matter change sign during the cosmological evolution?

In this paper we put forward a running coupling scenario for describing the interaction between dark energy and dark matter. The dark sector interaction in our scenario is free of the assumption that the interaction term Q is proportional to the Hubble expansion rate and the energy densities of dark sectors. We only use a time-variable coupling b(a) (with a the scale factor of the universe) to characterize the interaction Q. We propose a parametrization form for the running coupling b(a)=b ₀ a+b _e (1−a) in which the early-time coupling is given by a constant b _e , while today the coupling is given by another constant, b ₀. For investigating the feature of the running coupling, we employ three dark energy models, namely, the cosmological constant model (w=−1), the constant w model (w=w ₀), and the time-dependent w model (w(a)=w ₀+w ₁(1−a)). We constrain the models with the current observational data, including the type Ia supernova, the baryon acoustic oscillation, the cosmic microwave background, the Hubble expansion rate, and the X-ray gas mass fraction data. The fitting results indicate that a time-varying vacuum scenario is favored, in which the coupling b(z) crosses the noninteracting line (b=0) during the cosmological evolution and the sign changes from negative to positive. The crossing of the noninteracting line happens at around z=0.2–0.3, and the crossing behavior is favored at about 1σ confidence level. Our work implies that we should pay more attention to the time-varying vacuum model and seriously consider the phenomenological construction of a sign-changeable or oscillatory interaction between dark sectors.     

Constraints on unified models for dark matter and dark energy using <Emphasis Type="Italic">H</Emphasis>(<Emphasis Type="Italic">z</Emphasis>)

The differential age data of astrophysical objects that have evolved passively during the history of the universe (e.g. red galaxies) allows us to test theoretical cosmological models through the predicted Hubble function expressed in terms of the redshift z, H(z). We use the observational data for H(z) to test unified scenarios for dark matter and dark energy. Specifically, we focus our analysis on the Generalized Chaplygin Gas (GCG) and the viscous fluid (VF) models. For the GCG model, it is shown that the unified scenario for dark energy and dark matter requires some priors. For the VF model we obtain estimations for the free parameters, which may be compared with further analysis mainly at perturbative level.     

A mixed spectral and finite difference model to study baroclinic annulus waves

A mixed spectral and finite difference model to study finite amplitude baroclinic waves in a differentially heated rotating annulus is presented. The model consists of the full Navier-Stokes equations and the heat equation. The field variables f = f(r, φ z; t) are decomposed into zonally averaged components f_o(r, z; t) and eddy components f(r, φ, z; t), the latter being periodic in f and represented in terms of Fourier series. The unknowns f_o(r, z; t) and f^{c, s}(r, z; t), which are Fourier amplitudes of f′(r, φ, z; t) are governed by two-dimensional primitive equations with the addition of source terms. These equations are solved semi-implicitly by the alternating direction implicit method on variable grids.A simplified model with two Fourier components which permits self-interaction of the chosen wave and the interaction of the wave and the mean fields had been used to repeat a computation done by G. P. Williams, who used a fully three-dimensional finite difference algorithm. We can reproduce almost all of Williams' results in 1/20 of the computing time with the present model. It only requires 1/30 the additional computer storage of Williams' finite difference model over the axisymmetric problem.The potential of the present model for investigation of multiwave interaction as well as the advantages and disadvantages of the two different approaches is discussed.     

Bianchi Type-II String Cosmological Model with Magnetic Field in f (R,T) Gravity

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of f(R,T) gravity proposed by Harko et al. (Phys Rev D 84:024020, 2011). With the help of special law of variation for Hubble^’s parameter proposed by Berman (Nuovo Cimento B 74:182, 1983) cosmological model is obtained in this theory. We consider f(R,T) model and investigate the modification R+f(T) in Bianchi type-II cosmology with an appropriate choice of a function f(T)=μ T. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

An approach to radially symmetrical solutions of the sine-Gordon equation

The solution φ(r, t) of the radially symmetric sine-Gordon equation is considered in three and two spatial dimensions for initial curves, analogous to a 2π-kink, in the expanding and in the shrinking phase, for R(t)j? R(0). It is shown that the parameterization φ(r, t) = 4 arcian exp[γ(r?R(0)] + x(r, t), where R(t) describes the exact propagation of the maximum of φ,(r, t), is suitable. Using an appoximate differential equation, recently given for the propagation of the solitary ring wave, a rough analytic approximation for the correction function x(r = R(t), t) is found and tested numerically. A relationship between the fluctuations in x(r = R(t), t) and those in $\text{R}\text{?}\text{(t), t)}\text{and}\text{R(t)}$ explains why the solitary wave is almost stable. From x(r = R(t), t) and the supposition x(1, t) ≈ x(∞, t) ≈ 0 an assymetry in φ_r(r, t) with respect to r = R(t) is predicted. It also exhibits fluctuations corresponding to those in x(r = R(t), t). The condition for validity of this approximation apparently is also a limit for the stability of the solitary ring wave.