Testing the variation of the fine structure constant with strongly lensed gravitational waves

The possible variation of the electromagnetic fine structure constant, αe, at cosmological scales has aroused great interest in recent years. Strongly lensed gravitational waves(GWs) and their electromagnetic counterparts could be used to test this variation. Under the assumption that the speed of a photon can be modified,whereas the speed of a GW is the same as predicted by general relativity, and they both propagate in a flat FriedmanRobertson-Walker universe, we investigated the difference in time delays of the images and derived the upper bound of the variation of αe. For a typical lensing system in the standard cosmological models, we obtained B cosθ 1.85×10~(-5),where B is the dipolar amplitude and θ is the angle between observation and the preferred direction. Our result is consistent with the most up-to-date observations on αe. In addition, the observations of strongly lensed GWs and their electromagnetic counterparts could be used to test which types of alternative theories of gravity can account for the variation of α_e.     

高频引力波与现代宇宙学

文章简要综述了由典型现代宇宙学模型和膜振荡模型预期的微波频带的高频引力波的特性和可能的观测方案,以及研究这一课题的重要科学意义和所面临的挑战和机遇.     

A new method to test the cosmic distance duality relation using the strongly lensed gravitational waves

We propose a new method to test the cosmic distance duality relation using the strongly lensed gravitational waves. The simultaneous observation of the image positions, relative time delay between different images, redshift measurements of the lens and the source, together with the mass modelling of the lens galaxy, provide the angular diameter distance to the gravitational wave source. On the other hand, the luminosity distance to the source can be obtained from the observation of the gravitational wave signals. To our knowledge this is the first time a method is proposed to simultaneously measure the angular diameter distance and the luminosity distance from the same source. Hence, the strongly lensed gravitational waves provide a unique method to test the cosmic distance duality relation. With the construction of the third generation gravitational detectors such as the Einstein Telescope, it will be possible to test the cosmic distance duality relation with an accuracy of a few percent.     

引力、引力波和引力波的探测

简要地回顾了引力和引力波概念的由来,以及人们为探测引力波所作的各种努力．     

Improved calculation of relic gravitational waves

In this paper, we have improved the calculation of the relic gravitational waves (RGW) in two aspects. First, we investigate the transfer function by taking into consideration the redshift-suppression effect, the accelerating expansion effect, the damping effect of free-streaming relativistic particles, and the damping effect of cosmic phase transition, and give a simple approximate analytic expression, which clearly illustrates the dependence on the cosmological parameters. Second, we develop a numerical method to calculate the primordial power spectrum of RGW in a very wide frequency range, where the observed constraints on $n_{\rm s}$ (the scalar spectral index) and $P_{\rm S}(k_0)$ (the amplitude of primordial scalar spectrum) and the Hamilton--Jacobi equation are used. This method is applied to two kinds of inflationary models, which satisfy the current constraints on $n_{\rm s}$, $\alpha$ (the running of $n_{\rm s}$) and $r$ (the tensor--scalar ratio). We plot them in the $r-{\it\Omega}_{\rm g}$ diagram, where ${\it\Omega}_{\rm g}$ is the strength of RGW, and study their measurements from the cosmic microwave background (CMB) experiments and laser interferometers.     

On constraining the speed of gravitational waves following GW150914

We point out that the observed time delay between the detection of the signal at the Hanford and Livingston LIGO sites from the gravitational wave event GW150914 places an upper bound on the speed of propagation of gravitational waves, c_gw ? 1.7 in the units of speed of light. Combined with the lower bound from the absence of gravitational Cherenkov losses by cosmic rays that rules out most of subluminal velocities, this gives a model-independent double-sided constraint 1 ? c_gw ? 1.7. We compare this result to model-specific constraints from pulsar timing and cosmology.     

含物质纯重力场部分贡献的静态和稳态重力场研究

给出了包含重力场贡献在内具有宇宙因子项最普遍形式的重力场方程为Rμν-gμνR/2+λgμν=8πG(T(Ⅰ)μν+T(Ⅱ)μν)/c4，这里λ为Einstein宇宙常数，Ｔ（Ⅰ）μν，Ｔ（Ⅱ）μν分别代表物质纯物质部分和纯重力场部分的能量-动量张量.物质纯重力场部分的能量-动量张量表述为T(Ⅱ)μν=(DμρＤρν-gμνＤαβＤαβ/4)/4πG，式中Dμν的定义为Ｄμν＝ωμ／xν-ων／xμ，ωμ≡-c2gμ0/g00.并用重力场贡献在内最普遍形式的重力场方程分别研究了几个大家所熟悉的静态和稳态重力场，像带有Einstein宇宙因子λ项球对称纯物质球外部静态度规、静态荷电球外部度规、匀速转动星体外部度规及理想纯物质星体内部静态平衡等,并进行了讨论. 关键词： 能量动量张量 重力场方程 静态重力场 稳态重力场     

Detection of gravitational waves using a network of detectors

We formulate the data analysis problem for the detection of the Newtonian coalescing-binary signal by a network of laser interferometric gravitational wave detectors that have arbitrary orientations, but are located at the same site. We use the maximum likelihood method for optimizing the detection problem. We show that for networks comprising of up to three detectors, the optimal statistic is just the matched network-filter. Alternatively, it is simply a linear combination of the signal-to-noise ratios of the individual detectors. This statistic, therefore, can be interpreted as the signal-to-noise ratio of the network. The overall sensitivity of the network is shown to increase roughly as the square-root of the number of detectors in the network. We further show that these results continue to hold even for the restricted post-Newtonian filters. Finally, our formalism is general enough to be extended, in a straightforward way, to address the problem of detection of such waves from other sources by some other types of detectors, eg., bars or spheres, or even by networks of spatially well-separated detectors.     

Astrophysics from data analysis of spherical gravitational wave detectors

The direct detection of gravitational waves will provide valuable astrophysical information about many celestial objects. Also, it will be an important test to general relativity and other theories of gravitation. The gravitational wave detector SCHENBERG has recently undergone its first test run. It is expected to have its first scientific run soon. In this work the data analysis system of this spherical, resonant mass detector is tested through the simulation of the detection of gravitational waves generated during the inspiralling phase of a binary system. It is shown from the simulated data that it is not necessary to have all six transducers operational in order to determine the source’s direction and the wave’s amplitudes.     

宇宙起源与阿里原初引力波探测

20世纪建立起的宇宙大爆炸模型取得了巨大的成功,但仍期待着新的革命性的突破。探知宇宙起源及其演化是新世纪对全世界科学家的新挑战,其重要性在近期公布的中国“十三五”规划纲要中得到了高度的肯定。现代宇宙学理论,暴胀以及非奇异宇宙模型如反弹等,预言了原初引力波的存在,但至今还没有被实验证实。不同于近期LIGO合作组探测到的黑洞引力波,原初引力波是宇宙诞生时期产生的,携带着丰富的宇宙学信息,是引力波探测的全新波段,是引力波探测的下一个突破方向。文章简述了中国的阿里原初引力波实验计划及相关的科学问题。     

Wide-band measurement of gravitational waves: the VIRGO project

Summary To detect gravitational waves (GW) in a frequency range between 10 Hz and few kHz a ground-based antenna was designed by the French-Italian collaboration VIRGO. The antenna is a 3 km long interferometer with special suspensions for the optical components, planned to reduce the seismic noise in order to reach the low-frequency region. Results on the seismic isolation devices are given together with some preliminary results on the use of permanent magnets on the VIRGO suspensions. Paper presented at the V Cosmic Physics National Conference, S. Miniato, November 27–30, 1990.     

The Virgo interferometric gravitational antenna

The interferometric gravitational wave detectors represent the ultimate evolution of the classical Michelson interferometer. In order to measure the signal produced by the passage of a gravitational wave, they aim to reach unprecedent sensitivities in measuring the relative displacements of the mirrors. One of them, the 3-km-long Virgo gravitational wave antenna, which will be particularly sensitive in the low-frequency range (10–100 Hz), is presently in its commissioning phase. In this paper the various techniques developed in order to reach its target extreme performance are outlined.     

旋转致密双星的引力波特征

研究了轨道和旋转效果到2.5阶后牛顿旋转致密双星拉格朗日动力学与引力波的关系, 分析了有序和混沌轨道的引力波特征.发现当加速度不考虑辐射项时, 有序双星系统辐射的引力波具有周期或拟周期的特征, 而混沌双星系统辐射的引力波却具有明显的混沌特征.当加速度含有辐射项贡献时, 双星必会出现并合现象.此时, 原保守有序双星系统需较长时间才能完成并合过程, 引力波形在双星并合前仍保留拟周期的基本特点;然而, 原保守混沌双星系统仅在较短时间内就会并合, 但因并合时间太短, 无法获取足够的动力学信息导致引力波形的特征不易分辨.     

Physics of interferometric gravitational wave detectors

The Caltech-MIT joint LIGO project is operating three long-baseline interferometers (one of 2 km and two of 4 km) in order to unambiguously measure the infinitesimal displacements of isolated test masses which convey the signature of gravitational waves from astrophysical sources. An interferometric gravitational wave detector like LIGO is a complex, non-linear, coupled, dynamic system. This article summarizes various interesting design characteristics of these detectors and techniques that were implemented in order to reach and maintain its operating condition. Specifically, the following topics are discussed: (i) length sensing and control, (ii) alignment sensing and control and (iii) thermal lensing which changes the performance and operating point of the interferometer as the input power to LIGO is increased.     

Orbit optimization for ASTROD-GW and its time delay interferometry with two arms using CGC ephemeris

Astrodynamical space test of relativity using optical devices optimized for gravitation wave detection (ASTROD- GW) is an optimization of ASTROD to focus on the goal of detection of gravitation waves. The detection sensitivity is shifted 52 times toward larger wavelength compared with that of laser interferometer space antenna (LISA). The mission orbits of the three spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4, and L5. The three spacecrafts range interferometrically with one another with an arm length of about 260 million kilometers. In order to attain the required sensitivity for ASTROD-GW, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise, etc. For suppressing laser frequency noise, we need to use time delay interferometry (TDI) to match the two different optical paths (times of travel). Since planets and other solar-system bodies perturb the orbits of ASTROD-GW spacecraft and affect the TDI, we simulate the time delay numerically using CGC 2.7 (here, CGC stands for center for gravitation and cosmology) ephemeris framework. To conform to the ASTROD-GW planning, we work out a set of 20-year optimized mission orbits of ASTROD-GW spacecraft starting at June 21, 2028, and calculate the differences in optical path in the first and second generation TDIs separately for one-detector case. In our optimized mission orbits of 20 years, changes of arm lengths are less than 0.0003 AU; the relative Doppler velocities are all less than 3m/s. All the second generation TDI for one-detector case satisfies the ASTROD-GW requirement.     

The gravitational wave symphony of the Universe

The new millennium will see the upcoming of several ground-based interferometric gravitational wave antennas. Within the next decade a space-based antenna may also begin to observe the distant Universe. These gravitational wave detectors will together operate as a network taking data continuously for several years, watching the transient and continuous phenomena occurring in the deep cores of astronomical objects and dense environs of the early Universe where gravity was extremely strong and highly nonlinear. The network will listen to the waves from rapidly spinning non-axisymmetric neutron stars, normal modes of black holes, binary black hole inspiral and merger, phase transitions in the early Universe, quantum fluctuations resulting in a characteristic background in the early Universe. The gravitational wave antennas will open a new window to observe the dark Universe unreachable via other channels of astronomical observations.     

Formation of black hole and emission of gravitational waves

Numerical simulations were performed for the formation process of rotating black holes. It is suggested that Kerr black holes are formed for wide ranges of initial parameters. The nature of gravitational waves from a test particle falling into a Kerr black hole as well as the development of 3D numerical relativity for the coalescing binary neutron stars are discussed.     

空间引力波探测计划-LISA系统设计要点

为了验证广义相对论,世界各国竞相开展了空间引力波探测方面的研究。本文以欧洲空间引力波探测LISA(Laser Interferometer Space Antenna)计划为例,根据基线设计,对LISA系统有效载荷及主要组件的设计进行了分析和阐述。LISA主要探测和研究低频引力波辐射,其工作频段为10^-3~1 Hz,工作距离为5×10⁶ km,预计能探测到双致密星系统以及星系合并引起的超大质量并合等波源,测距精度达到pm量级。以上研究希望能对我国未来的空间引力波探测计划有一定启示。     

Gravitational waves from the axial perturbations of hyperon stars

The eigen-frequencies of the axial w-mode oscillations of hyperon stars are examined.It is shown that as the appearance of hyperons softens the equation of state of the super-density matter,the frequency of gravitational waves from the axial w-mode of hyperon star becomes smaller than that of a traditional neutron star at the same stellar mass.Moreover,the eigenfrequencies of hyperon stars also have scaling universality.It is shown that the EURO thirdgeneration gravitational-wave detector has the potential to detect the gravitational-wave signal emitted from the axial w-mode oscillations of a hyperon star.