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Space-based gravitational wave detection is based on the astrodynamical equations derived from gravitational theory to detect changes in distance between spacecraft/celestial bodies and/or their state changes caused by gravitational waves. The fundamental method involves using electromagnetic waves (including radio waves, microwaves, light waves, X-rays, gamma rays, etc.) for Doppler tracking and comparing to the stable frequency standards (sources) at both the transmitting and receiving ends. Examples include microwave Doppler tracking, optical clock gravitational wave detection, atom interferometry gravitational wave detection, and laser interferometry gravitational wave detection. If the frequency sources at both ends are not sufficiently stable, a generalized dual-path Michelson interferometer based on Doppler tracking combinations is needed. Currently, the main space-based gravitational wave detectors under construction or planning are laser interferometers, which cover medium frequency (0.1-10 Hz) and low-frequency (millihertz 0.1-100 mHz and microhertz 0.1-100 {\mu}Hz) gravitational wave detection bands. This article reviews the current status and prospects of these gravitational wave detection methods., Comment: 101 pages, 31 figures, 11 tables. This is a quick English translation with the assistance of ChatGPT and Baidu from the Chinese article, Ni W-T. Space gravitational wave detection: Progress and outlook (in Chinese). Sci Sin-Phys Mech Astron, 2024, 54: 270402, doi: 10.1360/SSPMA-2024-0186 (Open Access)

For space gravitational wave (GW) detection, arm locking is a proposal useful in decreasing the frequency noise of the laser sources for current developing space missions LISA and Taiji/TianQin. In this paper, we study the application of arm locking to the Astrodynamical Middle-frequency Interferometric Gravitational wave Observatory (AMIGO) to decrease the frequency noise of laser sources. For AMIGO, the arm-locking technique can suppress the laser frequency noise by three orders of magnitude. The advantage of this is to make the auxiliary noise assignment for AMIGO easier and more relaxed. For the first-generation time-delay interferometry (TDI) configuration, the laser frequency noise contribution is already below the core noise contribution. For the simple Michelson TDI configuration (X0), the arm locking makes the acceleration-thrust scheme, the delay-line scheme, or the combined scheme easier to implement. Within a relatively short period of less than a day (compared to less than twenty days for LISA/Taiji), the Doppler frequency pulling can be efficiently reduced to within $\pm$ 0.001 Hz and does not affect the mission duty cycle much., Comment: 27 pages, 21 figures; V2: More details are added, and the main results remain the same

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions., Comment: Summary of the Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at CERN: https://indico.cern.ch/event/1208783/

The theoretical calculations of the dynamic E2-M1 polarizability at the magic wavelength of the Sr optical clock are inconsistent with experimental results. We investigate role of negative-energy states in the E2 and M1 polarizabilities. Our result for E2-M1 polarizability difference $-$7.74(3.92)$\times$10$^{-5}$ a.u. is dominated by the contribution from negative-energy states to M1 polarizability and has the same sign as and consistent with all the experimental values. In addition, we apply the present calculations to various other optical clocks, further confirming the importance of negative-energy states to the M1 polarizability., Comment: 7 pages, 3 figures, arXiv admin note: this is an extended version of arXiv:2301.06740

The ground-based gravitational wave (GW) observatories discover a population of merging stellar binary black holes (BBHs), which are promising targets for multiband observations by the low-, middle-, and high-frequency GW detectors. In this paper, we investigate the multiband GW detections of BBHs and demonstrate the advantages of such observations in improving the localization and parameter estimates of the sources. We generate mock samples of BBHs by considering different formation models as well as the merger rate density constrained by the current observations (GWTC-3). We specifically consider the astrodynamical middle-frequency interferometer GW observatory (AMIGO) in the middle-frequency band and estimate that it may detect $21$-$91$ BBHs with signal-to-noise ratio $\varrho\geq8$ in a $4$-yr observation period. The multiband observations by the low-frequency detectors [Laser Interferometer Space Antenna (LISA) and Taiji] and AMIGO may detect $5$-$33$ BBHs with $\varrho_{\rm LT}\geq5$ and $\varrho_{\rm AMI}\geq5$, which can evolve to the high-frequency band within $4$ yr and can be detected by the Cosmic Explorer (CE) and Einstein Telescope (ET). The joint observations of LISA-Taiji-AMIGO-ET-CE may localize the majority of the detectable BBHs in sky areas of $7\times10^{-7}$ to $2\times10^{-3}$ deg$^2$, which is improved by a factor of $\sim120$, $\sim2.4\times10^{5}$, $\sim1.8\times10^{4}$, or $\sim1.2\times10^{4}$, comparing with those by only adopting CE-ET, AMIGO, LISA-Taiji, or LISA-Taiji-AMIGO. These joint observations can also lead to an improvement of the measurement precision of the chirp mass (symmetric mass ratio) by a factor of $\sim5.5\times10^{4}$ ($33$), $\sim16$ ($8$), $\sim120$ ($90$), or $\sim5$ ($5$), comparing with those by CE-ET, AMIGO, LISA-Taiji, or LISA-Taiji-AMIGO., Comment: 16 pages, 12 figures, MNRAS published

The space-based laser interferometers, LISA, Taiji and TianQin, are targeting to observe milliHz gravitational waves (GWs) in the 2030s. The joint observations from multiple space-based detectors yield significant advantages. In this work, we recap the studies and investigations for the joint space-based GW detector networks to highlight: 1) the high precision of sky localization for the massive binary black hole (BBH) coalescences and the GW sirens in the cosmological implication, 2) the effectiveness to test the parity violation in the stochastic GW background observations, 3) the efficiency of subtracting galactic foreground, 4) the improvement in stellar-mass BBH observations. We inspect alternative networks by trading off massive BBH observations and stochastic GW background observation., Comment: 32 pages, 14 figures, reviews on recent studies about space-borne GW networks, comments and feedbacks are welcome

A large number of galactic binary systems emit gravitational waves (GW) continuously with frequencies below $\sim$10 mHz. The LISA mission could identify tens of thousands of binaries over years of observation and will be subject to the confusion noise around 1 mHz yielded by the unresolved sources. Beyond LISA, there are several missions have been proposed to observe GWs in the sub-mHz range where the galactic foreground is expected to be overwhelming the instrumental noises. In this study, we investigate the detectability of sub-mHz GW missions to detect the galactic double white dwarf (DWD) binaries and evaluate the confusion noise produced by the undistinguished DWDs. This confusion noise could also be viewed as a stochastic GW foreground and be effectively observed in the sub-mHz band. The parameter determinations for the modeled foreground are examined by employing different detector sensitivities and population models. By assuming the determined foregrounds could be subtracted from the data, we evaluate the residuals which are expected to have power spectral densities two orders of magnitude lower than the originals data., Comment: 17 pages, 11 figures, accepted for publication in PRD

We realize a Mach-Zehnder-type dual-atom-interferometer gyroscope with an interrogation arm of 40 cm length and the interference area up to 1.2 cm$^2$. The precise angular alignment of the large-scale separated Raman lasers is demonstrated by seeking the phase intersection of Ramsey-Bord$\acute{e}$ interferometers after the gravity effect is compensated and by decoupling the velocity dependent crosstalk phase shifts, and applied to build the Mach-Zehnder atom interferometer. Then a compact inertial rotation sensor is realized based on dual large-area Mach-Zehnder atom interferometers by precisely aligning the large-scale separated Raman lasers, in which the coherence is well preserved and the common noise is differentially suppressed. The sensor presents a sensitivity of $1.5\times10^{-7}$ rad/s/Hz$^{1/2}$, and a stability of $9.5\times10^{-10}$ rad/s at 23000 s. The absolute rotation measurement is carried out by adjusting the atomic velocity which corresponds to modulating the scale factor., Comment: 6 pages, 4 figures

This article summarizes the talks in the session GW2 of the Sixteenth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation, and Relativistic Field Theories, 5-10 July, 2021, on Mid-frequency (0.1-10 Hz) gravitational waves: Sources and detection methods with a review on strain power spectral density amplitude of various mid-frequency gravitational wave projects/concepts and with extended summaries on the progress of ZAIGA project and on the conceptual study of AMIGO., Comment: 16 pages, 3 figures, 1 table

AMIGO - The Astrodynamical Middle-frequency Interferometric GW (Gravitation-Wave) Observatory is a first-generation mid-frequency GW mission bridging the sensitivity gap between the high-frequency GW detectors and low-frequency space GW detectors. In our previous works, we have obtained appropriate heliocentric orbit formations of nominal arm length 10,000 km with their first-generation time-delay configurations satisfying frequency noise reduction requirement, and we have also worked out thrust-fuel friendly constant-arm heliocentric orbit formations. In this paper, we review and study noise requirements and present the corresponding GW sensitivities. From the design white position noises and acceleration noises, we obtain the GW sensitivities for the first-generation Michelson X TDI configuration of b-AMIGO (baseline AMIGO), AMIGO, and e-AMIGO (enhanced AMIGO). In view of the current technology development, we study and indicate steps to implement the AMIGO mission concept., Comment: revision to match the IJMPD in-press version

The space-borne gravitational wave (GW) detectors, LISA and TAIJI, are planned to be launched in the 2030s. The dual detectors with comparable sensitivities will form a network observing GW with significant advantages. In this work, we investigate the three possible LISA-TAIJI networks for the different location and orientation compositions of LISA orbit ($+60^\circ$ inclination and trailing the Earth by $20^\circ$) and alternative TAIJI orbit configurations including TAIJIp ($+60^\circ$ inclination and leading the Earth by $20^\circ$), TAIJIc ($+60^\circ$ inclination and co-located with LISA), TAIJIm ($-60^\circ$ inclination and leading the Earth by $20^\circ$). In the three LISA-TAIJI configurations, the LISA-TAIJIm network shows the best performance on the sky localization and polarization determination for the massive binary system due to their better complementary antenna pattern, and LISA-TAIJIc could achieve the best cross-correlation and observe the stochastic GW background with an optimal sensitivity., Comment: 12 pages, 6 figures

We introduce a generic algorithm to determine the time delays and spacecraft (S/C) positions to compose any time-delay interferometry (TDI) channel in the dynamical case and evaluate its sensitivity by using a full numerical method. We select 11 second-generation TDI channels constructed from four approaches and investigate their gravitational wave responses, noise levels, and averaged sensitivities under a numerical LISA orbit. The sensitivities of selected channels are various especially for frequencies lower than 20 mHz. The optimal channel A$_2$ (or equivalently E$_2$) combined from second-generation Michelson TDI channels (X$_1$, X$_2$, and X$_3$) achieves the best sensitivity among the channels, while the Sagnac $\alpha_1$ channel shows the worse sensitivity. Multiple channels show better sensitivities at some characteristic frequencies compared to the fiducial X$_1$ channel. The joint $\mathrm{A_2+E_2+T_2}$ observation not only enhances the sensitivity of the X$_1$ channel by a factor of $\sqrt{2}$ to 2 but also improves the capacity of sky coverage., Comment: 13 pages, 8 figures

Three spacecraft of LISA/TAIJI mission follow their respective geodesic trajectories, and their interferometric arms are unequal and time-varying due to orbital dynamics. Time-delay interferometry (TDI) is proposed to suppress the laser frequency noise caused by the unequal-arm. By employing the numerical orbit, we investigate the sensitivity of the first-generation TDI configurations and their corresponding optimal A, E, and T channels. The sensitivities of T channels from Michelson and Monitor/Beacon configurations diverge from the equal-arm case in frequencies lower than 10 mHz, and their performances vary with the inequality of the arm lengths. The mismatches of the laser beam paths are evaluated in a dynamic case, and the residual laser noise in the first-generation TDI could not satisfy the mission requirement., Comment: 25 pages, 12 figures

A brief history and various themes of mid-frequency gravitational wave detection are presented more or less following historical order -- Laser Interferometry, Atom Interferometry (AI), Torsion Bar Antenna (TOBA), and Superconducting Omni-directional Gravitational Radiation Observatory (SOGRO). Both Earth-based and Space-borne concepts are reviewed with outlook on expected astrophysical sources, Comment: reference update and minor corrections

LISA is considered to be launched alongside the Athena to probe the energetic astrophysical processes. LISA can determine the direction of sources for Athena's follow-up observation. As another space gravitational wave mission, TAIJI is expected to be launched in the 2030s. The LISA-TAIJI network would provide abundant merits for sources understanding. In this work, we simulate the joint LISA-TAIJI observations for gravitational waves from coalescing supermassive black hole binaries and monochromatic sources. By using the numerical mission orbits, we evaluate the performances of sky localization for various time-delay interferometry channels. For 30 days observation until coalescence, the LISA-TAIJI network in optimal operation can localize all simulated binary sources, $(10^7,\ 3.3 \times 10^6)\ M_\odot$, $(10^6,\ 3.3 \times 10^5)\ M_\odot$ and $(10^5,\ 3.3 \times 10^4)\ M_\odot$ at redshift $z=2$, in 0.4 deg$^2$ (field of view of Wide Field Imager on Athena). The angular resolution can be improved by more than 10 times comparing to LISA or TAIJI single detector at a given percentage of population. The improvements for monochromatic sources at 3 mHz and 10 mHz are relatively moderate in one-year observation. The precision of sky localization could be improved by around 1 to 3 times comparing to single LISA at a given percentage of sources. For a simulated 90 days observation for monochromatic waves, the LISA-TAIJI network still represents a considerable localization advantage which could be more than 10 times better., Comment: 18 pages, 12 figures; accepted for publication in PRD

This article is a foreword for the special issue on Gravitational Wave Detection and Fundamental Physics in Space for International Journal of Physics D. In the foreword, we review briefly the history of the development of mission concepts and projects for the gravitational wave detection in space together with fundamental physics missions. We summarize briefly the gravitational-wave detection-in-space science goals and the current progress in the experimental & technological developments presented in the articles of this special issue, and list the articles with publication information and arXiv numbers., Comment: 5 pages. arXiv admin note: text overlap with arXiv:1610.01148

AMIGO is a first-generation Astrodynamical Middle-frequency Interferometric GW Observatory. The scientific goals of AMIGO are: to bridge the spectra gap between first-generation high-frequency and low-frequency GW sensitivities; to detect intermediate mass BH coalescence; to detect inspiral phase and predict time of binary black hole coalescence together with neutron star coalescence for ground interferometers; to detect compact binary inspirals for studying stellar evolution and galactic population. The mission concept is to use time delay interferometry for a nearly triangular formation of 3 drag-free spacecraft with nominal arm length 10,000 km, emitting laser power 2-10 W and telescope diameter 300-500 mm. The design GW sensitivity in the middle frequency band is 3 x 10^(-21) Hz^(-1/2). Both heliocentric and geocentric orbits are under study. All options have LISA-like formations, that is the triangular formation is 60 deg inclined to the orbit plane. For AMIGO, the first-generation time delay interferometry is good enough for the laser frequency noise suppression. We also investigate for each options of orbits under study, whether constant equal-arm implementation is feasible. For the solar-orbit option, the acceleration to maintain the formation can be designed to be less than 15 nm/s2 with the thruster requirement in the 15 {\mu}N range. AMIGO would be a good place to implement the constant equal-arm option. Fuel requirement, thruster noise requirement and test mass acceleration actuation requirement are briefly considered. From the orbit study, the solar orbit option is the first mission orbit choice. We study the deployment for this orbit option. A last-stage launch from 300 km LEO (Low Earth Orbit) to an appropriate 2-degree-behind-the-Earth AMIGO formation in 95 days requires only a {\delta}v of 75 m/s., Comment: 29 pages, 21 figures, 6 tables. arXiv admin note: text overlap with arXiv:1709.05659

In previous papers, we have addressed the issues of orbit design and thruster requirement for the constant arm versions of AMIGO (Astrodynamical Middle-frequency Interferometric Gravitational-wave Observatory) mission concept and for the constant arm GW (gravitational wave) mission concept of AIGSO (Atom Interferometric Gravitational-wave Space Observatory). In this paper, we apply similar methods to the orbit design and thruster requirement for the constant arm GW missions B-DECIGO and DECIGO, and estimate the yearly propellant requirements at the specific impulse Isp = 300 sec and Isp = 1000 sec. For the geocentric orbit options of B-DECIGO which we have explored, the fuel mass requirement is a concern. For the heliocentric orbit options of B-DECIGO and DECIGO, the fuel requirement to keep the arm equal and constant should be easily satisfied. Furthermore, we explore the thruster and propellant requirements for constant arm versions of LISA and TAIJI missions and find the fuel mass requirement is not a show stopper either. The proof mass actuation noise is a concern. To have enough dynamical range, an alternate proof mass is required. Detailed laboratory study is warranted, Comment: 13 pages, 6 figures, 1 table

Atom Interferometric Gravitational-wave (GW) Space Observatory (AIGSO) is a mission concept mainly aimed at the middle-frequency (0.1 Hz - 10 Hz) GW detection. AIGSO proposes to have three spacecraft in linear formation with extension of 10 km. The three spacecraft need to maintain 5 km + 5 km constant arm-length formation. In this study, we address the issue of orbit design and thruster requirement. The acceleration to maintain the formation can be designed to be less than 30 pm/s$^2$ and the thruster requirement is in the 30 nN range. Application to other arm-length-maintaining missions is also discussed., Comment: 14 pages, 8 figures, accepted by IJMPD

We use both mass and internal energy specified rubidium atoms to jointly test the weak equivalence principle (WEP). We improve the four-wave double-diffraction Raman transition method (FWDR) we proposed before to select atoms with certain mass and angular momentum state, and perform dual-species atom interferometer. By combining $^{87}$Rb and $^{85}$Rb atoms with different angular momenta, we compare the differential gravitational acceleration of them, and determine the value of E\"{o}tv\"{o}s parameter, $\eta$, which measures the strength of the violation of WEP. For one case ($^{87}$Rb$|\emph{F}=1\rangle$ - $^{85}$Rb$|\emph{F}=2\rangle$),the statistical uncertainty of $\eta$ is $1.8 \times 10^{-10}$ at integration time of 8960 s. With various systematic errors correction, the final value is $\eta=(-4.4 \pm 6.7) \times 10^{-10}$. Comparing with the previous WEP test experiments using atoms, this work gives a new upper limit of WEP violation for $^{87}$Rb and $^{85}$Rb atom pairs., Comment: 5 pages, 3 figures

The Zhaoshan long-baseline Atom Interferometer Gravitation Antenna (ZAIGA) is a new type of underground laser-linked interferometer facility, and is currently under construction. It is in the 200-meter-on-average underground of a mountain named Zhaoshan which is about 80 km southeast to Wuhan. ZAIGA will be equipped with long-baseline atom interferometers, high-precision atom clocks, and large-scale gyros. ZAIGA facility will take an equilateral triangle configuration with two 1-km-apart atom interferometers in each arm, a 300-meter vertical tunnel with atom fountain and atom clocks mounted, and a tracking-and-ranging 1-km-arm-length prototype with lattice optical clocks linked by locked lasers. The ZAIGA facility will be used for experimental research on gravitation and related problems including gravitational wave detection, high-precision test of the equivalence principle of micro-particles, clock based gravitational red-shift measurement, rotation measurement and gravito-magnetic effect., Comment: 20 pages, 15 figures

After first reviewing the gravitational wave (GW) spectral classification. we discuss the sensitivities of GW detection in space aimed at low frequency band (100 nHz-100 mHz) and middle frequency band (100 mHz-10 Hz). The science goals are to detect GWs from (i) Supermassive Black Holes; (ii) Extreme-Mass-Ratio Black Hole Inspirals; (iii) Intermediate-Mass Black Holes; (iv) Galactic Compact Binaries; (v) Stellar-Size Black Hole Binaries; and (vi) Relic GW Background. The detector proposals have arm length ranging from 100 km to 1.35x109 km (9 AU) including (a) Solar orbiting detectors and (b) Earth orbiting detectors. We discuss especially the sensitivities in the frequency band 0.1-10 microHz and the middle frequency band (0.1 Hz-10 Hz). We propose and discuss AMIGO as an Astrodynamical Middle-frequency Interferometric GW Observatory., Comment: 10 pages, 2 figures, 1 table, Plenary talk given in Joint Meeting of 13th International Conference on Gravitation, Astrophysics, and Cosmology and 15th Italian-Korean Symposium on Relativistic Astrophysics, Ewha Womans University, Seoul, Korea, July 3-7, 2017

The success of LISA Pathfinder in demonstrating the LISA drag-free requirement paved the road of using space missions for detecting low-frequency and middle-frequency GWs. The new LISA GW mission proposes to use arm length of 2.5 Gm (1 Gm = 106 km). The TAIJI GW mission proposes to use arm length of 3 Gm. In order to attain the requisite sensitivity, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise etc. In previous papers, we have performed the numerical simulation of the time delay interferometry (TDI) for original LISA, ASTROD-GW and eLISA together with a LISA-type mission with a nominal arm length of 2 Gm using the CGC 2.7/CGC2.7.1 ephemeris framework. In this paper, we follow the same procedure to simulate the time delay interferometry numerically for the new LISA mission and the TAIJI mission together with LISA-like missions of arm length 1, 2, 4, 5 and 6 Gm. The resulting optical path differences of the second-generation TDI calculated for new LISA, TAIJI, and LISA-like missions or arm length 1, 2, 4, 5 & 6 Gm are well below their respective limits which the laser frequency noise is required to be suppressed. However, for of the first generation X, Y, and Z TDI configurations, the original requirements need to be relaxed by 3 to 30 fold to be satisfied. For the new LISA and TAIJI, about one order of magnitude relaxation would be good and recommended; this could be borne on the laser stability requirement in view of recent progress in laser stability. Compared with X, Y and Z, the X+Y+Z configuration does have a good cancellation of path length differences and could serve as a null string detection check. We compile and compare the resulting differences of various TDI configurations due to the different arm lengths for various LISA-like mission proposals and for the ASTROD-GW mission proposal., Comment: The supplement is added in this version. arXiv admin note: text overlap with arXiv:1204.2125

We indicate the progress of experimental gravity, present an outlook in this field, and summarise the Observational/Experimental Parallel Session together with a related plenary talk on gravitational waves of the 2nd LeCosPA Symposium., Comment: 1 figure, Second LeCosPa Simposium, December 2015, Taipei Taiwan

This short exposition starts with a brief discussion of situation before the completion of special relativity (Le Verrier's discovery of the Mercury perihelion advance anomaly, Michelson-Morley experiment, E\"otv\"os experiment, Newcomb's improved observation of Mercury perihelion advance, the proposals of various new gravity theories and the development of tensor analysis and differential geometry) and accounts for the main conceptual developments leading to the completion of the general relativity: gravity has finite velocity of propagation; energy also gravitates; Einstein proposed his equivalence principle and deduced the gravitational redshift; Minkowski formulated the special relativity in 4-dimantional spacetime and derived the 4-dimensional electromagnetic stress-energy tensor; Einstein derived the gravitational deflection from his equivalence principle; Laue extended the Minkowski's method of constructing electromagnetic stress-energy tensor to stressed bodies, dust and relativistic fluids; Abraham, Einstein, and Nordstr\"om proposed their versions of scalar theories of gravity in 1911-13; Einstein and Grossmann first used metric as the basic gravitational entity and proposed a "tensor" theory of gravity (the "Entwurf" theory, 1913); Einstein proposed a theory of gravity with Ricci tensor proportional to stress-energy tensor (1915); Einstein, based on 1913 Besso-Einstein collaboration, correctly derived the relativistic perihelion advance formula of his new theory which agreed with observation (1915); Hilbert discovered the Lagrangian for electromagnetic stress-energy tensor and the Lagrangian for the gravitational field (1915), and stated the Hilbert variational principle; Einstein equation of general relativity was proposed (1915); Einstein published his foundation paper (1916)., Comment: 23 pages, 3 tables, Chapter 2 of the book One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, edited by Wei-Tou Ni (World Scientific, Singapore, 2016); IJMPD, 1630004 (2016)

In 1859, Le Verrier discovered the Mercury perihelion advance anomaly. This anomaly turned out to be the first relativistic-gravity effect observed. During the 157 years to 2016, the precisions and accuracies of laboratory and space experiments, and of astrophysical and cosmological observations on relativistic gravity have been improved by 3-4 orders of magnitude. The improvements have been mainly from optical observations at first followed by radio observations. The achievements for the past 50 years are from radio Doppler tracking and radio ranging together with lunar laser ranging. At the present, the radio observations and lunar laser ranging experiments are similar in the accuracy of testing relativistic gravity. We review and summarize the present status of solar-system tests of relativistic gravity. With planetary laser ranging, spacecraft laser ranging and interferometric laser ranging (laser Doppler ranging) together with the development of drag-free technology, the optical observations will improve the accuracies by another 3-4 orders of magnitude in both the equivalence principle tests and solar-system dynamics tests of relativistic gravity. Clock tests and atomic interferometry tests of relativistic gravity will reach an ever-increasing precision. These will give crucial clues in both experimental and theoretical aspects of gravity, and may lead to answers to some profound issues in gravity and cosmology., Comment: 30 pages, 3 tables, Chapter 8 in One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, ed. W.-T. Ni (World Scientific, Singapore, 2016); matches the published version of IJMPD. This article is an 11-year update of the solar-system tests part of arXiv:gr-qc/0504116 on Empirical Foundations of Relativistic Gravity

In the last two decades we have seen important mutual stimulations between the community working on electrodynamics of continuous media and the community working on spacetime structure. This is highlighted by the publication of two important monographs from two communities: Foundations of Classical Electrodynamics by F. W. Hehl and Yu. N. Obukhov (Birkh\"auser, Boston 2003) and Differential Forms in Electromagnetics by I. V. Lindell (IEEE Press-Wiley, Piscataway, NJ 2004; see also a new book "Multiforms, Dyadics, and Electromagnetic Media" by the same author in 2015). Starting around 1960, magnetoelectric effects and magnetoelectric media have been a focus of study. Somewhat later, the constitutive tensor density framework was used to construct spacetime structure theoretically and empirically. Earlier, in putting Maxwell equations into a form compatible with general relativity, Einstein noticed that the Maxwell equations can be formulated in a form independent of the metric gravitational potential in 1916; only the constitutive tensor density depends on the metric. This was followed by further stimulating and clarifying works of Weyl in 1918, Murnaghan in 1921, Kottler in 1922 and Cartan in 1923. Year 2016 is the centennial of the start of this historical development. International Journal of Modern Physics D of World Scientific is celebrating the occasion by publishing this special issue on Spacetime Structure and Electrodynamics. We have invited researchers to submit original research articles that would contribute to a better understanding of the phenomena inherent to spacetime structure and electrodynamic media., Comment: 5 pages with links to arXiv

For the benefit of the readers of this journal, the editors requested that we prepare a brief review of the history of the development of the theory, the experimental attempts to detect them, and the recent direct observations of gravitational waves (GWs). The theoretical ideas and disputes beginning with Einstein in 1916 regarding the existence and nature of GWs and the extent to which one can rely on the electromagnetic analogy, especially the controversies regarding the quadrupole formula and whether GWs carry energy, are discussed. The theoretical conclusions eventually received strong observational support from the binary pulsar. This provided compelling, although indirect, evidence for GWs carrying away energy--as predicted by the quadrupole formula. On the direct detection experimental side, Weber started more than 50 years ago. In 1966, his bar for GW detection reached a strain sensitivity of a few times 10^-16. His announcement of coincident signals (now considered spurious) stimulated many experimental efforts from room temperature resonant masses to cryogenic detectors and laser-interferometers. Now there are km-sized interferometric detectors (LIGO Hanford, LIGO Livingston, Virgo and KAGRA). Advanced LIGO first reached a strain sensitivity of the order of 10^-22. During their first 130 days of observation (O1 run), with the aid of templates generated by numerical relativity, they did make the first detections: two 5-sigma GW events and one likely event. Besides earth-based GW detectors, the drag-free sensitivity of the LISA Pathfinder has already reached to the LISA goal level, paving the road for space GW detectors. Over the whole GW spectrum (from aHz to THz) there are efforts for detection, notably the very-low-frequency band (pulsar timing array [PTA], 300 pHz-100 nHz) and the extremely-low (Hubble)-frequency (cosmic microwave background [CMB] experiment, 1 aHz-10 fHz)., Comment: revised version to appear in Chinese Journal of Physics

With the LIGO announcement of the first direct detection of gravitational waves (GWs), the GW Astronomy was formally ushered into our age. After one-hundred years of theoretical investigation and fifty years of experimental endeavor, this is a historical landmark not just for physics and astronomy, but also for industry and manufacturing. The challenge and opportunity for industry is precision and innovative manufacturing in large size - production of large and homogeneous optical components, optical diagnosis of large components, high reflectance dielectric coating on large mirrors, manufacturing of components for ultrahigh vacuum of large volume, manufacturing of high attenuating vibration isolation system, production of high-power high-stability single-frequency lasers, production of high-resolution positioning systems etc. In this talk, we address the requirements and methods to satisfy these requirements. Optical diagnosis of large optical components requires large phase-shifting interferometer; the 1.06 {\mu}m Phase Shifting Interferometer for testing LIGO optics is an example. High quality mirrors are crucial for laser interferometric GW detection, so as for ring laser gyroscope, high precision laser stabilization via optical cavities, quantum optomechanics, cavity quantum electrodynamics and vacuum birefringence measurement. There are stringent requirements on the substrate materials and coating methods. For cryogenic GW interferometer, appropriate coating on sapphire or silicon are required for good thermal and homogeneity properties. Large ultrahigh vacuum components and high attenuating vibration system together with an efficient metrology system are required and will be addressed. For space interferometry, drag-free technology is well-developed; weak-light phase locking is demonstrated in the laboratories while weak-light manipulation technology still needs developments., Comment: 12 pages, 3 tables, invited talk for Photonics Asia 2016, October 12-14, Beijing. To be published in Proceedings of SPIE

Since almost all phenomena electrodynamics deal with have energy scales much lower than the Higgs mass energy and intermediate boson energy, electrodynamics of continuous media should be applicable and the constitutive relation of spacetime/vacuum should be local and linear. What is the key characteristic of the spacetime/vacuum? It is the Weak Equivalence Principle (WEP I) for photons/wave packets of light which states that the spacetime trajectory of light in a gravitational field depends only on its initial position and direction of propagation, and does not depend on its frequency (energy) and polarization, i.e. nonbirefringence of light propagation in spacetime/vacuum. With this principle it is proved by the author in 1981 in the weak field limit, and by Lammerzahl and Hehl in 2004 together with Favaro and Bergamin in 2011 without assuming the weak-field condition that the constitutive tensor must be of the core metric form with only two additional degrees of freedom - the pseudoscalar (Abelian axion or EM axion) degree of freedom and the scalar (dilaton) degree of freedom (i.e. metric with axion and dilaton). In this paper, we review this connection and the ultrahigh precision empirical tests of nonbirefringence together with present status of tests of cosmic Abelian axion and dilaton. If the stronger version of WEP is assumed, i.e. WEP II for photons (wave packets of light) which states in addition to WEP I also that the polarization state of the light would not change (e.g. no polarization rotation for linear polarized light) and no amplification/attenuation of light, then no Abelian (EM) axion and no dilaton, and we have a pure metric theory., Comment: 32 pages, 2 tables, review for the special issue on "Spacetime Structure and Electrodynamics" of International Journal of Modern Physics D, Vol. 25, No.14 (2016). arXiv admin note: substantial text overlap with arXiv:1512.08426

Gravitational wave (GW) detection in space is aimed at low frequency band (100 nHz - 100 mHz) and middle frequency band (100 mHz - 10 Hz). The science goals are the detection of GWs from (i) Supermassive Black Holes; (ii) Extreme-Mass-Ratio Black Hole Inspirals; (iii) Intermediate-Mass Black Holes; (iv) Galactic Compact Binaries and (v) Relic GW Background. In this paper, we present an overview on the sensitivity, orbit design, basic orbit configuration, angular resolution, orbit optimization, deployment, time-delay interferometry and payload concept of the current proposed GW detectors in space under study. The detector proposals under study have arm length ranging from 1000 km to 1.3 x 109 km (8.6 AU) including (a) Solar orbiting detectors -- ASTROD-GW (ASTROD [Astrodynamical Space Test of Relativity using Optical Devices] optimized for GW detection), BBO (Big Bang Observer), DECIGO (DECi-hertz Interferometer GW Observatory), e-LISA (evolved LISA [Laser Interferometer Space Antenna]), LISA, other LISA-type detectors such as ALIA, TAIJI etc. (in Earth-like solar orbits), and Super-ASTROD (in Jupiter-like solar orbits); and (b) Earth orbiting detectors -- ASTROD-EM/LAGRANGE, GADFLI/GEOGRAWI/g-LISA, OMEGA and TIANQIN., Comment: 48 pages, 10 figures, Chapter 12 in One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, ed.W.-T. Ni (World Scientific, Singapore, 2016); Int. J. Mod. Phys. D, to be published. arXiv admin note: substantial text overlap with arXiv:1212.2816

In the centenary year of Einstein's General Theory of Relativity, this paper reviews the current status of gravitational wave astronomy across a spectrum which stretches from attohertz to kilohertz frequencies. Sect. 1 of this paper reviews the historical development of gravitational wave astronomy from Einstein's first prediction to our current understanding the spectrum. It is shown that detection of signals in the audio frequency spectrum can be expected very soon, and that a north-south pair of next generation detectors would provide large scientific benefits. Sect. 2 reviews the theory of gravitational waves and the principles of detection using laser interferometry. The state of the art Advanced LIGO detectors are then described. These detectors have a high chance of detecting the first events in the near future. Sect. 3 reviews the KAGRA detector currently under development in Japan, which will be the first laser interferometer detector to use cryogenic test masses. Sect. 4 of this paper reviews gravitational wave detection in the nanohertz frequency band using the technique of pulsar timing. Sect. 5 reviews the status of gravitational wave detection in the attohertz frequency band, detectable in the polarisation of the cosmic microwave background, and discusses the prospects for detection of primordial waves from the big bang. The techniques described in sects. 1-5 have already placed significant limits on the strength of gravitational wave sources. Sects. 6 and 7 review ambitious plans for future space based gravitational wave detectors in the millihertz frequency band. Sect. 6 presents a roadmap for development of space based gravitational wave detectors by China while sect. 7 discusses a key enabling technology for space interferometry known as time delay interferometry., Comment: published (2015)

After reviewing the meaning of various equivalence principles and the structure of electrodynamics, we give a fairly detailed account of the construction of the light cone and a core metric from the equivalence principle for the photon (no birefringence, no polarization rotation and no amplification/attenuation in propagation) in the framework of linear electrodynamics using cosmic connections/observations as empirical support. The cosmic nonbirefringent propagation of photons independent of energy and polarization verifies the Galileo Equivalence Principle [Universality of Propagation] for photons/electromagnetic wave packets in spacetime. This nonbirefringence constrains the spacetime constitutive tensor to high precision to a core metric form with an axion degree and a dilaton degree of freedom. Thus comes the metric with axion and dilation. Constraints on axion and dilaton from astrophysical/cosmic propagation are reviewed. E\"otv\"os-type experiments, Hughes-Drever-type experiments, redshift experiments then constrain and tie this core metric to agree with the matter metric, and hence a unique physical metric and universality of metrology. We summarize these experiments and review how the Galileo equivalence principle constrains the Einstein Equivalence Principle (EEP) theoretically. In local physics this physical metric gives the Lorentz/Poincar\'e covariance. Understanding that the metric and EEP come from the vacuum as a medium of electrodynamics in the linear regime, efforts to actively look for potential effects beyond this linear scheme are warranted., Comment: 47 pages, 3 tables

After giving a brief introduction and presenting a complete classification of gravitational waves (GWs) according to their frequencies, we review and summarize the detection methods, the sensitivities, and the sources. We notice that real-time detections are possible above 300 pHz. Below 300 pHz, the detections are possible on GW imprints or indirectly. We are on the verge of detection. The progress in this field will be promising and thriving. We will see improvement of a few orders to several orders of magnitude in the GW detection sensitivities over all frequency bands in the next hundred years., Comment: 38 pages, 4 figures, 6 tables. Chapter 10 in One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, ed.W.-T. Ni (World Scientific, Singapore, 2015); Int. J. Mod. Phys. D, to be published

This year marks the hundredth anniversary of Einstein's 1915 landmark paper "Die Feldgleichungen der Gravitation" in which the field equations of general relativity were correctly formulated for the first time, thus rendering general relativity a complete theory. Over the subsequent hundred years physicists and astronomers have struggled with uncovering the consequences and applications of these equations. This contribution, which was written as an introduction to six chapters dealing with the connection between general relativity and cosmology that will appear in the two-volume book "One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity," endeavors to provide a historical overview of the connection between general relativity and cosmology, two areas whose development has been closely intertwined., Comment: 15 pages PDF, 4 figures, to appear as introductory chapter in "One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity"

We present a bird's-eye survey on the development of fundamental ideas of quantum gravity, placing emphasis on perturbative approaches, string theory, loop quantum gravity, and black hole thermodynamics. The early ideas at the dawn of quantum gravity as well as the possible observations of quantum gravitational effects in the foreseeable future are also briefly discussed., Comment: Invited review article. A few parts based on arXiv:1410.1486 and arXiv:1412.4362. To appear in Int. J. Mod. Phys. D and in "One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity," edited by Wei-Tou Ni (World Scientific, Singapore, 2015)

Searches for the role of spin in gravitation dated before the firm establishment of the electron spin in 1925. Since mass and spin, or helicity in the case of zero mass, are the Casimir invariants of the Poincar\'e group and mass participates in universal gravitation, these searches are natural steps to pursue. In this update, we report on the progress on this topic in the last five years after our last review. We begin with how is Lorentz/Poincar\'e group in local physics arisen from spacetime structure as seen by photon and matter through experiments/observations. The cosmic verification of the Galileo Equivalence Principle for photons/electromagnetic wave packets (Universality of Propagation in spacetime independent of photon energy and polarization, i.e. nonbirefringence) constrains the spacetime constitutive tensor to high precision to a core metric form with an axion degree and a dilaton degree of freedom. Hughes-Drever-type experiments then constrain this core metric to agree with the matter metric. Thus comes the metric with axion and dilation. In local physics this metric gives the Lorentz/Poincar\'e covariance. Constraints on axion and dilaton from polarized/unpolarized laboratory/astrophysical/cosmic experiments/observations are presented. In the end, we review the theoretical progress on the issue of gyrogravitational ratio for fundamental particles and the experimental progress on the measurements of possible long range/intermediate range spin-spin, spin-monopole and spin-cosmos interactions., Comment: 12 pages, 2 tables; Plenary talk presented in the 21st International Symposium on Spin Physics (Spin2014), 19 October 2014 - 24 October 2014, Peking University, Beijing, China; Based partly on arXiv:1411.0460, arXiv:1410.0126 and arXiv:0912.5057

Recently ACTPol has measured the cosmic microwave background (CMB) B-mode and E-mode polarizations and obtained TE, EE, BB, TB and EB power spectra in the multipole range 225-8725. In our previous paper (Ap. J. 792 (2014) 35 [Paper I]), we have analyzed jointly the results of three experiments on the CMB B-mode polarization -- SPTpol, POLARBEAR and BICEP2 to include in the model, in addition to the gravitational lensing and the inflationary gravitational waves components, also the fluctuation effects induced by the cosmic polarization rotation (CPR), if it exists within the upper limits at the time. In this paper, we fit both the mean CPR angle <{\alpha}> and its fluctuation <{\delta}{\alpha}2> from the new ACTPol data, and update our fitting of CPR fluctuations using BICEP2 data taking the new Planck dust measurement results into consideration. We follow the method of Paper I. The mean CPR angle is constrained from the EB correlation power spectra to |<{\alpha}>| < 14 mrad (0.8{\deg}) and the fluctuation (rms) is constrained from the BB correlation power spectra to <{\delta}{\alpha}2>1/2 < 29.3 mrad (1.68{\deg}). Assuming that the polarization angle of Tau A does not change from 89.2 to 146 GHz, the ACTPol data give <{\alpha}> = 1.0 {\pm} 0.63{\deg}. These results suggest that the inclusion of the present ACTPol data is consistent with no CPR detection. With the new Planck dust measurement, we update our fits of the BICEP2 CPR fluctuation constraint to be 32.8 mrad (1.88{\deg}). The joint ACTpol-BICEP2-POLARBEAR CPR fluctuation constraint is 23.7 mrad (1.36{\deg})., Comment: 15 pages, 2 figures, 2 tables, version to match the accepted submission to ApJ. Unfortunately there is a sign error in equation (6b). This propagated to equations (7b) and (8a) and to the results for \alpha_\beta. The errors in the last raw of Table 1 had been overestimated and corrected

After reviewing the construction of metric from premetric electrodynamics with empirical improvement of accuracy in the skewonless case, we explore the role of skewons in the construction of spacetime metric in the full premetric electrodynamics. For metric principal part plus skewon part, we have shown that the Type I skewon part is constrained to < a few x 10^(-35) in the weak field/weak EEP violation limit. Type II skewon part is not constrained in the first order. However, in the second order it induces birefringence; the nonbirefringence observations constrain the Type II skewon part to 10^(-19). Nevertheless, an additional nonmetric induced second-order contribution to the principal part constitutive tensor compensates the Type II skewon birefringence and makes it nonbirefringent. This second-order contribution is just the extra piece to the core-metric principal constitutive tensor induced by the antisymmetric tensor. From the Tamm-Rubilar tensor density and the dispersion relation for the spacetime medium with the asymmetric-metric-induced constitutive tensor, we know that it is nonbirefringent. The antisymmetric metric induced constitutive tensor has a pseudoscalar part in the decomposition. The variation of his part is constrained by observation on cosmic polarization rotation to < 0.03, and gives one constraint on the 6-degree-of-freedom antisymmetric metric. Further studies of these 6 degrees of freedom experimental and theoretically are desired., Comment: 22 pages, 2 tables

We study the electromagnetic wave propagation in the joint dilaton field and axion field. Dilaton field induces amplification/attenuation in the propagation while axion field induces polarization rotation. The amplification/attenuation induced by dilaton is independent of the frequency (energy) and the polarization of electromagnetic waves (photons). From observations, the agreement with and the precise calibration of the cosmic microwave background (CMB) to blackbody radiation constrains the fractional change of dilaton |{\Delta}{\psi}|/{\psi} to less than about 8 x 10^(-4) since the time of the last scattering surface of the CMB., Comment: 16 pages, Physics Letters A in press

ASTROD-GW (ASTROD [Astrodynamical Space Test of Relativity using Optical Devices] optimized for Gravitational Wave detection) is a gravitational-wave mission with the aim of detecting gravitational waves from massive black holes, extreme mass ratio inspirals (EMRIs) and galactic compact binaries, together with testing relativistic gravity and probing dark energy and cosmology. Mission orbits of the 3 spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4 and L5. The 3 spacecrafts range interferometrically with one another with arm length about 260 million kilometers. For 260 times longer arm length, the detection sensitivity of ASTROD-GW is 260 fold better than that of eLISA/NGO in the lower frequency region by assuming the same acceleration noise. Therefore, ASTROD-GW will be a better cosmological probe. In previous papers, we have worked out the time delay interferometry (TDI) for the ecliptic formation. To resolve the reflection ambiguity about the ecliptic plane in source position determination, we have changed the basic formation into slightly inclined formation with half-year precession-period. In this paper, we optimize a set of 10-year inclined ASTROD-GW mission orbits numerically using ephemeris framework starting at June 21, 2035, including cases of inclination angle is 0{\deg} (no inclination), 0.5{\deg}, 1.0{\deg}, 1.5{\deg}, 2.0{\deg}, 2.5{\deg} and 3.0{\deg}. We simulate the time delays of the first and second generation TDI configurations for the different inclinations, and compare/analyse the numerical results to attain the requisite sensitivity of ASTROD-GW by suppressing laser frequency noise below the secondary noises. To explicate our calculation process for different inclination cases, we take the 1.0{\deg} as example to show the orbit optimization and TDI simulation., Comment: 25 pages, 7 figures and 5 tables. arXiv admin note: text overlap with arXiv:1205.5175

STPpol, POLARBEAR and BICEP2 have recently measured the cosmic microwave background (CMB) B-mode polarization in various sky regions of several tens of square degrees and obtained BB power spectra in the multipole range 20-3000, detecting the components due to gravitational lensing and to inflationary gravitational waves. We analyze jointly the results of these three experiments and propose modifications of their analysis of the spectra to include in the model, in addition to the gravitational lensing and the inflationary gravitational waves components, also the effects induced by the cosmic polarization rotation (CPR), if it exists within current upper limits. Although in principle our analysis would lead also to new constraints on CPR, in practice these can only be given on its fluctuations <{\delta}{\alpha}^2>, since constraints on its mean angle are inhibited by the de-rotation which is applied by current CMB polarization experiments, in order to cope with the insufficient calibration of the polarization angle. The combined data fits from all three experiments (with 29% CPR-SPTpol correlation, depending on theoretical model) gives constraint <{\delta}{\alpha}^2>^1/2 < 27.3 mrad (1.56{\deg}) with r = 0.194 \pm 0.033. These results show that the present data are consistent with no CPR detection and the constraint on CPR fluctuation is about 1.5{\deg}. This method of constraining the cosmic polarization rotation is new, is complementary to previous tests, which use the radio and optical/UV polarization of radio galaxies and the CMB E-mode polarization, and adds a new constraint for the sky areas observed by SPTpol, POLARBEAR and BICEP2., Comment: Accepted for publication by The Astrophysical Journal

We study the problem of axion-photon coupling in the magnetic field influenced by gravitational radiation. We focus on exact solutions to the equations for axion electrodynamics in the pp-wave gravitational background for two models with initially constant magnetic field. The first model describes the response of an initially constant magnetic field in a gravitational-wave vacuum with unit refraction index; the second model is characterized by a non-unit refraction index prescribed to the presence of ordinary and/or dark matter. We show that both models demonstrate anomalous behavior of the electromagnetic field generated by the axion-photon coupling in the presence of magnetic field, evolving in the gravitational wave background. The role of axionic dark matter in the formation of the anomalous response of this electrodynamic system is discussed., Comment: 26 pages, no figures

For the study of the gravitational coupling of electromagnetism and the equivalence principle, we have used the spacetime constitutive tensor density {chi}ijkl, and discovered the nonmetric (axion) part (A){chi}ijkl (equal to {phi}eijkl) of {chi}ijkl worthy investigation. Since we have used Lagrangian formalism, {chi}ijkl is effectively symmetric under the interchange of index pairs, ij and kl, and has 21 independent degrees of freedom. Hehl, Obukhov and Rubilar have started from charge-flux formalism to study electromagnetism, discovered the antisymmetric part (Sk){chi}ijkl (15 degrees of freedom) of {chi}ijkl under the interchange of index pairs ij and kl worthy investigation, and called it skewon field. In this paper, we study the propagation of the Hehl-Obukhov-Rubilar skewon field in weak gravity field/dilute matter or with weak violation of the Einstein Equivalence Principle (EEP), and further classify it into Type I and Type II skewons. From the dispersion relation we show that no dissipation/no amplification condition implies that the additional skewon field must be of Type II. For Type I skewon field, the dissipation/amplification is proportional to the frequency and the CMB spectrum would deviate from Planck spectrum. From the high precision agreement of the CMB spectrum to 2.755 K Planck spectrum, we constrain the Type I cosmic skewon field (SkI){chi}ijkl to less than a few x 10-35. The skewon part of constitutive tensor constructed from asymmetric metric is of Type II, hence is allowed. This study may also find applications in macroscopic electrodynamics in the case of laser pumped medium or dissipative medium., Comment: 16 pages, additional references added and section 4.2 shortened to match the PLA accepted version

We propose a theoretical scenario to solve the proton radius puzzle which recently arises from the muonic hydrogen experiment. In this framework, 4 + n dimensional theory is incorporated with modified gravity. The extra gravitational interaction between the proton and muon at very short range provides an energy shift which accounts for the discrepancy between spectroscopic results from muonic and electronic hydrogen experiments. Assuming the modified gravity is a small perturbation to the existing electromagnetic interaction, we find the puzzle can be solved with stringent constraint on the range of the new force. Our result not only provides a possible solution to the proton radius puzzle but also suggest a direction to test new physics at very small length scale., Comment: 6 pages, 1 table. 10 more references added

ASTROD I is the first planned space mission in a series of ASTROD missions for testing relativity in space using optical devices. The main aims are: (i) to test General Relativity with an improvement of three orders of magnitude compared to current results, (ii) to measure solar and solar system parameters with improved accuracy, (iii) to test the constancy of the gravitational constant and in general to get a deeper understanding of gravity. The first ideas for the ASTROD missions go back to the last century when new technologies in the area of laser physics and time measurement began to appear on the horizon. ASTROD is a mission concept that is supported by a broad international community covering the areas of space technology, fundamental physics, high performance laser and clock technology and drag free control. While ASTROD I is a single-spacecraft concept that performes measurements with pulsed laser ranging between the spacecraft and earthbound laser ranging stations, ASTROD-GW is planned to be a three spacecraft mission with inter-spacecraft laser ranging. ASTROD-GW would be able to detect gravitational waves at frequencies below the eLISA/NGO bandwidth. As a third step Super-ASTROD with larger orbits could even probe primordial gravitational waves. This article gives an overview on the basic principles especially for ASTROD I., Comment: 10 pages,5 figures, 1 tables,to be published in IJMPD Vol. 22,1341003 (2013)

In this paper, we present an overview of ASTROD-GW (ASTROD [Astrodynamical Space Test of Relativity using Optical Devices] optimized for Gravitational Wave [GW] detection) mission concept and its studies. ASTROD-GW is an optimization of ASTROD which focuses on low frequency gravitational wave detection. The detection sensitivity is shifted by a factor of 260 (52) towards longer wavelengths compared with that of NGO/eLISA (LISA). The mission consists of three spacecraft, each of which orbits near one of the Sun-Earth Lagrange points (L3, L4 and L5), such that the array forms an almost equilateral triangle. The 3 spacecraft range interferometrically with one another with an arm length of about 260 million kilometers. The orbits have been optimized resulting in arm length changes of less than 0.00015 AU or, fractionally, less than 10^(-4) in twenty years, and relative Doppler velocities of the three spacecraft of less than 3 m/s. In this paper, we present an overview of the mission covering: the scientific aims, the sensitivity spectrum, the basic orbit configuration, the simulation and optimization of the spacecraft orbits, the deployment of ASTROD-GW formation, TDI (Time Delay Interferometry) and the payload. The science goals are the detection of GWs from (i) Supermassive Black Holes; (ii) Extreme-Mass-Ratio Black Hole Inspirals; (iii) Intermediate-Mass Black Holes; (iv) Galactic Compact Binaries and (v) Relic Gravitational Wave Background. For the purposes of primordial GW detection, a six spacecraft formation would be needed to enable the correlated detection of stochastic GWs. A brief discussion of the six spacecraft orbit optimization is also presented., Comment: 32 pages,9 figures, 2 tables,to be published in IJMPD vol. 22,1341004 (2013); in this version, references are added and typos corrected