Constraints on Horndeski Theory Using the Observations of Nordtvedt Effect, Shapiro Time Delay and Binary Pulsars

Alternative theories of gravity not only modify the polarization contents of the gravitational wave, but also affect the motions of the stars and the energy radiated away via the gravitational radiation. These aspects leave imprints in the observational data, which enables the test of General Relativity and its alternatives. In this work, the Nordtvedt effect and the Shapiro time delay are calculated in order to constrain Horndeski theory using the observations of lunar laser ranging experiments and Cassini time-delay data. The effective stress-energy tensor is also obtained using the method of Isaacson. Gravitational wave radiation of a binary system is calculated, and the change of the period of a binary system is deduced for the elliptical orbit. These results can be used to set constraints on Horndeski theory with the observations of binary systems, such as PSR J1738+0333. Constraints have been obtained for some subclasses of Horndeski theory, in particular, those satisfying the gravitational wave speed limits from GW170817 and GRB 170817A.Comment: 17 pages, 1 figure. Correct typos, add new references. Match the published versio

Strong Equivalence Principle and Gravitational Wave Polarizations in Horndeski Theory

The relative acceleration between two nearby particles moving along accelerated trajectories is studied, which generalizes the geodesic deviation equation. The polarization content of the gravitational wave in Horndeski theory is investigated by examining the relative acceleration between two self-gravitating particles. It is found out that the longitudinal polarization exists no matter whether the scalar field is massive or not. It would be still very difficult to detect the enhanced longitudinal polarization with the interferometer, as the violation of the strong equivalence principle of mirrors used by interferometers is extremely small. However, the pulsar timing array is promised to relatively easily detect the effect of the violation as neutron stars have large self-energy. The advantage of using this method to test the violation of the strong equivalence principle is that neutron stars are not required to be present in the binary systems.Comment: 25 pages, 2 figures. Matched the published versio

Gravitational Wave Polarizations in f(R)f(R) Gravity and Scalar-Tensor Theory

The detection of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory opens a new era to use gravitational waves to test alternative theories of gravity. We investigate the polarizations of gravitational waves in $f(R)$ gravity and Horndeski theory, both containing scalar modes. These theories predict that in addition to the familiar $+$ and $\times$ polarizations, there are transverse breathing and longitudinal polarizations excited by the massive scalar mode and the new polarization is a single mixed state. It would be very difficult to detect the longitudinal polarization by interferometers, while pulsar timing array may be the better tool to detect the longitudinal polarization.Comment: 10 pages, 3 figures, contribution to the proceedings of the International Conference on Gravitation : Joint Conference of ICGAC-XIII and IK1

Polarizations of Gravitational Waves in Horndeski Theory

We analyze the polarization content of gravitational waves in Horndeski theory. Besides the familiar plus and cross polarizations in Einstein's General Relativity, there is one more polarization state which is the mixture of the transverse breathing and longitudinal polarizations.The additional mode is excited by the massive scalar field. In the massless limit, the longitudinal polarization disappears, while the breathing one persists. The upper bound on the graviton mass severely constrains the amplitude of the longitudinal polarization, which makes its detection highly unlikely by the ground-based or space-borne interferometers in the near future. However, pulsar timing arrays might be able to detect the polarization excited by the massive scalar field. Since additional polarization states appear in alternative theories of gravity, the measurement of the polarizations of gravitational waves can be used to probe the nature of gravity. In addition to the plus and cross states, the detection of the breathing polarization means that gravitation is mediated by massless spin 2 and spin 0 fields, and the detection of both the breathing and longitudinal states means that gravitation is propagated by the massless spin 2 and massive spin 0 fields.Comment: 15 two column pages, 6 captioned figures, EPJC in pres

Spatio-Temporal Analysis of Sea Surface Temperature in the East China Sea Using TERRA/MODIS Products Data

Sea surface temperature (SST) is an important parameter in determining the atmospheric and oceanic circulations, and satellite thermal infrared remote sensing can obtain the SST with very high spatio-temporal resolutions. The study first validated the accuracy of TERRA MODIS SST daytime and nighttime products with the timing SST measurements from the ships in the East China Sea (ECS) in February, May, August and November, 2001, and then the daily variation of daytime and nighttime SST difference was analyzed. Using 16-year MODIS SST monthly products data from February 2000 to January 2016, when all SST monthly products in February, May, August and November were averaged respectively, the seasonal spatial distribution pattern of SST in the ECS was discovered. After monthly sea surface temperature anomaly was finally processed by the empirical orthogonal function (EOF), the interannual variability of SST in the ECS was discussed. The results show that the MODIS SST daily products have a good accuracy with a mean absolute percentage error (MAPE) below 5%. The SST difference between day and night is the largest in winter, followed by spring, then for autumn and the smallest in summer, while the diurnal SST difference is very low for the same season in the different seas. The SST in the ECS displays the obvious seasonal spatial distribution pattern, in which the SST of winter is gradually increasing from north to south, while local temperature difference is the largest for 26.5°C in a year. In comparison, the SST in summer tends uniform and the difference is not more than 5°C in the whole sea. From the EOF analysis of SST anomaly, the interannual variability of SST in the ECS is affected by the East Asian monsoon, the latitudinal difference of solar radiation, the offshore circulation and the submarine terrain

Gravitational waves in Einstein-{\AE}ther theory and generalized TeVeS theory after GW170817

In this paper, the polarization contents of Einstein-\ae ther theory and the generalized TeVeS theory are studied. The Einstein-\ae ther theory has five polarizations, while the generalized TeVeS theory has six. In particular, transverse and longitudinal breathing polarization are mixed. The~possibility of using pulsar timing arrays to detect the extra polarizations in Einstein-\ae{}ther theory was also investigated. The analysis showed that different polarizations cannot be easily distinguished by using pulsar timing arrays in this theory. For generalized TeVeS theory, one of the propagating modes travels much faster than the speed of light due to the speed bound set by GW170817. In some parameter subspaces, the strong coupling does not take place, so this theory is excluded.Comment: 9 pages, 3 figures. Talk given in International Conference on Quantum Gravity held in SUSTech, Shenzhen, China. Matches the published versio

The Polarizations of Gravitational Waves

The direct detection of gravitational waves by LIGO/Virgo opened the possibility to test General Relativity and its alternatives in the high speed, strong field regime. Alternative theories of gravity generally predict more polarizations than General Relativity, so it is important to study the polarization contents of theories of gravity to reveal the nature of gravity. In this talk, we analyzed the polarizations contents of Horndeski theory and $f(R)$ gravity. We found out that in addition to the familiar plus and cross polarizations, a \emph{massless} Horndeski theory predicts an extra transverse polarization, and there is a mix of the pure longitudinal and transverse breathing polarizations in the \emph{massive} Horndeski theory and $f(R)$ gravity. It is possible to use pulsar timing arrays to detect the extra polarizations in these theories. We also pointed out that the classification of polarizations using Newman-Penrose variables cannot be applied to the massive modes. It cannot be used to classify polarizations in Einstein-\ae ther theory or generalized TeVeS theory, either.Comment: 20 pages, 4 figures, a talk given in International Conference on Quantum Gravity held in SUSTech, Shenzhen, Chin