By transforming the geodesic equation of the Schwarzschild solution of the Einstein’s equation of gravity field to flat space-time for description, the revised Newtonian formula of gravity is obtained. The formula can also describe the motion of object with mass in gravity field such as the perihelion precession of the Mercury. The space-time singularity in the Einstein’s theory of gravity becomes the original point r = 0 in the Newtonian formula of gravity. The singularity problem of gravity in curved space-time is eliminated thoroughly. When the formula is used to describe the expansive universe, the revised Friedmann equation of cosmology is obtained. Based on it, the high red-shift of Ia supernova can be explained well. We do not need the hypotheses of the universe accelerating expansion and dark energy again. It is also unnecessary for us to assume that non-baryon dark material is 5 - 6 times more than normal baryon material in the universe if they really exist. The problem of the universal age can also be solved well. The theory of gravity returns to the traditional form of dynamic description and becomes normal one. The revised equation can be taken as the foundation of more rational cosmology

The paper proves that due to the existence of electromagnetic interaction, the experiments of LIGO cannot detect gravitational waves. This is also the reason why Weber's experiments of gravitational waves failed. In fact, the formulas of general relativity that gravitational waves affect distances are only suitable for particles in vacuum. LIGO experiments are carried out on the earth. The laser interferometers are fixed on the steel pipes on the earth's surface in the balanced state of electromagnetic force. Electromagnetic force is 10 40 times greater than gravity. Gravitational waves are too weak to overcome electromagnetic force and change the length of steel pipes. Without considering this factor, the design principle of LIGO experiment has serious problem. The experiments to detect gravitational waves should move to space to avoid the influence of electromagnetic interaction. Besides, LIGO experiments have the following problems. 1) No explosion source of gravitational waves is really founded. 2) The argument that the Einstein's theory of gravity is verified is a vicious circle and invalid in logic. 3) The results of experiments cause sharp contradiction for the energy currents of gravitational waves. The difference reaches to 1024 times and is unacceptable. 4) The method of numerical relativity causes great errors due to the existence of singularities. The errors are enlarged by the effect of butterfly due to the non-linearity of Einstein's equation of gravity. 5) The so-called change of length 10 −18 m between two glasses of interferometers detected in the experiment exceeds the ability of current technique. This kind of precise has entered micro-scalar. The uncertain principle of quantum mechanics makes it impossible. The signs appeared in LIGO experiments are not caused by distance change. 6) LIGO experiments have not detected gravitational waves. What detected may be the signs of disturbances coming from the middle region between two laser interferometers.

The true meaning of the constant in the Robertson-Walker metric is discussed when the scalar factor s the function of time. By strict calculation based on the Riemannian geometry, it is proved that the spatial curvature of the R-W metric is K=(κ-R²)/R² . The result indicates that the R-W metric has no constant curvature when R(t)≠0 and κ is not spatial curvature factor. We can only consider κ as an adjustable parameter with κ≠0 in general situations. The result is completely different from the current understanding which is based on the precondition that the scalar factor R(t) is fixed. Due to this result, many conclusions in the current cosmology such as the densities of dark material and dark energy should be re-estimated. In this way, we may overcome the current puzzling situation of cosmology thoroughly

In the classical Newtonian mechanics, the gravity fields of static thin loop and double spheres are two simple but foundational problems. However, in the Einstein's theory of gravity, they are not simple. In fact, we do not know their solutions up to now. Based on the coordinate transformations of the Kerr and the Kerr-Newman solutions of the Einstein's equation of gravity field with axial symmetry, the gravity fields of static thin loop and double spheres are obtained. The results indicate that, no matter how much the mass and density are, there are singularities at the central point of thin loop and the contact point of double spheres. What is more, the singularities are completely exposed in vacuum. Space near the surfaces of thin loop and spheres are highly curved, although the gravity fields are very weak. These results are inconsistent with practical experience and completely impossible. By reasonable analogy, black holes with singularity in cosmology and astrophysics are something illusive. Caused by the mathematical description of curved space-time, they do not exist in real world actually. If there are black holes in the universe, they can only be the types of the Newtonian black holes without singularities, rather than the Einstein's singularity black holes. In order to escape the puzzle of singularity thoroughly, the description of gravity should return to the traditional form of dynamics in flat space. The renormalization of gravity and the unified description of four basic interactions may be possible only based on the frame of flat space-time. Otherwise, theses problems can not be solved forever. Physicists should have a clear understanding about this problem.

This article presents a new type of whitening filter (allowing the "passing" of some noise sources) applied to process the data recorded in LIGO's GW150914 and GW151226 events. This new analysis shows that in the GW150914 event, the signals from the collision of two black holes are very similar to the 32.5 Hz noise sources observed in both of LIGO's detectors. It also points out that these 32.5 Hz noise sources are powered by a 30 Hz sub harmonic, coming from the 60 Hz power system. In the GW1226 event, the same analysis points out that the NR template is very similar to the 120 Hz noise source. Therefore, the signals recorded in these events were probably generated by some small changes with the 60 Hz frequency in the US power grid. This can be caused, for example, by a power variation in the DC link, which can appear in both detectors in the same 10 ms time window. As this kind of power grid occurrence did not change the voltage levels, it may have gone unnoticed by LIGO's electrical power supply's monitoring system.