Ding-Fang Zeng

We derive the metric of an expanding universe with zero accelerations by pure kinematic method. By doing so we expatiate physics related with co-moving coordinate system in details. The most important discovery or our study is, in an expanding universe with zero accelerations, the red-shift of photons from distance galaxies is determined by the co-moving coordinate of the source galaxy instead of the scale factor's time dependence. Our discovery is consistent with the current observed super-novaes's luminosity-distance v.s. red-shift relations.

In 1+1 dimensional case, Einstein equation cannot give us any information on the evolution of the universe because the Einstein tensor of the system is identically zero. We study such a 1+1 dimensional cosmology and find the metric of it according to cosmological principle and special relativity, but the results contradict the usual expression of cosmological principle of standard cosmology. So we doubt in 1+3 dimensional case, cosmological principle is expressed faithfully by standard cosmology.

This is a second paper of a series of two. In this paper, we directly correct the problem pointed out in the first paper of this series, dark energy does not cluster on the scale of galaxy clusters, but the current describing the flowing of dark energies outside the clusters is ignored in almost all the previous papers. We set up and solve a first order differential equation which describes the evolution of the clusters in a back ground universe containing dark energies. From the solution we extract the key parameters of the model and find them depending on the equation of state coefficients of dark energies rather non-trivially. We then apply the results in Press-Scheter theory and calculate the number density of galaxy clusters and its evolutions, we find the observable quantities are strongly affected by the equation of state coefficients of dark energies.

We ask if the conventional variable separation techniques in the studying of standard cosmology and the collapsing of extremely dense stars introduce Newton's absolute space-time concepts. If this is the case, then a completely relative cosmology is needed. We build the basic frame-works for such a cosmology and illustrate that, the observed luminosity-distance v.s. red-shift relations of supernovaes can be explained naturally even without any conception of dark energies.

In existing literatures about the top-hat spherical collapse model of galaxy clusters formation in cosmology containing dark energies, dark energies are usually assumed not to cluster on this scale. But all these literatures ignored the current describing the flowing of dark energies outside the clusters which should exist under this assumption, so the conclusions of these literatures are worth further explorations. In this paper we study this model in QCDM or Phantom-CDM cosmologies(flat) by assuming that dark energies will cluster synchronously with ordinary matters on the scale of galaxy clusters so the dark energy current flowing outside the clusters does not exist at all and find that in this case, the key parameters of the model exhibit rather non-trivial and remarkable dependence on the equation of state coefficients of dark energies. We then apply the results in Press-Scheter theory and calculate the number density of galaxy clusters and its evolutions. We find that this two quantities are both affected exponentially by the equation of state coefficients of dark energies. We leave the study of this model with the assumption that dark energies do not cluster on the scale of galaxy clusters at all as the topic of another paper where similar conclusions will be obtained also.

We provided a gedanken experiment and argued that since observers inside a given Hubble volume could not detect the super horizon perturbation modes as real perturbations, these modes could only affect the average value of the cosmic microwave background (CMB), but not its anisotropy properties (CMBA) in that Hubble volume.