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As is well known, one can explain the current cosmic acceleration by considering an inhomogeneous and/or anisotropic universe (which violates the cosmological principle), without invoking dark energy or modified gravity. The well-known one of this kind of models is the so-called Lema\^{\i}tre-Tolman-Bondi (LTB) void model, in which the universe is spherically symmetric and radially inhomogeneous, and we are living in a locally underdense void centered nearby our location. In the present work, we test various LTB void models with some old high redshift objects (OHROs). Obviously, the universe cannot be younger than its constituents. We find that an unusually large $r_0$ (characterizing the size of the void) is required to accommodate these OHROs in LTB void models. There is a serious tension between this unusually large $r_0$ and the much smaller $r_0$ inferred from other observations (e.g. SNIa, CMB and so on). However, if we instead consider the lowest limit 1.7\,Gyr for the quasar APM 08279+5255 at redshift $z=3.91$, this tension could be greatly alleviated., Comment: 17 pages, 9 figures, revtex4; v2: discussions added, Phys. Lett. B in press; v3: published version

The so-called Einstein-Aether theory is General Relativity coupled (at second derivative order) to a dynamical unit time-like vector field (the aether). It is a Lorentz-violating theory, and gained much attention in the recent years. In the present work, we study the cosmological evolution of Einstein-Aether models with power-law-like potential, by using the method of dynamical system. In the case without matter, there are two attractors which correspond to an inflationary universe in the early epoch, or a de Sitter universe in the late time. In the case with matter but there is no interaction between dark energy and matter, there are only two de Sitter attractors, and no scaling attractor exists. So, it is difficult to alleviate the cosmological coincidence problem. Therefore, we then allow the interaction between dark energy and matter. In this case, several scaling attractors can exist under some complicated conditions, and hence the cosmological coincidence problem could be alleviated., 15 pages, 6 tables, revtex4; v2: discussions added, Gen. Rel. Grav. in press; v3: published version

The current accelerated expansion of our universe could be due to an unknown energy component with negative pressure (dark energy) or a modification to general relativity (modified gravity). On the other hand, recently warm dark matter (WDM) remarkably rose as an alternative of cold dark matter (CDM). Obviously, it is of interest to distinguish these different types of models. In fact, many attempts have been made in the literature. However, in the present work, we show that WDM, modified gravity and coupled CDM form a trinity, namely, they are indistinguishable by using the cosmological observations of both cosmic expansion history and growth history. Therefore, to break this degeneracy, the other complementary probes beyond the ones of cosmic expansion history and growth history are required., 13 pages, 4 figures, revtex4; v2: discussions added, Phys. Rev. D in press; v3: published version

As is well known, in mathematics, any function could be approximated by the Pad\'e approximant. The Pad\'e approximant is the best approximation of a function by a rational function of given order. In fact, the Pad\'e approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Pad\'e approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Pad\'e approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Pad\'e approximant could be an useful tool in cosmology, and it deserves further investigation., Comment: 19 pages, 8 figures, 1 table, revtex4; v2: discussions added, accepted for publication in JCAP; v3: published version