The cosmological principle assumes that the universe is homogeneous and isotropic on cosmic scales. There exist many works testing the cosmic homogeneity and/or the cosmic isotropy of the universe in the literature. In fact, some observational hints of the cosmic anisotropy have been claimed. However, we note that the paucity of the data considered in the literature might be responsible for the "found" cosmic anisotropy. So, it might disappear in a large enough sample. Very recently, the Pantheon sample consisting of 1048 type Ia supernovae (SNIa) has been released, which is the largest spectroscopically confirmed SNIa sample to date. In the present work, we test the cosmic anisotropy in the Pantheon SNIa sample by using three methods, and hence the results from different methods can be cross-checked. All the results obtained by using the hemisphere comparison (HC) method, the dipole fitting (DF) method and HEALPix suggest that no evidence for the cosmic anisotropy is found in the Pantheon SNIa sample. 98.80.Es, 95.36.+x *

In the recent years, the field of Fast Radio Bursts (FRBs) is thriving and growing rapidly. It is of interest to study cosmology by using FRBs with known redshifts. In the present work, we try to test the possible cosmic anisotropy with the simulated FRBs. We find that at least 2800, 190, 100 FRBs are competent to find the cosmic anisotropy with a dipole amplitude 0.01, 0.03, 0.05, respectively. Unfortunately, even 10000 FRBs are not competent to find the tiny cosmic anisotropy with a dipole amplitude of O(10 −3 ). On the other hand, at least 20 FRBs with known redshifts are competent to find the cosmic anisotropy with a dipole amplitude 0.1. We expect that such a big cosmic anisotropy can be ruled out by using only a few tens of FRBs with known redshifts in the near future.PACS numbers: 98.80.Es, 95.36.+x, 98.70.Dk

The cosmological principle is one of the cornerstones in modern cosmology. It assumes that the universe is homogeneous and isotropic on cosmic scales. Both the homogeneity and the isotropy of the universe should be tested carefully. In the present work, we are interested in probing the possible preferred direction in the distribution of type Ia supernovae (SNIa). To our best knowledge, two main methods have been used in almost all of the relevant works in the literature, namely the hemisphere comparison (HC) method and the dipole fitting (DF) method. However, the results from these two methods are not always approximately coincident with each other. In this work, we test the cosmic anisotropy by using these two methods with the Joint Light-Curve Analysis (JLA) and simulated SNIa datasets. In many cases, both methods work well, and their results are consistent with each other. However, in the cases with two (or even more) preferred directions, the DF method fails while the HC method still works well. This might shed new light on our understanding of these two methods.PACS numbers: 98.80.Es, 95.36.+x *

Since Lorentz invariance plays an important role in modern physics, it is of interest to test the possible Lorentz invariance violation (LIV). The time-lag (the arrival time delay between light curves in different energy bands) of Gamma-ray bursts (GRBs) has been extensively used to this end. However, to our best knowledge, one or more particular cosmological models were assumed a priori in (almost) all of the relevant works in the literature. So, this makes the results on LIV in those works model-dependent and hence not so robust in fact. In the present work, we try to avoid this problem by using a model-independent approach. We calculate the time delay induced by LIV with the cosmic expansion history given in terms of cosmography, without assuming any particular cosmological model. Then, we constrain the possible LIV with the observational data, and find weak hints for LIV.As is well known, Lorentz invariance plays an important role in modern physics. Actually, it is one of the foundation stones of special/general relativity and particle physics, which have been well tested in solar system and colliders. If Lorentz invariance is violated, the pillars of modern physics will be shocked and new physics is needed. So, it is of interest to test the possible Lorentz invariance violation (LIV) with various terrestrial experiments and astrophysical/cosmological observations [1,2].In the literature, there exist many theories inducing LIV. Here we are interested in the possible violation of Lorentz invariance induced by quantum gravity (QG). Commonly, most theories of QG (e.g. string theory, loop quantum gravity, doubly special relativity) predict that LIV might happen on high energy scales [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]49]. The propagation of high energy photons through the spacetime foam might exhibit a non-trivial dispersion relation in vacuum (which should be regarded as a non-trivial medium in QG). The deformed dispersion relation for photons usually takes the form, where E QG is the effective QG energy scale, f is a dimensionless function depending on the particular QG model, c is the limiting speed of light on low energy scales, p and E are the momentum and energy of photons, respectively. On low energy scales E ≪ E QG , one can consider a series expansion of this dispersion relation, namely. Such a series expansion corresponds to an energy-dependent speed ofSo, the high and low energy photons will not reach us at the same time. A signal of energy E that travels a distance L acquires a time delay (measured with respect to the ordinary case of an energy-independent speed c), namely ∆t ∼ ξ(E/E QG )(L/c). Although the QG effect is expected to be very weak (since E QG is typically close to the Planck energy scale E P ∼ 10 19 GeV), a very long distance L can still make it testable. In the pioneer work [3], Amelino-Camelia et al. proposed that Gamma-ray bursts (GRBs) at a cosmological distance can be used to test the possible LIV, while time-lag (the arrival time delay between light curves in diff...

AdS black holes show richer transition behaviors in extended phase space by assuming the cosmological constant and its conjugate quantity to behave like thermodynamic pressure and thermodynamic volume. We study the extended thermodynamics of charged dilatonic AdS black holes in a class of Einstein-Maxwell-dilaton theories that can be embedded in gauged supergravities in various dimensions. We find that the transition behaviors of higher dimensional dilatonic AdS black holes are different from the four dimensional counterparts, and new transition behaviors emerge in higher dimensions. First, there exists a standard Van der Waals transition only in a five dimensional dilatonic AdS black hole with two equal charges. Second, there emerges a new phase transition branch in negative pressure region in six and seven dimensional dilatonic black holes with two equal charges. Third, there emerge transition behaviors in higher dimensional black hole with single charge cases, which are absent in four dimensions.