The accelerated cosmic expansion could be due to dark energy within general relativity (GR), or modified gravity. It is of interest to differentiate between them, by using both the expansion history and the growth history. In the literature, it was proposed that the growth index γ is useful to distinguish these two scenarios. In this work, we consider the non-parametric reconstruction of the growth index γ as a function of redshift z from the latest observational data as of July 2018 via Gaussian Processes. We find that f (R) theories and dark energy models within GR (especially ΛCDM) are inconsistent with the results in the moderate redshift range far beyond 3σ confidence level. A modified gravity scenario different from f (R) theories is favored. However, these results can also be due to other non-trivial possibilities, in which dark energy models within GR (especially ΛCDM) and f (R) theories might still survive. In all cases, our results suggest that new physics is required.PACS numbers: 98.80.Es, 95.36.+x, 04.50.Kd

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...

In the literature, it was proposed that the growth index γ is useful to distinguish the scenarios of dark energy and modified gravity. In the present work, we consider the constraints on the growth index γ by using the latest observational data. To be model-independent, we use cosmography to describe the cosmic expansion history, and also expand the general γ(z) as a Taylor series with respect to redshift z or y-shift, y = z/(1 + z). We find that the present value γ0 = γ(z = 0) ≃ 0.42 (for most of viable f (R) theories) is inconsistent with the latest observational data at high confidence level (C.L.). On the other hand, γ0 ≃ 0.55 (for dark energy models in GR) can be consistent with the latest observational data at 1σ C.L. in 5 of the 9 cases under consideration, but is inconsistent beyond 2σ C.L. in the other 4 cases (while it is still consistent within the 3σ region). Thus, we can say nothing firmly about γ0 ≃ 0.55. We also find that a varying γ(z) is favored. 98.80.Es, 95.36.+x, 04.50.Kd