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Gamma-ray bursts (GRBs), have been widely used as distance indicators to measure the cosmic expansion and explore the nature of dark energy. A popular method adopted in previous works is to calibrate the luminosity relations which are responsible for distance estimation of GRBs with more primary (low redshift) cosmic distance ladder objects, type Ia supernovae (SNe Ia). Since distances of SNe Ia in all SN Ia samples used to calibrate GRB luminosity relations were usually derived from the global fit in a specific cosmological model, the distance of GRB at a given redshift calibrated with matching SNe Ia was still cosmological-model-dependent. In this paper, we first directly determine the distances of SNe Ia with the Angular Diameter Distances (ADDs) of galaxy clusters without any assumption for the background of the universe, and then calibrate GRB luminosity relations with our cosmology-independent distances of SNe Ia. The results suggest that, compared to the previous original manner where distances of SNe Ia used as calibrators are determined from the global fit in a particular cosmological model, our treatments proposed here yield almost the same calibrations of GRB luminosity relations and the cosmological implications of them do not suffer any circularity. [ABSTRACT FROM AUTHOR]

Because of the dynamical equivalence between the f(R) gravity and the Brans-Dicke theory, the dynamical equation in the f(R) gravity is suggested to be derived from a view point of thermodynamics here. By a conformal transformation, the Brans-Dicke theory in the Jordan frame could be expressed as a minimal coupling scalar field theory in Einstein frame. Using the entropy-area relation $d\tilde{S} = d\tilde{A}/4 G$, the correct Friedmann equations could be gotten in both frames. Furthermore, we also discuss the corresponding generalized Misner-Sharp energies for theoretical consistence. [ABSTRACT FROM AUTHOR]

For the use of gamma-ray bursts (GRBs) to probe cosmology in a cosmology-independent way, a new method has been proposed to obtain luminosity distances of GRBs by interpolating directly from the Hubble diagram of SNe Ia, and then calibrating GRB relations at high redshift. In this paper, following the basic assumption in the interpolation method that objects at the same redshift should have the same luminosity distance, we propose another approach to calibrate GRB luminosity relations with cosmographic fitting directly from SN Ia data. In cosmography, there is a well-known fitting formula which can reflect the Hubble relation between luminosity distance and redshift with cosmographic parameters which can be fitted from observation data. Using the Cosmographic fitting results from the Union set of SNe Ia, we calibrate five GRB relations using GRB sample at z ≤ 1.4 and deduce distance moduli of GRBs at 1.4 < z ≤ 6.6 by generalizing above calibrated relations at high redshift. Finally, we constrain the dark energy parameterization models of the Chevallier-Polarski-Linder (CPL) model, the Jassal-Bagla-Padmanabhan (JBP) model and the Alam model with GRB data at high redshift, as well as with the cosmic microwave background radiation (CMB) and the baryonic acoustic oscillation (BAO) observations, and we find the ΛCDM model is consistent with the current data in 1-σ confidence region. [ABSTRACT FROM AUTHOR]

A new conception is proposed in [E. P. Verlinde, arXiv:1001.0785 [hep-th] and [T. Padmanabhan, Mod. Phys. Lett. A25 (2010) 1129] that gravity is one kind of entropic force. In this letter, we try to discuss its applications to the modified gravities by using three different corrections to the area law of entropy which are derived from the quantum effects and extra dimensions. According to the assumption of holographic principle, the number of bits N which is related to the equipartition law of energy is modified. Then, the modified law of Newton's gravity and the modified Friedmann equations are obtained by using the new notion. By choosing suitable parameters, the modified area law of entropy leads to de Sitter solutions which can be used to explain the accelerating expansion of our universe. It suggests that the accelerating phase in our universe may be an emergent phenomenon based on holographic principle and thermodynamics. [ABSTRACT FROM AUTHOR]

Inspired by the holographic principle, we suggest that the density of dark energy is proportional to the spatial Ricci scalar curvature (SRDE). Such a model is phenomenologically viable. The best fit values of its parameters at 68% confidence level are found to be Ωm 0 = 0.259±0.016 and α = 0.261±0.0122, constrained from the Union+CFA3 sample of 397 SNIa and the BAO measurement. We find that the equation of state of SRDE crosses -1 at z ≃ -0.14. The present value of the deceleration parameter q(z) for SRDE is found to be qz = 0~-0.85. The phase transition from deceleration to acceleration of the Universe for SRDE occurs at the redshift zq = 0~0.4. After studying the perturbation of each component of the Universe, we show that the matter power spectra and cosmic microwave background temperature anisotropy are slightly affected by SRDE, compared with ΛCDM. [ABSTRACT FROM AUTHOR]

Hybrid Chaplygin gas model is put forward, in which the gases play the role of dark energy. For this model the coincidence problem is greatly alleviated. The effective equation of state of the dark energy may cross the phantom divide w = -1. Furthermore, the crossing behavior is decoupled from any gravity theories. In the present model, w < -1 is only a transient behavior. There is a de Sitter attractor in the future infinity. Hence, the big rip singularity, which often afflicts the models with matter whose effective equation of state less than -1, naturally disappears. There exist stable scaling solutions, both at the early universe and the late universe. We discuss the perturbation growth of this model. We find that the index is consistent with observations. [ABSTRACT FROM AUTHOR]

Various astronomical observations have been consistently making a strong case for the existence of a component of dark energy with negative pressure in the universe. It is now necessary to take the dark energy component(s) into account in gravitational lensing statistics and other cosmological tests. By using the comoving distance we derive analytic but simple expressions for the optical depth of multiple image, the expected value of image separation and the probability distribution of image separation caused by an assemble of singular isothermal spheres in general FRW cosmological models with dark energy component(s). We also present the kinematical and dynamical properties of these kinds of cosmological models and calculate the age of the universe and the distance measures, which are often used in classical cosmological tests. In some cases we are able to give formulae that are simpler than those found elsewhere in the literature, which could make the cosmological tests for dark energy component(s) more convenient. [ABSTRACT FROM AUTHOR]

By using the comoving distance, we derive an analytic expression for the optical depth of gravitational lensing, which depends on the redshift to the source and the cosmological model characterized by the cosmic mass density parameter Ω[sub m], the dark energy density parameter Ω[sub x]. and its equation of state ω[sub x] = p[sub x]/ρ[sub x]. It is shown that, the larger the dark energy density and the more negative its pressure, the higher is the gravitational lensing probability. This fact can provide an independent constraint for dark energy. [ABSTRACT FROM AUTHOR]

The Wheeler–DeWitt equation for the induced gravity theory is constructed in the mini superspace approximation, and then solved using the WKB method under three types of boundary condition proposed respectively by Hartle & Hawking (“no boundary”), Linde and Vilenkin (“tunneling from nothing”). It is found that no matter how the gravitational and cosmological “constants” vary in the classical models, they will acquire constant values when the universe comes from quantum creation, and that, in particular, the resulting tunneling wave function under the Linde or Vilenkin boundary condition reaches its maximum value if the cosmological constant vanishes. [ABSTRACT FROM AUTHOR]