Observations provide increasingly strong evidence that the universe is accelerating. This revolutionary advance in cosmological observations confronts theoretical cosmology with a tremendous challenge, which it has so far failed to meet. Explanations of cosmic acceleration within the framework of general relativity are plagued by difficulties. General relativistic models are nearly all based on...

Given the expansion rate of the universe in terms of the Hubble constant H0 = (ȧ/a)0, one can define a critical energy density ρc = 3H 2 0/8πG which is required to make the spatial sections of the universe compact. It is convenient to measure the energy densities of the different species, which drive the expansion of the universe, in terms of this critical density using the dimensionless parame...

There is now strong observational evidence that the expansion of the Universe is accelerating. The standard explanation invokes an unknown "dark energy" component. But such scenarios are faced with serious theoretical problems, which has led to increased interest in models where instead general relativity is modified in a way that leads to the observed accelerated expansion. The question then a...

Explanations of the late-time cosmic acceleration within the framework of general relativity are plagued by difficulties. General relativistic models are mostly based on a dark energy field with fine-tuned, unnatural properties. There is a great variety of models, but all share one feature in common – an inability to account for the gravitational properties of the vacuum energy, and a failure t...

This phenomenological review stresses the distinction between kinematics), the description of the recently inflationary universe (cosmography), and dynamics, the mechanism driving this accelerating expansion. Because the homogeneous expansion history H(z) of the universe measures only kinematic variables, it cannot fix the underlying dynamics: cosmographic measurements of the homogeneous univer...

In (T. Ma and S. Wang. Gravitational field equations and theory of dark matter and dark energy, Discrete and Continuous Dynamical Systems, Ser. A, 34(2): 335–366, 2014; arXiv:1206.5078v2), a new set of gravitational field equations are derived based only on 1) the Einstein principle of general relativity, and 2) the principle of interaction dynamics, due to the the presence of dark energy and d...

We calculate the time delays of neutrinos emitted in gamma ray bursts due to the effects of neutrino mass and quantum gravity using a time dependent Hubble constant which can significantly change the naive results presented hitherto in the literature for large redshifts, and gives some sensitivity to the details of dark energy. We show that the effects of neutrino mass, quantum gravity and dark...

In this letter, dark energy is obtained using dual role of the Ricci scalar (physical as well as geometrical role of the Ricci scalar curvature) in a natural way without any input in the theory for it. In contrast to other models, where an idea for dark energy is introduced in the beginning of the theory, here it emerges from the gravitational sector spontaneously. Dark energy density, obtained...