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Recent cosmological observations show that the unknown energy element called dark energy dominates in the universe. In this letter, we investigate to what extent dark energy models influence supernova relic neutrino (SRN) spectra when the supernova rate could be determined by direct counting and discuss the possibility to distinguish dark energy models using future observation of SRN. We found that the total number of SRN events in GCG model will be larger than those in ΛCDM and holographic dark energy models by 20%. As a result, we find a possibility to distinguish GCG model from ΛCDM and holographic dark energy models using observation of SRN. SRN should be a unique probe into dark energy models and will play complementary roles to other observables.

We consider the possibility of observing the onset of the late time inflation of our patch of the Universe. The Hubble size criterion and the event horizon criterion are applied to several dark energy models to discuss the problem of future inflation of the Universe. We find that the acceleration has not lasted long enough to confirm the onset of inflation by present observations for the dark energy model with constant equation of state, the holographic dark energy model and the generalized Chaplygin gas (GCG) model. For the flat ΛCDM model with Ω_m0 = 0.3, we find that if we use the Hubble size criterion, we need to wait until the a_v which is the scale factor at the time when the onset of inflation is observed reaches 3.59 times of the scale factor a_T when the Universe started acceleration, and we need to wait until a_v = 2.3a_T to see the onset of inflation if we use the event horizon criterion. For the flat holographic dark energy model with d = 1, we find that a_v = 3.46a_T with the Hubble horizon and a_v = 2.34a_T with the event horizon, respectively. For the flat GCG model with the best supernova fitting parameter α = 1.2, we find that a_v = 5.50a_T with the Hubble horizon and a_v = 2.08a_T with the event horizon, respectively.

In this paper, we regard dilaton in Weyl-scaled induced gravitational theory as coupled quintessence, which is called DCQ model by us. Parametrization of the dark energy model is a good method by which we can construct the scalar potential directly from the effective equation of state function ω_σ(z) describing the properties of the dark energy. Applying this method to the DCQ model, we consider four parametrizations of ω(z) and investigate the features of the constructed DCQ potentials, which possess two different evolutive behaviors called "O" mode and "E" mode. Lastly, we comprise the results of the constructed DCQ model with those of quintessence model numerically.

The collapse dynamics of an inhomogeneous quasi-spherical star is investigated in the background of dark matter (DM) and dark energy (DE). The dark matter is taken in the usual form of dust cloud and for dark energy, anisotropic fluid is chosen. The gravitational collapse is studied in two different situations: (a) a simple choice of the metric coefficient, (b) the radial pressure is assumed to be zero. The role of dark energy in the formation of apparent horizon is studied and it is examined how dark energy modifies the collapsing process.

The energy density of the universe today may be dominated by the vacuum energy of a slowly rolling scalar field. Making a quantum expansion around such a time-dependent solution breaks fundamental symmetries of quantum field theory. We call this mechanism cosmological symmetry breaking and argue that it is different from the standard phenomenon of spontaneous symmetry breaking. We illustrate this with a toy scalar field theory, whose action displays a U(1) symmetry. We identify a symmetry, called pseudo-scale invariance, which sets the cosmological constant exactly equal to zero, both in classical and quantum theories. This symmetry is also broken cosmologically and leads to a nonzero vacuum or dark energy. The slow-roll condition along with the observed value of dark energy leads to a value of the background scalar field of the order of Planck mass. We also consider a U(1) gauge symmetry model. Cosmological symmetry breaking, in this case, leads to a nonzero mass for the vector field. We also show that a cosmologically broken pseudo-scale invariance can generate a wide range of masses.

We study the existence of black holes in a homogeneous and isotropic expanding Friedmann–Robertson–Walker (FRW) universe dominated by dark energy. We show that black holes exist in such a universe by considering some specific McVittie solutions, for which the FRW background satisfies the weak (but not the strong) energy condition.

Recently it was suggested that the dark energy maybe related to the well-known hierarchy between the Planck scale (~ 10¹⁹GeV) and the TeV scale. The same brane-world setup to address this hierarchy problem may also in principle address the smallness problem of dark energy. Specifically, the Planck-SM hierarchy ratio was viewed as a quantum gravity-related, dimensionless fine structure constant where various physical energy scales in the system are associated with the Planck mass through different powers of the 'gravity fine structure constant'. In this paper we provide a toy model based on the Randall-Sundrum geometry where SUSY-breaking is induced by the coupling between a SUSY-breaking Higgs field on the brane and the KK gravitinos. We show that the associated Casimir energy density indeed conforms with the dark energy scale.

Considering the general Lagrangian of k-essence models, we study and classify them through variables connected to the fluid equation of state parameter w_κ. This allows one to find solutions around which the scalar field describes a mixture of dark matter and cosmological constant-like dark energy, an example being the purely kinetic model proposed by Scherrer. Making the stronger assumption that the scalar field Lagrangian is exactly constant along solutions of the equation of motion, we find a general class of k-essence models whose classical trajectories directly describe a unified dark matter/dark energy (cosmological constant) fluid. While the simplest case of a scalar field with canonical kinetic term unavoidably leads to an effective sound speed c_s = 1, thereby inhibiting the growth of matter inhomogeneities, more general non-canonical k-essence models allow for the possibility that c_s≪1 whenever matter dominates.

In this paper we study the statefinder parameters for the tachyon dark energy model. There are two kinds of stable attractor solutions in this model. The statefinder diagrams characterize the properties of the tachyon dark energy model. Our results show that the evolving trajectories of the attractor solutions lie in the total region and pass through the LCDM fixed point, which is different from other dark energy model.

In this paper a variable generalized Chaplygin gas (VGCG) proposal for unification of dark matter and dark energy is considered, in which dark energy interacts with dark matter. The equation of state of the VGCG is given by p = -A₀a^-n/ρ^α, where a is the scale factor. By calculations some cosmological quantities such as density parameters of baryons, dark matter and dark energy as well as the deceleration parameter are all obtained. Furthermore, the transition from deceleration to acceleration is described and the interaction between dark energy and dark matter is considered in this model. We find the behavior of VGCG is similar to dust-like matter at early times and will be quintessence or phantom at late stage. In addition the evolution trajectory of the VGCG model in the statefinder parameter s-r plane is plotted and the discrimination between this scenario and the generalized Chaplygin gas (GCG) model is illustrated.

We study the statefinder parameter in the five-dimensional big bounce model, and apply it to differentiate the attractor solutions of quintessence and phantom field. It is found that the evolving trajectories of these two attractor solutions in the statefinder parameters plane are quite different, and that are different from the statefinder trajectories of other dark energy models.

In this paper we study the statefinder parameters for the coupled tachyon dark energy model which has two types of stable scaling solutions. It is found that the evolving trajectories of the solutions are different in the statefinder parameters plane. These trajectories lie in the two regions r > 1, s < 0 and r < 1, s > 0, and pass through the LCDM fixed point. So, through the statefinder diagnostic, we not only characterize the properties of the coupled tachyon dark energy model, but also show the difference from other dark energy model.

In this paper, two simple parametrized deceleration parameters and areconstrained by using the latest SNe Ia Gold dataset, observational Hubble data and their combination. It is found that the transition redshift from decelerated expansion to accelerated expansion z_T and current decelerated parameter values q₀ are consistent with each other in 1σ region by only using SNe Ia Gold dataset and observational Hubble data in three parametrizations respectively. By combining the SNe Ia Gold dataset and observational Hubble data together, a tight constraint is obtained. With this combined constraint, z_T is and with 1σ error in the parametrizations respectively.

To explain the cosmic speed up, brought to light by the recent SNIa and CMB observations, we propose the following: (a) In a spacetime endowed with a FRW metric, we choose an empirical scale factor that best explains the observations. (b) We assume a modified gravity, generated by an unspecified field Lagrangian, f(R). (c) We use the adopted empirical scale factor to work back retroactively to obtain f(R), hence the term "Inverse f(R)". (d) Next we consider the classic GR and a conventional FRW universe that, in addition to its known baryonic content, possesses a hypothetical "Dark Energy" component. We compare the two scenarios and find the density, the pressure, and the equation of the state of the Dark Energy required to make up for the differences between the conventional and the modified GR models.

In this paper, the 1σ confidence level of transition redshift and present deceleration parameter are studied using modified Chaplygin gas (MCG) model from recent observations: the 182 Gold SNe Ia, three-year WMAP, SDSS baryon acoustic peak and X-ray gas mass fraction in clusters. Concretely, the best fit values of the transition redshift and present deceleration parameter with the 1σ confidence level are and , which indicate the best fit values of z_T and q₀ for MCG case are surprisingly close to the central values given by Refs. 20 and 21. Furthermore, we plot the evolution of cosmological quantities from MCG model by using the best-fit parameters given by combining constraint, and compare them with ΛCDM model.

Various TeVeS-inspired and f(R)-inspired theories of gravity have added an interesting twist to the search for dark matter and vacuum energy, modifying the landscape of astrophysics day by day. These theories can be together called a Non-uniform Dark Energy fluid (a Nu-Lambda fluid or a VΛ fluid); a common thread of these theories, according of an up-to-date summary by HZL¹, is a non-uniform vector field, describing an uneven vacuum energy fluid. The so-called "alternative" gravity theories are in fact in the standard GR gravity framework except that the cosmological "constant" is replaced by a nontrivial non-uniform vacuum energy, which couples the effects of Dark Matter and Dark Energy together by a single field. Built initially bottom-up rather than top-down as most gravity theories, TeVeS-inspired theories are healthily rooted on empirical facts. Here we attempt a review of some sanity checks of these fast-developing theories from galaxy rotation curves, solar system constraints, and gravitational lensing. We will also discuss some theoretical aspects of these theories related to the vacuum energy, and point out some analogies with electromagnetism and the Casimir effect.

In order to investigate more features of the Brans–Dicke cosmology in the five-dimensional spacetime, we explore the solutions of its dynamical systems. A behavior of the universe in its early and late time by means of the scale factor is considered. As a result, we show that it is possible to avoid the big rip singularity and to cross the phantom divide line. Furthermore, we review the dark energy component of the universe and its agreement with the observation data for this 3-brane Brans–Dicke cosmology by means of the cosmological parameters.

Models where the accelerated expansion of our Universe is caused by a quintessence scalar field are reviewed. In the framework of high energy physics, the physical nature of this field is discussed and its interaction with ordinary matter is studied and explicitly calculated. It is shown that this coupling is generically too strong to be compatible with local tests of gravity. A possible way out, the chameleon effect, is also briefly investigated.

I describe and critically evaluate a variety of methods, from simple parametrizations to non-parametric methods, to model the background expansion history in the presence of dark energy. Motivated by these approaches, I review the prospects of determining the properties of dark energy with future experiments, in particular the Dark Energy Survey (DES) and SuperNova/Acceleration Probe (SNAP). Finally, I outline the importance of being able to constrain whole classes of dark energy models, and present recent work that comprehensively studied the observational signature of general scalar field models.

In this review article, we go over some of the consequences that the interactions between dark energy and dark matter may have for the dynamics of the Universe and its observational signatures.