Abstract:
We study the robustness of the quintessence tracking scenario in the context of more general cosmological models that derive from high-energy physics. We consider the effects of inclusion of multiple scalar fields, corrections to the Hubble expansion law (such as those that arise in brane cosmological models), and potentials that decay with expansion of the Universe. We find that in a successful tracking quintessence model the average equation of state must remain nearly constant. Overall, the conditions for successful tracking become more complex in these more general settings. Tracking can become more fragile in presence of multiple scalar fields, and more stable when temperature dependent potentials are present. Interestingly though, most of the cases where tracking is disrupted are those in which the cosmological model is itself non-viable due to other constraints. In this sense tracking remains robust in models that are cosmologically viable.

Abstract:
New solutions to the non perturbative renormalization group equation for the effective action of a scalar field theory in the Local Potential Approximation having the exponential form $e^{\pm\phi}$ are found. This result could be relevant for those quintessence phenomenological models where this kind of potentials are already used, giving them a solid field theoretical derivation. Other non perturbative solutions, that could also be considered for the quintessence scenario, are also found. Apart from this particular cosmological application, these results could be relevant for other models where scalar fields are involved, in particular for the scalar sector of the standard model.

Abstract:
The stability of scalar quintessence potentials under quantum fluctuations is investigated for both uncoupled models and models with a coupling to fermions. We find that uncoupled models are usually stable in the late universe. However, the coupling to fermions is severely restricted. We check whether a graviton induced fermion-quintessence coupling is compatible with this restriction.

Abstract:
The stability of scalar quintessence potentials under quantum fluctuations is investigated both for uncoupled models and models with a coupling to fermions. We find that uncoupled models are usually stable in the late universe. However, a coupling to fermions is severely restricted. We check whether a graviton induced fermion-quintessence coupling is compatible with this restriction.

Abstract:
We report a significant finding in Quintessence theory that the the scalar fields with tracker potentials have a model-independent scaling behaviour in the expanding universe. So far widely discussed exponential,power law or hyperbolic potentials can simply mimic the tracking behaviour over a limited range of redshift. In the small redshift range where the variation of the tracking parameter $\epsilon$ may be taken to be negligible, the differential equation of generic potentials leads to hyperbolic sine and hyperbolic cosine potentials which may approximate tracker field in the present day universe. We have plotted the variation of tracker potential and the equation of state of the tracker field as function of the redshift $z$ for the model-independent relation derived from tracker field theory; we have also plotted the variation of $V(\Phi)$ in terms of the scalar field $\Phi$ for the chosen hyperbolic cosine function and have compared with the curves obtained by reconstruction of $V(\phi)$ from the real observational data from the supernovae.

Abstract:
We propose an holographic quintessence and tachyon models of dark energy. The correspondence between the quintessence and tachyon energy densities with the holographic density, allows the reconstruction of the potentials and the dynamics for the quintessence and tachyon fields, in flat FRW background. The proposed infrared cut-off for the holographic energy density works for two cases of the constant $\alpha$: for $\alpha<1$ we reconstructed the holographic quintessence model in the region before the $\omega=-1$ crossing for the EoS parameter. The cosmological dynamics for $\alpha>1$ was also reconstructed for the holographic quintessence and tachyon models.

Abstract:
In this paper, we investigate the quintessence models with an oscillating equation of state (EOS) and its potentials. From the constructed potentials, which have an EOS of $\omega_{\phi}=\omega_0+\omega_1\sin z$, we find that they are all the oscillating functions of the field $\phi$, and the oscillating amplitudes decrease (or increase) with $\phi$. From the evolutive equation of the field $\phi$, we find that this is caused by the expansion of the universe. This also makes it very difficult to build a model whose EOS oscillates forever. However one can build a model with EOS oscillating for a certain period of time. Then we discuss three quintessence models, which are the combinations of the invert power law functions and the oscillating functions of the field $\phi$. We find that they all follow the oscillating EOS.

Abstract:
We demonstrate how exponential potentials that could arise in the early Universe as a result of Kaluza-Klein type compactifications of string theory, can lead to cosmological solutions which correspond to the currently observed accelerating Universe. The idea is simple, relying solely on the known scaling properties associated with exponential potentials. In particular we show that the existence of stable attractor solutions implies that the results hold for a wide range of coupling constants and initial conditions.

Abstract:
We have investigated the generality of inflation (the probability of inflation in other words) in closed FRW models for a wide class of quintessence potentials. It is shown that inflation is not suppressed for most of them and for a wide enough range of their parameters. It allows us to decide inflation is common enough even in the case of closed Universe.

Abstract:
We present general exact solutions for two classes of exponential potentials in scalar field models for quintessence. The coupling is minimal and we consider only dust and scalar field. To some extent, it is possible to reproduce experimental results from supernovae.