Search for Tracker Potentials in Quintessence Theory

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.Comment: 11 pages, 3 figures, late

Quintessence Model and Observational Constraints

The recent observations of type Ia supernovae strongly support that the universe is accelerating now and decelerated in the recent past. By assuming a general relation between the quintessence potential and the quintessence kinetic energy, a general relation is found between the quintessence energy density and the scale factor. The potential includes both the hyperbolic and the double exponential potentials. A detailed analysis of the transition from the deceleration phase to the acceleration phase is then performed. We show that the current constraints on the transition time, the equation of state and the energy density of the quintessence field are satisfied in the model.Comment: update references,add acknowledgements and correct some errors, accepted for publication in class. and quant. gra

Phenomemology of a Realistic Accelerating Universe Using Tracker Fields

We present a realistic scenario of tracking of scalar fields with varying equation of state. The astrophysical constraints on the evolution of scalar fields in the physical universe are discussed. The nucleosynthesis and the galaxy formation constraints have been used to put limits on $\Omega_\phi$ and estimate $\epsilon$ during cosmic evolution. Interpolation techniques have been applied to estimate $\epsilon\simeq0.772$ at the present epoch. The epoch of transition from matter to quintessence dominated era and consequent onset of acceleration in cosmic expansion is calculated and taking the lower limit $\Omega_n^0 = 0.2$ as estimated from $SN_e I_a$ data, it is shown that the supernova observations beyond redshift $z=1$ would reveal deceleration in cosmic expansion.Comment: 10 pages, 4 figures, late

Genesis of Dark Energy: Dark Energy as Consequence of Release and Two-stage Tracking Cosmological Nuclear Energy

Recent observations on Type-Ia supernovae and low density ($\Omega_{m} = 0.3$) measurement of matter including dark matter suggest that the present-day universe consists mainly of repulsive-gravity type `exotic matter' with negative-pressure often said `dark energy' ($\Omega_{x} = 0.7$). But the nature of dark energy is mysterious and its puzzling questions, such as why, how, where and when about the dark energy, are intriguing. In the present paper the authors attempt to answer these questions while making an effort to reveal the genesis of dark energy and suggest that `the cosmological nuclear binding energy liberated during primordial nucleo-synthesis remains trapped for a long time and then is released free which manifests itself as dark energy in the universe'. It is also explained why for dark energy the parameter $w = - {2/3}$. Noting that $w = 1$ for stiff matter and $w = {1/3}$ for radiation; $w = - {2/3}$ is for dark energy because $"-1"$ is due to `deficiency of stiff-nuclear-matter' and that this binding energy is ultimately released as `radiation' contributing $"+ {1/3}"$, making $w = -1 + {1/3} = - {2/3}$. When dark energy is released free at $Z = 80$, $w = -{2/3}$. But as on present day at $Z = 0$ when radiation strength has diminished to $\delta \to 0$, $w = -1 + \delta{1/3} = - 1$. This, thus almost solves the dark-energy mystery of negative pressure and repulsive-gravity. The proposed theory makes several estimates /predictions which agree reasonably well with the astrophysical constraints and observations. Though there are many candidate-theories, the proposed model of this paper presents an entirely new approach (cosmological nuclear energy) as a possible candidate for dark energy.Comment: 17 pages, 4 figures, minor correction

Cosmic Evolution with Early and Late Acceleration Inspired by Dual Nature of the Ricci Scalar Curvature

In the present paper, it is found that dark energy emerges spontaneously from the modified gravity. According to cosmological scenario, obtained here, the universe inflates for $\sim 10^{-37}$ sec. in the beginning and late universe accelerates after 8.58 Gyrs. During the long intermediate period, it decelerates driven by radiation and subsequently by matter. Emerged gravitational dark energy mimics quintessence and its density falls by 115 orders from its initial value $2.58\times 10^{68} {\rm GeV}^4$ to its current value $2.19\times 10^{-47} {\rm GeV}^4$ .Comment: 40 pages. To appearin Int. J. Mod. Phys.

The Genesis of Cosmological Tracker Fields

The role of the quintessence field as a probable candidate for the repulsive dark energy, the conditions for tracking and the requisites for tracker fields are examined. The concept of `integrated tracking' is introduced and a new criterion for the existence of tracker potentials is derived assuming monotonic increase in the scalar energy density parameter \Omega_\phi with the evolution of the universe as suggested by the astrophysical constraints. It provides a technique to investigate generic potentials of the tracker fields. The general properties of the tracker fields are discussed and their behaviour with respect to tracking parameter \epsilon is analyzed. It is shown that the tracker fields around the limiting value \epsilon \simeq \frac 23 give the best fit with the observational constraints.Comment: 8 pages, Latex file, 1 figure, comments adde

CMBR Constraint on a Modified Chaplygin Gas Model

In this paper, a modified Chaplygin gas model of unifying dark energy and dark matter with exotic equation of state $p=B\rho-\frac{A}{\rho^{\alpha}}$ which can also explain the recent accelerated expansion of the universe is investigated by the means of constraining the location of the peak of the CMBR spectrum. We find that the result of CMBR measurements does not exclude the nonzero value of parameter $B$, but allows it in the range $-0.35\lesssim B\lesssim0.025$.Comment: 4 pages, 3 figure

Cosmological Dynamics of Phantom Field

We study the general features of the dynamics of the phantom field in the cosmological context. In the case of inverse coshyperbolic potential, we demonstrate that the phantom field can successfully drive the observed current accelerated expansion of the universe with the equation of state parameter $w_{\phi} < -1$. The de-Sitter universe turns out to be the late time attractor of the model. The main features of the dynamics are independent of the initial conditions and the parameters of the model. The model fits the supernova data very well, allowing for $-2.4 < w_{\phi} < -1$ at 95 % confidence level.Comment: Typos corrected. Some clarifications and references added. To appear in Physical Review

Viscous cosmologies in scalar-tensor theories for Kasner type metrics

In a viscous Bianchi type I metric of the Kasner form, it is well known that it is not possible to describe an anisotropic physical model of the universe, which satisfies the second law of thermodynamics and the dominant energy condition (DEC) in Einstein's theory of gravity. We examine this problem in scalar-tensor theories of gravity. In this theory we show that it is possible to describe the growth of entropy, keeping the thermodynamics and the dominant energy condition.Comment: 6 pages, Latex, accepted in Phys. Rev.

Viscous FRW model with particle creation in the early universe

We discuss the dynamical effects of bulk viscosity and particle creation on the early evolution of the Friedmann -Robertson -Walker model in the framework of open thermodynamical systems. We consider bulk viscosity and Particle creation as separate irreversible processes. Exact solutions of the Einstein field equations are obtained by using the "gamma-law" equation of state $p=(\gamma -1)\rho$, where the adiabatic parameter $\gamma$ varies with scale factor of the metric. We consider the cosmological model to study the early phases of the evolution of the universe as it goes from an inflationary phase to a radiation -dominated era in the presence of bulk viscosity and particle creation. Analytical solutions are obtained for particle number density and entropy for all models. It is seen that, by choosing appropriate functions for particle creation rate and bulk viscous coefficient, the models exhibit singular and non-singular beginnings.Comment: 19 pages, abstract submitted to ICGC, 2011, corrected some typo errors and added one ref. in version 1, Accepted for Publication in Mod. Phys. Lett.