On A Cosmological Invariant as an Observational Probe in the Early Universe

k-essence scalar field models are usually taken to have lagrangians of the form ${\mathcal L}=-V(\phi)F(X)$ with $F$ some general function of $X=\nabla_{\mu}\phi\nabla^{\mu}\phi$. Under certain conditions this lagrangian in the context of the early universe can take the form of that of an oscillator with time dependent frequency. The Ermakov invariant for a time dependent oscillator in a cosmological scenario then leads to an invariant quadratic form involving the Hubble parameter and the logarithm of the scale factor. In principle, this invariant can lead to further observational probes for the early universe. Moreover, if such an invariant can be observationally verified then the presence of dark energy will also be indirectly confirmed.Comment: 4 pages, Revte

K-essence and the coincidence problem

K-essence has been proposed as a possible means of explaining the coincidence problem of the Universe beginning to accelerate only at the present epoch. We carry out a comprehensive dynamical systems analysis of the k-essence models given so far in the literature. We numerically study the basin of attraction of the tracker solutions and we highlight the behaviour of the field close to sound speed divergences. We find that, when written in terms of parameters with a simple dynamical interpretation, the basins of attraction represent only a small region of the phase space.Comment: 5 pages RevTeX4 file with two figures incorporated. Minor changes to match PRD accepted versio

Estimating Temperature Fluctuations in the Early Universe

A lagrangian for the $k-$ essence field is constructed for a constant scalar potential and its form determined when the scale factor was very small compared to the present epoch but very large compared to the inflationary epoch. This means that one is already in an expanding and flat universe. The form is similar to that of an oscillator with time-dependent frequency. Expansion is naturally built into the theory with the existence of growing classical solutions of the scale factor. The formalism allows one to estimate fluctuations of the temperature of the background radiation in these early stages (compared to the present epoch) of the universe. If the temperature at time $t_{a}$ is $T_{a}$ and at time $t_{b}$ the temperature is $T_{b}$ ($t_{b}>t_{a}$), then for small times, the probability for the logarithm of inverse temperature evolution can be estimated to be given by $$P(b,a)= |\langle ln~({1\over T_{b}}),t_{b}| ln~({1\over T_{a}}),t_{a}\rangle|^{2}$$ $$\approx\biggl({3m_{\mathrm Pl}^{2}\over \pi^{2} (t_{b}-t_{a})^{3}}\biggr) (ln~ T_{a})^{2}(ln~T_{b})^{2}\biggl(1 - 3\gamma (t_{a} + t_{b})\biggr)$$ where $0<\gamma<1$, $m_{\mathrm Pl}$ is the Planck mass and Planck's constant and the speed of light has been put equal to unity. There is the further possibility that a single scalar field may suffice for an inflationary scenario as well as the dark matter and dark energy realms.Comment: 8 pages, Revtex, title,abstract and format changed for journal publication,no change in basic results, clarifications and a figure added. Keywords: physics of the early universe,inflation, dark matter theory, dark energy theory. PACS: 95.35.+d ; 95.36.+x ; 98.80.Cq ; 98.80.-

Perturbations in cosmologies with a scalar field and a perfect fluid

We study the properties of cosmological density perturbations in a multi-component system consisting of a scalar field and a perfect fluid. We discuss the number of degrees of freedom completely describing the system, introduce a full set of dynamical gauge-invariant equations in terms of the curvature and entropy perturbations, and display an efficient formulation of these equations as a first-order system linked by a fairly sparse matrix. Our formalism includes spatial gradients, extending previous formulations restricted to the large-scale limit, and fully accounts for the evolution of an isocurvature mode intrinsic to the scalar field. We then address the issue of the adiabatic condition, in particular demonstrating its preservation on large scales. Finally, we apply our formalism to the quintessence scenario and clearly underline the importance of initial conditions when considering late-time perturbations. In particular, we show that entropy perturbations can still be present when the quintessence field energy density becomes non-negligible.Comment: RevTex4, 9 pages, 3 figures. Significant additions on the quintessence scenario (new appendix and additional numerical example). Conclusions unchanged, but more robus

Reconstruction of Five-dimensional Bounce cosmological Models From Deceleration Factor

In this paper, we consider a class of five-dimensional Ricci-flat vacuum solutions, which contain two arbitrary functions $\mu(t)$ and $\nu(t)$. It is shown that $\mu(t)$ can be rewritten as a new arbitrary function $f(z)$ in terms of redshift $z$ and the $f(z)$ can be determined by choosing particular deceleration parameters $q(z)$ which gives early deceleration and late time acceleration. In this way, the $5D$ cosmological model can be reconstructed and the evolution of the universe can be determined.Comment: 5 pages, 1 figure, to be published in IJT

How does Inflation Depend Upon the Nature of Fluids Filling Up the Universe in Brane World Scenario

By constructing different parameters which are able to give us the information about our universe during inflation,(specially at the start and the end of the inflationary universe) a brief idea of brane world inflation is given in this work. What will be the size of the universe at the end of inflation,i.e.,how many times will it grow than today's size is been speculated and analysed thereafter. Different kinds of fluids are taken to be the matter inside the brane. It is observed that in the case of highly positive pressure grower gas like polytropic,the size of the universe at the end of inflation is comparitively smaller. Whereas for negative pressure creators (like chaplygin gas) this size is much bigger. Except thse two cases, inflation has been studied for barotropic fluid and linear redshift parametrization $\omega(z) = \omega_{0} + \omega_{1} z$ too. For them the size of the universe after inflation is much more high. We also have seen that this size does not depend upon the potential energy at the end of the inflation. On the contrary, there is a high impact of the initial potential energy upon the size of inflation.Comment: 20 page

A new view of k-essence

K-essence models, relying on scalar fields with non-canonical kinetic terms, have been proposed as an alternative to quintessence in explaining the observed acceleration of the Universe. We consider the use of field redefinitions to cast k-essence in a more familiar form. While k-essence models cannot in general be rewritten in the form of quintessence models, we show that in certain dynamical regimes an equivalence can be made, which in particular can shed light on the tracking behaviour of k-essence. In several cases, k-essence cannot be observationally distinguished from quintessence using the homogeneous evolution, though there may be small effects on the perturbation spectrum. We make a detailed analysis of two k-essence models from the literature and comment on the nature of the fine tuning arising in the models.Comment: 7 pages RevTeX4 file with four figures incorporate

Variable Modified Chaplygin Gas in Anisotropic Universe with Kaluza-Klein Metric

In this work, we have consider Kaluza-Klein Cosmology for anisotropic universe where the universe is filled with variable modified chaplygin gas (VMCG). Here we find normal scalar field $\phi$ and the self interacting potential $V(\phi)$ to describe the VMCG Cosmology. Also we graphically analyzed the geometrical parameters named {\it statefinder parameters} in anisotropic Kaluza-Klein model. Next, we consider a Kaluza-Klein model of interacting VMCG with dark matter in the Einstein gravity framework. Here we construct the three dimensional autonomous dynamical system of equations for this interacting model with the assumption that the dark energy and the dark matter are interact between them and for that we also choose the interaction term. We convert that interaction terms to its dimensionless form and perform stability analysis and solve them numerically. We obtain a stable scaling solution of the equations in Kaluza-Klein model and graphically represent solutions.Comment: 11 pages, 13 figure

Pure kinetic k-essence as the cosmic speed-up

In this paper, we consider three types of k-essence. These k-essence models were presented in the parametric forms. The exact analytical solutions of the corresponding equations of motion are found. It is shown that these k-essence models for the presented solutions can give rise to cosmic acceleration.Comment: 10 pages, typos corrected, main results remain the same, minor changes to match IJTP accepted versio

OmOm Diagnostic for Dilaton Dark Energy

$Om$ diagnostic can differentiate between different models of dark energy without the accurate current value of matter density. We apply this geometric diagnostic to dilaton dark energy(DDE) model and differentiate DDE model from LCDM. We also investigate the influence of coupled parameter $\alpha$ on the evolutive behavior of $Om$ with respect to redshift $z$. According to the numerical result of $Om$, we get the current value of equation of state $\omega_{\sigma0}$=-0.952 which fits the WMAP5+BAO+SN very well.Comment: 6 pages and 6 figures