From the production of primordial perturbations to the end of inflation

In addition to generating the appropriate perturbation power spectrum, an inflationary scenario must take into account the need for inflation to end subsequently. In the context of single-field inflation models where inflation ends by breaking of the slow-roll condition, we constrain the first and second derivatives of the inflaton potential using this additional requirement. We compare this with current observational constraints from the primordial spectrum and discuss several issues relating to our results.Comment: RevTex4, 6 pages, 7 figures. To match version accepted by PR

Early Tracking Behavior in Small-field Quintessence Models

We study several quintessence models which are singular at Q=0, and use a simple initial constraint $Q_i\ge H_{inflation}/2\pi$ to see when they enter tracking regime, disregarding the details of inflation. We find it can give strong constraints for the inverse power-law potential $V=V_0Q^{-\alpha}$, which has to enter tracking regime for ${\rm ln}z \sim 10$. While for the supergravity model $V=V_0Q^{-\alpha}{\rm exp}(kQ^2/2)$, the constraint is much weakened. For another kind inverse power-law potential $V=V_0{\rm exp}(\lambda/Q)$, it exhibits no constraints.Comment: 11 pages,5 figures. Improved versio

K-essential Phantom Energy: Doomsday around the Corner? Revisited

We generalize some of those results reported by Gonz\'{a}lez-D\'{i}az by further tuning the parameter ($\beta$) which is closely related to the canonical kinetic term in $k$-essence formalism. The scale factor $a(t)$ could be negative and decreasing within a specific range of $\beta$ ($\equiv -1/\omega$, $\omega$ : the equation-of-state parameter) during the initial evolutional period.Comment: 1 Figure, 6 page

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

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

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

Quintessence as k-essence

Quintessence and k-essence have been proposed as candidates for the dark energy component of the universe that would be responsible of the currently observed accelerated expansion. In this paper we investigate the degree of resemblance between those two theoretical setups, and find that every quintessence model can be viewed as a k-essence model generated by a kinetic linear function. In addition, we show the true effects of k-essence begin at second order in the expansion of the kinetic function in powers of the kinetic energy.Comment: 14 pages, improved discussion, matches published 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.-

Gauge-Invariant Initial Conditions and Early Time Perturbations in Quintessence Universes

We present a systematic treatment of the initial conditions and evolution of cosmological perturbations in a universe containing photons, baryons, neutrinos, cold dark matter, and a scalar quintessence field. By formulating the evolution in terms of a differential equation involving a matrix acting on a vector comprised of the perturbation variables, we can use the familiar language of eigenvalues and eigenvectors. As the largest eigenvalue of the evolution matrix is fourfold degenerate, it follows that there are four dominant modes with non-diverging gravitational potential at early times, corresponding to adiabatic, cold dark matter isocurvature, baryon isocurvature and neutrino isocurvature perturbations. We conclude that quintessence does not lead to an additional independent mode.Comment: Replaced with published version, 12 pages, 2 figure

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