Logarithm of the scale factor as a generalised coordinate in a lagrangian for dark matter and dark energy

Abstract

A lagrangian for the $k-$ essence field is set up with canonical kinetic terms and incorporating the scaling relation of [1]. There are two degrees of freedom, {\it viz.},$q(t)=lna(t)$ ($a(t)$ is the scale factor) and the scalar field $\varphi$, and an interaction term involving $\varphi$ and $q(t)$.The Euler-Lagrange equations are solved for $q$ and $\varphi$. Using these solutions quantities of cosmological interest are determined. The energy density $\rho$ has a constant component which we identify as dark energy and a component behaving as $a^{-3}$ which we call dark matter. The pressure $p$ is {\it negative} for time $t\to \infty$ and the sound velocity $c_s^2=\frac{\partial p}{\partial \rho }<<1$. When dark energy dominates, the deceleration parameter $Q\to -1$ while in the matter dominated era $Q\sim \frac{1}{2}$. The equation of state parameter $w=\frac{p}{\rho }$ is shown to be consistent with $w=\frac{p}{\rho }\sim -1$ for dark energy domination and during the matter dominated era we have $w\sim 0$. Bounds for the parameters of the theory are estimated from observational data. Keywords: k-essence models, dark matter, dark energy PACS No: 98.80.-k

16 pages, latex, paper shortened by 2 pages for journal publication

References in corpus (26)

• Dynamics of dark energy
• A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
• k-Inflation
• Essentials of k-essence
• Kinetically Driven Quintessence
• Perturbations in k-inflation
• The Pre-Big Bang Scenario in String Cosmology
• Purely kinetic k-essence as unified dark matter
• Dark Matter and Dark Energy
• Extended tachyon field, Chaplygin gas and solvable k-essence cosmologies
• Tracking K-essence
• A new view of k-essence
• Dynamics of $k$-essence
• Haloes of k-Essence
• Power-law expansion in k-essence cosmology
• K-essence and the coincidence problem
• Phantom k-essence cosmologies
• K-Chameleon and the Coincidence Problem
• On the Stability of Phantom K-essence Theories
• K-essential Leptogenesis
• Dark matter to dark energy transition in k-essence cosmologies
• Atypical k-essence cosmologies
• Brans-Dicke Scalar Field as a Unique k-essence
• Advanced Topics in Cosmology: A Pedagogical Introduction
• Rigidity of cosmic acceleration in a class of k-essence cosmologies
• Quintessence as k-essence

Cited by in corpus (9)

• The Hawking temperature in the context of dark energy
• The Hawking Temperature in the context of Dark Energy for Reissner-Nordstrom and Kerr background
• The Hawking temperature in the context of dark energy for Kerr-Newman and Kerr-Newman-AdS backgrounds
• Thermodynamics for the k-essence Emergent Reissner-Nordstrom-de Sitter Spacetime
• Estimating Temperature Fluctuations in the Early Universe
• A Scaling Relation in Inhomogeneous Cosmology with k-essence scalar fields
• On A Cosmological Invariant as an Observational Probe in the Early Universe
• Non-Affine Extensions of the Raychaudhuri Equation in the K-essence Framework
• Masking a singularity with k-essence fields in an emergent gravity metric