Reconstruction of k-essence model

Abstract

We explicitly construct the k-essence models which reproduce the arbitrary FRW cosmology, that is, the arbitrary time-development of the scale factor or the Hubble rate. The k-essence model includes scalar quintessence model, tachyon dark energy model, ghost condensation model as special cases. Explicit formulas of the reconstruction are given. First we consider the case that the action only contains the kinetic term. In this case, we find that the model reproducing the development of the universe in the exact $\Lambda$CDM model cannot be constructed although there is a model which reproduces the development infinitely closing to $\Lambda$CDM model. We find, however, the solution is not stable. Another is more general case including potential etc., where we find that there appear infinite number of arbitrary functions of the scalar fields, which are redundant to the time development of the scale factor. By adjusting one of the redundant functions, however, we can obtain the model where any solution we need could be stable.

LaTeX 9 pages

References in corpus (4)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• New Hubble Space Telescope Discoveries of Type Ia Supernovae at z > 1: Narrowing Constraints on the Early Behavior of Dark Energy
• Modified gravity and its reconstruction from the universe expansion history

Cited by in corpus (22)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R,T) gravity
• Dark energy from modified gravity with Lagrange multipliers
• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• Pure kinetic k-essence as the cosmic speed-up
• $k$-essence $f(R)$ Gravity Inflation
• Constant-roll in the Palatini-$R^2$ models
• Constant-roll $k$-Inflation Dynamics
• Modified Einstein and Finsler Like Theories on Tangent Lorentz Bundles
• K-essence Models and Cosmic Acceleration in Generalized Teleparallel Gravity
• Dynamical Systems Analysis of K-essence Model
• The unification of inflation and late-time acceleration in the frame of $k$-essence
• The Phase Space of $k$-Essence $f(R)$ Gravity Theory
• Cosmological perturbations in $k$-essence model
• Generalized Galileon Model -- cosmological reconstruction and the Vainshtein mechanism --
• $k$-Inflation-corrected Einstein-Gauss-Bonnet Gravity with Massless Primordial Gravitons
• Exploring the Cosmological Model in $f(R,T^{\varphi })$ Gravity with Observational Constraints
• A Viable Dark Fluid Model
• Anisotropic cosmology using observational datasets: exploring via machine learning approaches
• A general method for the construction of stable Galileon models consistent with the Planck data results
• Constant Roll Inflationary Dynamics with Generalized Potentials in $f(R,\varphi ,X)$ Gravity
• Towards the unification of late-time acceleration and inflation by k-essence model