Dynamical analysis of $k$-essence cosmology in the light of Supernova Ia observations

Abstract

In this paper, we analyse the JLA data on Supernova observations in the context of $k-$essence dark energy model with Lagrangian $L=VF(X)$, with a constant potential $V$ and the dynamical term $X=(1/2){\nabla }_{\mu }\varphi {\nabla }_{\nu }\varphi ={\dot{\varphi }}^2/2$ for a homogeneous scalar field $\varphi (t)$, in a flat FRW spacetime background. Scaling relations are used to extract temporal behaviour of different cosmological quantities and the form of the function $F(X)$ from the data. We explore how the parameters of the model, viz. value of the constant potential $V$ and a constant $C$ appearing in the emergent scaling relation, control the dynamics of the model in the context of JLA data, by setting up and analysing an equivalent dynamical system described by a set of autonomous equations.

arXiv comment22 pages, 7 figures, 3 tables; Accepted for publication in European Physical Journal Plus

References in corpus (64)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• 4D Gravity on a Brane in 5D Minkowski Space
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Accelerating Universes with Scaling Dark Matter
• The Supernova Legacy Survey: Measurement of Omega_M, Omega_Lambda and w from the First Year Data Set
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
• Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples
• k-Inflation
• Essentials of k-essence
• The Hubble Space Telescope Cluster Supernova Survey: V. Improving the Dark Energy Constraints Above z>1 and Building an Early-Type-Hosted Supernova Sample
• Curvature Quintessence
• The Pan-STARRS1 Photometric System
• Observational Constraints on the Nature of the Dark Energy: First Cosmological Results from the ESSENCE Supernova Survey
• Supernova Constraints and Systematic Uncertainties from the First 3 Years of the Supernova Legacy Survey
• A Redetermination of the Hubble Constant with the Hubble Space Telescope from a Differential Distance Ladder
• Braneworld models of dark energy
• First-year Sloan Digital Sky Survey-II (SDSS-II) Supernova Results: Hubble Diagram and Cosmological Parameters
• Scaling solutions in general non-minimal coupling theories
• Purely kinetic k-essence as unified dark matter
• Curvature quintessence matched with observational data
• CfA3: 185 Type Ia Supernova Light Curves from the CfA
• Dynamical systems applied to cosmology: dark energy and modified gravity
• The Sloan Digital Sky Survey-II Supernova Survey: Technical Summary
• Cosmological scaling solutions of non-minimally coupled scalar fields
• SNLS3: Constraints on Dark Energy Combining the Supernova Legacy Survey Three Year Data with Other Probes
• WMAP constraints on low redshift evolution of dark energy
• Extended Quintessence
• The Carnegie Supernova Project: First Photometry Data Release of Low-Redshift Type Ia Supernovae
• The Carnegie Supernova Project: Analysis of the First Sample of Low-Redshift Type-Ia Supernovae
• Quintessence, the Gravitational Constant, and Gravity
• Scalar-Tensor Gravity and Quintessence
• The Carnegie Supernova Project: Second Photometry Data Release of Low-Redshift Type Ia Supernovae
• Observational constraints on low redshift evolution of dark energy: How consistent are different observations?
• Tracking K-essence
• Model-Independent Constraints on Dark Energy Density from Flux-averaging Analysis of Type Ia Supernova Data
• First-Year Sloan Digital Sky Survey-II (SDSS-II) Supernova Results: Constraints on Non-Standard Cosmological Models
• Uncorrelated Measurements of the Cosmic Expansion History and Dark Energy from Supernovae
• Systematic Uncertainties Associated with the Cosmological Analysis of the First Pan-STARRS1 Type Ia Supernova Sample
• First-year Sloan Digital Sky Survey-II (SDSS-II) supernova results: consistency and constraints with other intermediate-redshift datasets
• Flux-averaging Analysis of Type Ia Supernova Data
• Cosmology with Photometrically-Classified Type Ia Supernovae from the SDSS-II Supernova Survey
• Constraints on dark energy with the LOSS SN Ia sample
• A generalized equation of state for dark energy
• Dynamics of cosmological scalar fields
• Understanding the phenomenology of interacting dark energy scenarios and their theoretical bounds
• Scaling solutions and weak gravity in dark energy with energy and momentum couplings
• Exploring the Systematic Uncertainties of Type Ia Supernovae as Cosmological Probes
• Reconstructing the dark energy potential
• Cosmological dynamics of scalar fields with kinetic corrections: Beyond the exponential potential
• A Comparative Study of Dark Energy Constraints from Current Observational Data
• Probing the time dependence of dark energy
• Phase-space analysis of a class of k-essence cosmology
• Dynamical stability of K-essence field interacting non-minimally with a perfect fluid
• Distance Measurements from Supernovae and Dark Energy Constraints
• General formulation of cosmological perturbations in scalar-tensor dark energy coupled to dark matter
• Anisotropic k-essence cosmologies
• Kinetically coupled dark energy
• Dynamical Systems Analysis of K-essence Model
• Exploring the cosmological consequences of JLA supernova data with improved flux-averaging technique
• Implications of JLA data for $k-$essence model of dark energy with given equation of state