Recovering $\Lambda$CDM Model From a Cosmographic Study

Abstract

Using the mathematical definitions of deceleration and jerk parameters we obtain a general differential equation for squared Hubble parameter. For a constant jerk, this differential equation leads to an exact function for Hubble parameter. By the aid of this exact Hubble function we can exactly reconstruct any other cosmographic parameters. We also obtained a general function for transition redshift as well as spacetime curvature. Our derived functions clearly impose a lower limit on the jerk parameter which is $j_{min}\ge -0.125$. Moreover, we found that the jerk parameter indicates the geometry of the spacetime i.e any deviation from $j=1$ imply to a non-flat spacetime. In other word $j\ne 1$ reefers to a dynamical, time varying, dark energy. From obtained Hubble function we recover the analogue of $\Lambda$CDM model. To constrain cosmographic parameters as well as transition redshift and spacetime curvature of the recovered $\Lambda$CDM model, we used Metropolis-Hasting algorithm to perform Monte Carlo Markov Chain analysis by using observational Hubble data obtained from cosmic chronometric (CC) technique, BAO data, Pantheon compilation of Supernovae type Ia, and their joint combination. The only free parameters are $H$, $A({\Omega }_m)$ and $j$. From joint analysis we obtained $H_0=69.9\pm 1.7$, $A(\sim {\Omega }_{0m})=0.279_{-0.017}^{+0.013}$, $B(\sim {\Omega }_{0X})=0.721_{-0.013}^{+0.017}$, $j_0=1.038_{-0.023}^{+0.061}$ and $z_t=0.706_{-0.034}^{+0.031}$.

arXiv comment13 pages, 13 figures, 5 tables

References in corpus (59)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Planck 2015 results. XIII. Cosmological parameters
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
• 4D Gravity on a Brane in 5D Minkowski Space
• The Complete Light-curve Sample of Spectroscopically Confirmed Type Ia Supernovae from Pan-STARRS1 and Cosmological Constraints from The Combined Pantheon Sample
• The Cosmological Constant
• Discovery of a Supernova Explosion at Half the Age of the Universe and its Cosmological Implications
• A 2.4% Determination of the Local Value of the Hubble Constant
• Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples
• The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15
• Statefinder -- a new geometrical diagnostic of dark energy
• The High-Z Supernova Search: Measuring Cosmic Deceleration and Global Cur vature of the Universe Using Type Ia Supernovae
• A 6% measurement of the Hubble parameter at $z\sim 0.45$: direct evidence of the epoch of cosmic re-acceleration
• SALT2: using distant supernovae to improve the use of Type Ia supernovae as distance indicators
• Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2
• Cosmological implications of baryon acoustic oscillation (BAO) measurements
• Reconstructing Dark Energy
• Jerk, snap, and the cosmological equation of state
• The 6dF Galaxy Survey: z \approx 0 measurement of the growth rate and sigma_8
• The Atacama Cosmology Telescope: Cosmological Parameters from the 2008 Power Spectra
• Hubble parameter measurement constraints on the redshift of the deceleration-acceleration transition, dynamical dark energy, and space curvature
• Cosmography: Cosmology without the Einstein equations
• The WiggleZ Dark Energy Survey: Improved Distance Measurements to z = 1 with Reconstruction of the Baryonic Acoustic Feature
• The Atacama Cosmology Telescope: Cosmological parameters from three seasons of data
• Cosmography of f(R) gravity
• $H_0$ from cosmic chronometers and Type Ia supernovae, with Gaussian Processes and the novel Weighted Polynomial Regression method
• From cosmic deceleration to acceleration: new constraints from SN Ia and BAO/CMB
• Cosmography and constraints on the equation of state of the Universe in various parametrizations
• Cosmographic analysis of the equation of state of the universe through Padé approximations
• Median Statistics, H_0, and the Accelerating Universe
• Kinematic Constraints to the Transition Redshift from SNe Ia Union Data
• Cosmographic bounds on the cosmological deceleration-acceleration transition redshift in $f(\mathcal{R})$ gravity
• Inflationary paradigm after Planck 2013
• The Hubble series: Convergence properties and redshift variables
• Effect of inhomogeneities on the expansion rate of the Universe
• Accelerated expansion from structure formation
• Precision cosmology with Padé rational approximations: theoretical predictions versus observational limits
• Median statistics and the Hubble constant
• Cosmographic analysis with Chebyshev polynomials
• Determining the Hubble constant from Hubble parameter measurements
• Cosmographic Hubble fits to the supernova data
• Comprehensive cosmographic analysis by Markov Chain Method
• Constraints on dark energy dynamics and spatial curvature from Hubble parameter and baryon acoustic oscillation data
• Observational constraints on generalized Proca theories
• Probing the cosmographic parameters to distinguish between dark energy and modified gravity models
• Spatial Curvature Falsifies Eternal Inflation
• What can the observation of nonzero curvature tell us?
• In search of the dark matter dark energy interaction: a kinematic approach
• A parametric reconstruction of the cosmological jerk from diverse observational data sets
• Hiding dark energy transitions at low redshift
• Is there a concordance value for $H_0$?
• What do we know about cosmography
• Quantifying the evidence for the current speed-up of the Universe with low and intermediate-redshift data. A more model-independent approach
• Spatial curvature endgame: Reaching the limit of curvature determination
• Weak gravitational lensing effects on cosmological parameters and dark energy from gamma-ray bursts
• A cosmographic analysis of the transition to acceleration using SN-Ia and BAO
• Signatures of the Very Early Universe: Inflation, Spatial Curvature and Large Scale Anomalies
• Observable Signatures of a Classical Transition

Cited by in corpus (8)

• Isotropization of locally rotationally symmetric Bianchi-I universe in $f(Q)$-gravity
• Non-parametric reconstruction of the cosmological \textit{jerk} parameter
• Constraining An Exact Brans-Dicke gravity theory with Recent Observations
• Anisotropic LRS-BI Universe with $f(Q)$ gravity theory
• Curvature dominance DE-model in $f(R)$-gravity
• Dynamical system analysis of LRS-BI Universe with f(Q) gravity theory
• On the uniqueness of $\Lambda$CDM-like evolution for homogeneous and isotropic cosmology in General Relativity
• Determination of the Kinematic Parameters from SNe Ia and Cosmic Chronometers