The dynamics of background evolution and structure formation in phase space: a semi-cosmographic reconstruction

Abstract

The Baryon Acoustic Oscillation (BAO) feature, imprinted in the transverse and radial clustering of dark matter tracers, enables the simultaneous measurement of the angular diameter distance $D_A(z)$ and the Hubble parameter $H(z)$ at a given redshift. Further, measuring the redshift space anisotropy (RSD) allows us to measure the combination $f_8(z)\equiv f{\sigma }_8(z)$. Motivated by this, we simultaneously study the dynamics of background evolution and structure formation in an abstract phase space of dynamical quantities: $x=H_0{D}_A/c$, $p=dx/dz$, and $f_8$. We adopt a semi-cosmographic approach, whereby we do not pre-assume any specific dark energy model to integrate the dynamical system. The Luminosity distance is expanded as a Padé rational approximation in the variable $(1+z{)}^{1/2}$. The dynamical system is solved by using a semi-cosmographic equation of state, which incorporates the dark matter density parameter along with the parameters of the Padé expansion. The semi-cosmographic $D_A(z),H(z)$ and $f{\sigma }_8(z)$, thus obtained, are fitted with BAO and RSD data from the SDSS IV. The reconstructed phase trajectories in the $3D$ $(x,p,f_8)$ space are used to reconstruct some diagnostics of background cosmology and structure formation. At low redshifts, a discernible departure from the $\Lambda$CDM model is observed. The geometry of the phase trajectories in the projected spaces allows us to identify three key redshifts where future observations may be directed for a better understanding of cosmic tensions and anomalies.

Published

References in corpus (76)

• emcee: The MCMC Hammer
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Dynamics of dark energy
• Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies
• Cosmological Constant - the Weight of the Vacuum
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• The 6dF Galaxy Survey: Baryon Acoustic Oscillations and the Local Hubble Constant
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• A 2.4% Determination of the Local Value of the Hubble Constant
• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in the Data Release 10 and 11 galaxy samples
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Chameleon Cosmology
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological Implications from two Decades of Spectroscopic Surveys at the Apache Point observatory
• Disappearing cosmological constant in f(R) gravity
• Dark Energy Survey Year 3 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing
• Cosmic Chronometers: Constraining the Equation of State of Dark Energy. I: H(z) Measurements
• Constraining Cosmological Parameters Based on Relative Galaxy Ages
• Challenges for $\Lambda$CDM: An update
• Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectrum
• Cosmic Distances Calibrated to 1% Precision with Gaia EDR3 Parallaxes and Hubble Space Telescope Photometry of 75 Milky Way Cepheids Confirm Tension with LambdaCDM
• Two new diagnostics of dark energy
• Age-dating Luminous Red Galaxies observed with the Southern African Large Telescope
• Cosmology from cosmic shear power spectra with Subaru Hyper Suprime-Cam first-year data
• Beyond $\Lambda$CDM: Problems, solutions, and the road ahead
• The 6dF Galaxy Survey: z \approx 0 measurement of the growth rate and sigma_8
• The Primordial Lithium Problem
• Calibration of the Tip of the Red Giant Branch (TRGB)
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Baryon acoustic oscillations with Lyman-$\alpha$ forests
• Extended Gravity Cosmography
• Cosmography: Cosmology without the Einstein equations
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from anisotropic clustering analysis of the Quasar Sample in configuration space between redshift 0.8 and 2.2
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic correlation function between redshifts 0.6 and 1
• The Hubble Constant: A Summary of the HST Program for the Luminosity Calibration of Type Ia Supernovae by Means of Cepheids
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Interpretation of the TT and TE Angular Power Spectrum Peaks
• Gaussian Process Cosmography
• The Clustering of the SDSS Main Galaxy Sample II: Mock galaxy catalogues and a measurement of the growth of structure from Redshift Space Distortions at $z=0.15$
• 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
• Thawing quintessence with a nearly flat potential
• The Hubble series: Convergence properties and redshift variables
• On the theory and applications of modern cosmography
• The Hubble Constant from Infrared Surface Brightness Fluctuation Distances
• High-redshift cosmography: auxiliary variables versus Padé polynomials
• Model independent constraints on dark energy evolution from low-redshift observations
• Correlation Function in Deep Redshift Space as a Cosmological Probe
• Models of coupled dark matter to dark energy
• Dark energy and curvature from a future baryonic acoustic oscillation survey using the Lyman-alpha forest
• Precision cosmology with Padé rational approximations: theoretical predictions versus observational limits
• The Carnegie-Chicago Hubble Program. I. An Independent Approach to the Extragalactic Distance Scale Using only Population II Distance Indicators
• Beyond $\Lambda$CDM with Low and High Redshift Data: Implications for Dark Energy
• Nonparametric Reconstruction of the Dark Energy Equation of State from Diverse Data Sets
• Cosmography and flat $\Lambda$CDM tensions at high redshift
• Cosmological Applications of Pade Approximant
• Cosmographic reconstruction of $f(\mathcal{T})$ cosmology
• Arguments against using $h^{-1}\mathrm{Mpc}$ units in observational cosmology
• Dark Energy Survey Year 3 results: Cosmological constraints from galaxy clustering and galaxy-galaxy lensing using the MagLim lens sample
• Updated constraints on $f(\mathcal{R})$ gravity from cosmography
• Rational approximations of $f(R)$ cosmography through Padé polynomials
• Model-agnostic assessment of dark energy after DESI DR1 BAO
• Connecting early and late epochs by f(z)CDM cosmography
• Model-independent cosmological inference post DESI DR1 BAO measurements
• Is cosmography a useful tool for testing cosmology?
• Conformally Friedmann-Lemaitre-Robertson-Walker cosmologies
• Can high-redshift Hubble diagrams rule out the standard model of cosmology in the context of cosmographic method?
• Cosmographic analysis of redshift drift
• Dark energy reconstruction based on the PADE approximation; an expansion around the $\Lambda$CDM
• New Expansion Rate Anomalies at Characteristic Redshifts Geometrically Determined using DESI-DR2 BAO and DES-SN5YR Observations
• Measuring ${\sigma }_8$ using DESI Legacy Imaging Surveys Emission-Line Galaxies and Planck CMB Lensing and the Impact of Dust on Parameter Inference
• From Hubble to Snap Parameters: A Gaussian Process Reconstruction
• Inferring dark energy properties from the scale factor parametrisation
• Analytical Gaussian Process Cosmography: Unveiling Insights into Matter-Energy Density Parameter at Present
• Bias of reconstructing the dark energy equation of state from the Pad$\acute{e}$ cosmography
• A semi-cosmographic approach to study cosmological evolution in phase space