Inference of cosmological models with principal component analysis

Abstract

Determination of cosmological parameters is a major goal in cosmology at present. The availability of improved data sets necessitates the development of novel statistical tools to interpret the inference from a cosmological model. In this paper, we combine the Principal Component Analysis (PCA) and Markov Chain Monte Carlo (MCMC) method to infer the parameters of cosmological models. We use the No U-Turn Sampler (NUTS) to run the MCMC chains in the model parameter space. After determining the observable by PCA, we replace the observational and error parts of the likelihood analysis with the PCA reconstructed observable and find the most preferred model parameter set. As a demonstration of our methodology, we assume a polynomial expansion as the parametrization of the dark energy equation of state and plug it in the reconstruction algorithm as our model. After testing our methodology with simulated data, we apply the same to the observed data sets, the Hubble parameter data, Supernova Type Ia data, and the Baryon Acoustic oscillation data. This method effectively constrains cosmological parameters from data, including sparse data sets.

arXiv comment27 pages, 18 figures

References in corpus (63)

• Dynamics of dark energy
• The Cosmological Constant and Dark Energy
• Cosmological Imprint of an Energy Component with General Equation of State
• Cosmological Constant - the Weight of the Vacuum
• The Case for a Positive Cosmological Lambda-term
• Quintessence, Cosmic Coincidence, and the Cosmological Constant
• The Cosmological Constant
• Exploring the Expansion History of the Universe
• Accelerating Universes with Scaling Dark Matter
• Dark Energy and the Accelerating Universe
• Exponential potentials and cosmological scaling solutions
• Constraints on the redshift dependence of the dark energy potential
• Cosmic Chronometers: Constraining the Equation of State of Dark Energy. I: H(z) Measurements
• Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z$\sim$2
• Accelerated expansion of the universe driven by tachyonic matter
• The Pantheon+ Analysis: The Full Dataset and Light-Curve Release
• Cosmic Distances Calibrated to 1% Precision with Gaia EDR3 Parallaxes and Hubble Space Telescope Photometry of 75 Milky Way Cepheids Confirm Tension with LambdaCDM
• Quintessence: A Review
• CDM Models with a Smooth Component
• Age-dating Luminous Red Galaxies observed with the Southern African Large Telescope
• Cosmology with tachyon field as dark energy
• WMAP constraints on low redshift evolution of dark energy
• Uncorrelated Estimates of Dark Energy Evolution
• Comparison of the Legacy and Gold SnIa Dataset Constraints on Dark Energy Models
• Crossing the Phantom Divide: Theoretical Implications and Observational Status
• Parameterization of Dark-Energy Properties: a Principal-Component Approach
• New constraints on cosmological parameters and neutrino properties using the expansion rate of the Universe to z~1.75
• Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix
• Dynamical Lambda Models of Structure Formation
• A comparison of cosmological models using recent supernova data
• The Dynamics of Quintessence, The Quintessence of Dynamics
• Hubble Sinks In The Low-Redshift Swampland
• Reconstruction of the deceleration parameter and the equation of state of dark energy
• Constraining Dark Energy Dynamics in Extended Parameter Space
• The Paths of Quintessence
• Mapping the Cosmological Expansion
• Is Local $H_0$ At Odds With Dark Energy EFT?
• New Observational $H(z)$ Data from Full-Spectrum Fitting of Cosmic Chronometers in the LEGA-C Survey
• Cosmological parameter analyses using transversal BAO data
• Investigating dark energy experiments with principal components
• Direct reconstruction of dark energy
• Tracing The Sound Horizon Scale With Photometric Redshift Surveys
• Baryon Acoustic Oscillations from the SDSS DR10 galaxies angular correlation function
• Angular Baryon Acoustic Oscillation measure at z=2.225 from the SDSS quasar survey
• Dynamical behavior of generic quintessence potentials: constraints on key dark energy observables
• Cosmological tests of General Relativity: a principal component analysis
• Bias due to neutrinos must not uncorrect'd go
• Measuring the transverse baryonic acoustic scale from the SDSS DR11 galaxies
• Acceleration of the universe: a reconstruction of the effective equation of state
• Dark Matter and Dark Energy: Summary and Future Directions
• Clustering of Photometric Luminous Red Galaxies II: Cosmological Implications from the Baryon Acoustic Scale
• Null Signal for the Cosmic Anisotropy in the Pantheon Supernovae Data
• Comparative analysis of model-independent methods for exploring the nature of dark energy
• Beware of commonly used approximations I: errors in forecasts
• Low redshift observational constraints on tachyon models of dark energy
• Beware of commonly used approximations II: estimating systematic biases in the best-fit parameters
• Varying fundamental constants principal component analysis: additional hints about the Hubble tension
• A comparison of perturbations in fluid and scalar field models of dark energy
• Is dark energy evolving?
• Model-Independent Predictions for Smooth Cosmic Acceleration Scenarios
• Direct reconstruction of dynamical dark energy from observational Hubble parameter data
• Reconstructing equation of state of dark energy with principal component analysis
• Reconstruction of Dynamical Dark Energy Potentials: Quintessence, Tachyon and interacting models