How to do MCMC in Cosmology? | A complete python code tutorial for cosmological Model.

✍️ About: In this video, I fit the LambdaCDM (or any model) with several data sets, including the Hubble data, Supernova data (Pantheon+ data), DESI BAO data, and Planck data. We numerically integrate the model to estimate the sound horizon at the radiation-baryon recombination epoch and the photon-baryon decoupling epoch. The code is highly optimized and uses a polychord sampler to obtain the constraint on model parameters. MCMC, or EMCEE, is the most commonly used sampler to fit the cosmological model with the various data sets to understand the fundamentals of the universe, for example, the Hubble constant, the matter density, and the geometry of the universe. As the universe is itself a highly dynamic playground, obtaining data is a cumbersome task. Although we have various data sets, the error in the data is huge, and because of the unknown variables, one is required to heavily rely on statistical techniques to establish the viability of the cosmological model. Therefore, understanding data analysis in cosmology has become one of the central themes of this game. However, just writing basic code in Python won't do the job, because Python is not as fast as C or C++. Therefore, optimizing the cosmological algorithm becomes very important in this case. In this video, I have shown the optimization of the algorithm and achieved MCMC 100 times faster than conventional coding. I have used CYTHON and PYTHON to optimize my code to fit the LambdaCDM model with 43 Hubble data sets. Here I am listing my papers that you can see and also attaching the GitHub repository link where you can find this code: https://github.com/sleonardokap/cosmological_data Time Stamp: 00:00:00 - Introduction 00:29 - Outline 01:30 -- Installing and edit the code with vscode 21:45 -- Basics of LambdaCDM 40:29 -- Brief discussion on w0waCDM, so-called CPL parameterization 50:41 -- Build your equations so that python will understand 01:25:51 -- Python implementation of the model 01:55:41 -- Understanding of Polychord Sampler. 02:01:30 -- Execution of the code. ___________________ 📚 Research Articles : My Research Papers and Other Important Research Articles: [1] Dynamical stability of K-essence field interacting non-minimally with a perfect fluid -- https://arxiv.org/abs/2105.00361 [2] Dynamics of dark energy -- https://arxiv.org/abs/hep-th/0603057 [3] Dynamics of purely kinetic k-essence in presence of a perfect fluid -- https://arxiv.org/abs/2203.10607 [5] Dynamical Systems and Cosmology -- https://bit.ly/42KHcta [6] Dynamical Systems in Cosmology -- https://bit.ly/3TOM9wV [7] TASI Lectures on Inflation -- https://arxiv.org/abs/0907.5424 [8] Dynamical systems analysis of tachyon-dark-energy models from a new perspective -- https://doi.org/10.1103/PhysRevD.107.063515 _____________________ 👽 Tags: #desibao #planckdata #algorithm_data #mcmc #emcee #python_cosmology_code #cython_optimization #python_cython #cosmological_data_analysis #inflation #SlowRollinflaion #SlowRollParameter #ultraslowrollinflation #InflationaryCosmology #dark_energy #dark_matter #Physics_research #Quintessence #kessence #dynamical_stability #CosmicInflation #GravitationalWaves #CosmicMicrowaveBackground #TachyonDynamics 🎞️ Keywords ___________________________________________ Cython Python MCMC Optimization Cosmological Model Fitting Data analysis Emcee Parallelization Python_Code_Optimization Polychord Pantheon+ DESI Supernova DESI BAO data