Persistent Homology and Complex networks based analysis of cosmological fields

Seyed Mohammad Sadegh Movahed
Department of Physics, Shahid Beheshti University, Tehran, Iran
Computational cosmology group (CCG-SBU)
Ibn-Sina Multidisciplinary Lab

Sunday, 13 February 2021, 16:30 IRDT


Improving in observational achievements of the cosmological field, quantitatively and qualitatively, relying on methods that are essentially based on variety, volume, and production rate aspects have become an interesting method in clarifying properties that have been already characterized by traditional approaches in parameterization and put constraints. On the other hand, there are many challenges in determining the values of cosmological parameters and a new window for searching in the universe. i.e. gravitational wave has been introduced.

In this public talk, motivated to explore mentioned challenges and observing exotic features in our cosmos, I will introduce the complex networks and their implementation on the CMB temperature field and large-scale cosmic structures. Beyond the local properties, we introduce the Betti numbers (number of components, holes, etc.) and their persistent concerning changes in the value of the dynamic parameter of the threshold, which can provide information compared to the Minkowski’s functionals, Euler characteristic, and Genes topology, away from degeneracy.

Finally, I will point out that combining these tools as feature vectors in the machine learning method can also improve the accuracy. Take-home messages of my talk are as follows:

۱) It is time to take into account more powerful methods to do high precision estimation in Cosmology

۲) Inspired by other systems in nature and using those methods considered for studying complex networks can lead to interesting results.

۳) Topological features can be used as the new and nonlinear tools to constrain the cosmological parameters.

۴) Machine learning methods can determine the feature importance of some topological and geometrical measures.

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