Primordial Universe constraints using Minkowski Functionals and Persistence
Abstract
The Cosmic Microwave Background (CMB) is the "visible" remnant of the primordial plasma, this radiation was emitted when the Universe was 300,000 years old.
But looking at the statistics of its fluctuations, we can infer what happened at the very beginning,
in the first 10^-34 second and constrain fundamental theories and the origin of structures in the Universe.
For example, looking at how Gaussian (and isotropic and stationnary) the fluctuations distribution is gives access to extreme high energy physics.
In particular, primordial NG (non Gaussianity, any deviation from the Gaussian distribution)
could bring new information on the Inflation paradigm while NG sourced by cosmic strings and other topological defects could constrain supersymmetric and grand unified theories.
To constrain the potential NG features in CMB data, numerous methods have been developed, optimised and used, and here I will focus on one in particular,
the Minkowski Functionals (MFs), and its Bayesian statistical implementation. MFs describe the morphology of random fields -- topology and geometry --
and are sensitive to any NG, at any order.
Though generic they are not optimal for 1st order NG (parametrized by fNL)
and are used to validate results of the optimal estimators (bispectrum-based, 3-points correlation function transform).
However, for higher orders of NG (gNL), features such as cosmic strings, astrophysical signals, they proved to be a very powerful and robust tool.
Finally, I will describe the link of Minkowski Functionals with persistent homology, with the Betti numbers, and how the concept of persistence could be used to improve NG constraints with MFs.
