# Searching for Local Features in Primordial Power Spectrum using Genetic Algorithms

**Authors:** Kushal Lodha, Lucas Pinol, Savvas Nesseris, Arman Shafieloo, Wuhyun Sohn, Matteo Fasiello  
**arXiv:** [2308.04940](https://arxiv.org/abs/2308.04940)  
**Date:** 2023-08-09  
**Summary page:** https://www.summarizepaper.com/en/paper/2308.04940v1/

## Key points

- Novel methodology for exploring local features in the primordial power spectrum using a genetic algorithm (GA) pipeline coupled with a Boltzmann solver and Cosmic Microwave Background (CMB) data
- Goal is to provide an analytical reconstruction of the power spectra that best fits the CMB data, allowing for a model-independent approach
- Validation of pipeline using mock data and application to latest CMB data, including Planck 2018 and CamSpec PR4
- Significant improvements upon simple power-law behavior, with Δχ^2 ≲ -21
- Best-fits address lowℓ anomaly in TT spectrum and residual highℓ oscillations in TT, TE, and EE spectra
- Numerical solution of Einstein-Boltzmann equations using cosmological Boltzmann solvers to compute accurate angular power spectrum of CMB
- Genetic algorithms used to optimize feature selection and refine solution space iteratively
- Methodology provides adaptable tool for exploring features in primordial power spectrum in a model-independent way
- Offers valuable hints to theorists for constructing viable inflationary models consistent with current and upcoming CMB surveys

## Summary

In this paper, the authors present a novel methodology for exploring local features in the primordial power spectrum using a genetic algorithm (GA) pipeline coupled with a Boltzmann solver and Cosmic Microwave Background (CMB) data. The goal is to provide an analytical reconstruction of the power spectra that best fits the CMB data, allowing for a model-independent approach. The authors first validate their pipeline using mock data and then apply it to the latest CMB data, including Planck 2018 and CamSpec PR4. They find significant improvements upon the simple power-law behavior, with $\Delta \chi^2 \lesssim -21$, consistently with more traditional model-based approaches. Specifically, their best-fits address both the low$\ell$ anomaly in the TT spectrum and the residual high$\ell$ oscillations in the TT, TE, and EE spectra. To compute the angular power spectrum of the CMB accurately, they solve numerically Einstein-Boltzmann equations using cosmological Boltzmann solvers. These solvers take as input parameters such as dark matter density, baryon density, dark energy density, Hubble constant and amplitude of primordial perturbations along with primordial power spectrum which can be described by 𝑃(𝑘), where 𝑘 represents wave number. In their approach they represent desired power spectrum as chromosomes in genetic algorithms. Each chromosome corresponds to configuration of features in primordial power spectrum while fitness function is defined as sum of 𝜒2 values derived from different likelihoods. Genetic algorithms are used to optimize feature selection and refine solution space iteratively to identify configurations that best agree with available data. Overall this methodology provides an adaptable tool for exploring features in primordial power spectrum in model-independent way offering valuable hints to theorists for constructing viable inflationary models consistent with current and upcoming CMB surveys. The paper is organized as follows: Section 2 provides an overview of genetic algorithm and pipeline utilized; Section 3 describes datasets used and presents results; Section 4 concludes with summary and discussion of future directions.