Bayesian inference methodology for primordial power spectrum reconstructions from Large Scale Structure

Journal of Cosmology and Astroparticle Physics, vol. 2024, pp. 072

Abstract

Abstract We use Bayesian inference to develop a non-parametric method to reconstruct the primordial power spectrum Pℛ (k) from Large Scale Structure (LSS) data. The performance of the method is assessed by testing it against simulations of the clustering of high-z (QSOs) objects. Their clustering is derived from different templates of the primordial power spectrum motivated by models of inflation: the Standard Model power law characterized by the two parameters As and ns ; a local feature template; and a global oscillatory template. The primordial power spectrum is reconstructed using N knots in the log {k, Pℛ (k)} plane while sampling the cosmological parameters {H 0, Ω b , Ω c }. We use two statistical tests to examine the reconstructions for signs of primordial features: a global test comparing the evidences and a novel local test quantifying the power of the hypothesis test between the power law model and the marginalized probability over N model. We also discuss results of an application to low-z (ELGs) objects with two different photometric errors keeping the cosmology fixed. The method shows good performance in all scenarios considered. In particular, the tests show no feature detection for the standard power-law primordial power spectrum; yet, the method is able to detect power spectrum deviations at a percent level for all considered features, combining either the low-z or the high-z redshift bins. In addition, we include a test proof-of-concept application to real data from the Sloan Digital Sky Survey Luminous Red Galaxy Data Release 4 (SDSS LRG 04), finding no preference for deviations from the primordial power law. The method is flexible, model independent, and suitable for its application to existing and future LSS surveys.

Authors 4

1. Guillermo Martínez-Somonte

   Universidad de Cantabria · Consejo Superior de Investigaciones Científicas · Instituto de Física de Cantabria

   Affiliation as printed

   Departamento de Física Moderna, Universidad de Cantabria, Avenida de los Castros s/n, E-39005 Santander, Spain

   Instituto de Física de Cantabria, CSIC-Universidad de Cantabria, Avenida de los Castros s/n, E-39005 Santander, Spain

2. Airam Marcos-Caballero

   University of the Basque Country

   Affiliation as printed

   Department of Theoretical Physics, University of the Basque Country UPV/EHU Barrio Sarriena s/n, Leioa, Vizcaya, Spain

3. Enrique Martínez-González

   Universidad de Cantabria · Consejo Superior de Investigaciones Científicas · Instituto de Física de Cantabria

   Affiliation as printed

   Instituto de Física de Cantabria, CSIC-Universidad de Cantabria, Avenida de los Castros s/n, E-39005 Santander, Spain

4. G Cañas-Herrera Aachen Lorentz Institute for Theoretical Physics

   Leiden University · European Space Agency · European Space Research and Technology Centre

   Affiliation as printed

   European Space Agency/ESTEC Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands

   Lorentz Institute for Theoretical Physics, Leiden University PO Box 9506, Leiden 2300 RA, The Netherlands