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Tension between the power spectrum of density perturbations measured on large and small scales

Battye, Richard; Charnock, Tom; Moss, Adam


Richard Battye

Tom Charnock

Associate Professor


There is a tension between measurements of the amplitude of the power spectrum of density perturbations inferred using the cosmic microwave background (CMB) and directly measured by large-scale structure (LSS) on smaller scales. We show that this tension exists, and is robust, for a range of LSS indicators including clusters, lensing and redshift space distortions and using CMB data from either Planck or WMAP+SPT/ACT. One obvious way to try to reconcile this is the inclusion of a massive neutrino which could be either active or sterile. Using Planck and a combination of all the LSS data we find that (i) for an active neutrino ∑mν=(0.357±0.099)  eV and (ii) for a sterile neutrino meffsterile=(0.67±0.18)  eV and ΔNeff=0.32±0.20. This is, however, at the expense of a degraded fit to Planck temperature data, and we quantify the residual tension at 2.5σ and 1.6σ for massive and sterile neutrinos, respectively. We also consider alternative explanations including a lower redshift for reionization that would be in conflict with polarization measurements made by WMAP and ad hoc modifications to the primordial power spectrum.


Battye, R., Charnock, T., & Moss, A. (2015). Tension between the power spectrum of density perturbations measured on large and small scales. Physical Review D, 91(10),

Journal Article Type Article
Acceptance Date Feb 1, 2015
Online Publication Date May 12, 2015
Publication Date May 15, 2015
Deposit Date Sep 21, 2017
Publicly Available Date Oct 9, 2020
Journal Physical Review D
Print ISSN 2470-0010
Electronic ISSN 2470-0029
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 91
Issue 10
Article Number 103508
Public URL
Publisher URL
PMID 00035436


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