No Evidence for Extensions to the Standard Cosmological Model
File(s)
Accepted version
OA Location
Author(s)
Type
Journal Article
Abstract
We compute the Bayesian evidence for models considered in the main analysis of Planck cosmic microwave background data. By utilizing carefully defined nearest-neighbor distances in parameter space, we reuse the Monte Carlo Markov chains already produced for parameter inference to compute Bayes factors
B
for many different model-data set combinations. The standard 6-parameter flat cold dark matter model with a cosmological constant (
Λ
CDM
) is favored over all other models considered, with curvature being mildly favored only when cosmic microwave background lensing is not included. Many alternative models are strongly disfavored by the data, including primordial correlated isocurvature models (
ln
B
=
−
7.8
), nonzero scalar-to-tensor ratio (
ln
B
=
−
4.3
), running of the spectral index (
ln
B
=
−
4.7
), curvature (
ln
B
=
−
3.6
), nonstandard numbers of neutrinos (
ln
B
=
−
3.1
), nonstandard neutrino masses (
ln
B
=
−
3.2
), nonstandard lensing potential (
ln
B
=
−
4.6
), evolving dark energy (
ln
B
=
−
3.2
), sterile neutrinos (
ln
B
=
−
6.9
), and extra sterile neutrinos with a nonzero scalar-to-tensor ratio (
ln
B
=
−
10.8
). Other models are less strongly disfavored with respect to flat
Λ
CDM
. As with all analyses based on Bayesian evidence, the final numbers depend on the widths of the parameter priors. We adopt the priors used in the Planck analysis, while performing a prior sensitivity analysis. Our quantitative conclusion is that extensions beyond the standard cosmological model are disfavored by Planck data. Only when newer Hubble constant measurements are included does
Λ
CDM
become disfavored, and only mildly, compared with a dynamical dark energy model (
ln
B
∼
+
2
).
B
for many different model-data set combinations. The standard 6-parameter flat cold dark matter model with a cosmological constant (
Λ
CDM
) is favored over all other models considered, with curvature being mildly favored only when cosmic microwave background lensing is not included. Many alternative models are strongly disfavored by the data, including primordial correlated isocurvature models (
ln
B
=
−
7.8
), nonzero scalar-to-tensor ratio (
ln
B
=
−
4.3
), running of the spectral index (
ln
B
=
−
4.7
), curvature (
ln
B
=
−
3.6
), nonstandard numbers of neutrinos (
ln
B
=
−
3.1
), nonstandard neutrino masses (
ln
B
=
−
3.2
), nonstandard lensing potential (
ln
B
=
−
4.6
), evolving dark energy (
ln
B
=
−
3.2
), sterile neutrinos (
ln
B
=
−
6.9
), and extra sterile neutrinos with a nonzero scalar-to-tensor ratio (
ln
B
=
−
10.8
). Other models are less strongly disfavored with respect to flat
Λ
CDM
. As with all analyses based on Bayesian evidence, the final numbers depend on the widths of the parameter priors. We adopt the priors used in the Planck analysis, while performing a prior sensitivity analysis. Our quantitative conclusion is that extensions beyond the standard cosmological model are disfavored by Planck data. Only when newer Hubble constant measurements are included does
Λ
CDM
become disfavored, and only mildly, compared with a dynamical dark energy model (
ln
B
∼
+
2
).
Date Issued
2017-09-07
Date Acceptance
2017-07-11
Citation
PHYSICAL REVIEW LETTERS, 2017, 119 (10)
ISSN
0031-9007
Publisher
American Physical Society
Journal / Book Title
PHYSICAL REVIEW LETTERS
Volume
119
Issue
10
Copyright Statement
© 2017 American Physical Society. Phys. Rev. Lett. 119, 101301.
Sponsor
Imperial College Trust
Science and Technology Facilities Council
Science and Technology Facilities Council (STFC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000409560100002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
N/A
ST-N000838
ST/N000838/1
Subjects
Science & Technology
Physical Sciences
Physics, Multidisciplinary
Physics
BAYES
02 Physical Sciences
General Physics
Publication Status
Published
Article Number
ARTN 101301