Student or educator? Sign up with your school email and get 6 months of Pro free.
Cited by 375

The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index.

Dark energy at early times, the Hubble parameter, and the string axiverse

Open access
Karwal, Tanvi, Kamionkowski, Marc·2016·Physical Review D

Abstract

Precise measurements of the cosmic microwave background (CMB) power spectrum are in excellent agreement with the predictions of the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmological model. However, there is some tension between the value of the Hubble parameter ${H}_{0}$ inferred from the CMB and that inferred from observations of the Universe at lower redshifts, and the unusually small value of the dark-energy density is a puzzling ingredient of the model. In this paper, we explore a scenario with a new exotic energy density that behaves like a cosmological constant at early times and then decays quickly at some critical redshift ${z}_{c}$. An exotic energy density like this is motivated by some string-axiverse-inspired scenarios for dark energy. By increasing the expansion rate at early times, the very precisely determined angular scale of the sound horizon at decoupling can be preserved with a larger Hubble constant. We find, however, that the Planck temperature power spectrum tightly constrains the magnitude of the early dark-energy density and thus any shift in the Hubble constant obtained from the CMB. If the reionization optical depth is required to be smaller than the Planck 2016 $2\ensuremath{\sigma}$ upper bound $\ensuremath{\tau}\ensuremath{\lesssim}0.0774$, then early dark energy allows a Hubble-parameter shift of at most $1.6\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ (at ${z}_{c}\ensuremath{\simeq}1585$), too small to fully alleviate the Hubble-parameter tension. Only if $\ensuremath{\tau}$ is increased by more than $5\ensuremath{\sigma}$ can the CMB Hubble parameter be brought into agreement with that from local measurements. In the process, we derive strong constraints to the contribution of early dark energy at the time of recombination---it can never exceed $\ensuremath{\sim}2%$ of the radiation/matter density for $10\ensuremath{\lesssim}{z}_{c}\ensuremath{\lesssim}1{0}^{5}$.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physrevd.94.103523

Cites

27 of 27 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 27 references

Cited by

See all 375

Metadata

Authors
Karwal, T., & Kamionkowski, M.
Venue
Physical Review D
Published
2016-11-28
Volume
94
Issue
10
ISSN
  • 2470-0010 (ISSN-L)
  • 2470-0029
OpenAlex
W2487623152
Cited by
375
References
27
FWCI
6.67
Type
journal article
Language
en
Open access
green

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Dark energy at early times, the Hubble parameter, and the string axiverse. https://app.cochat.ai/papers/10.1103/physrevd.94.103523
The paper
Karwal, T., & Kamionkowski, M. (2016). Dark energy at early times, the Hubble parameter, and the string axiverse. Physical Review D. https://doi.org/10.1103/physrevd.94.103523

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.