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# Clustering and halo abundances in early dark energy cosmological models

Oxford University Press (OUP)

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### ABSTRACT

Cold Dark Matter with cosmological constant (ΛCDM) cosmological models with early dark energy (EDE) have been proposed to resolve tensions between the Hubble constant $H_0=100\, h$ km ṡ−1Ṁpc−1 measured locally, giving h ≈ 0.73, and H0 deduced from Planck cosmic microwave background (CMB) and other early-Universe measurements plus ΛCDM, giving h ≈ 0.67. EDE models do this by adding a scalar field that temporarily adds dark energy equal to about 10 per cent of the cosmological energy density at the end of the radiation-dominated era at redshift z ∼ 3500. Here, we compare linear and non-linear predictions of a Planck-normalized ΛCDM model including EDE giving h = 0.728 with those of standard Planck-normalized ΛCDM with h = 0.678. We find that non-linear evolution reduces the differences between power spectra of fluctuations at low redshifts. As a result, at z = 0 the halo mass functions on galactic scales are nearly the same, with differences only 1–2 per cent. However, the differences dramatically increase at high redshifts. The EDE model predicts 50 per cent more massive clusters at z = 1 and twice more galaxy-mass haloes at z = 4. Even greater increases in abundances of galaxy-mass haloes at higher redshifts may make it easier to reionize the universe with EDE. Predicted galaxy abundances and clustering will soon be tested by the James Webb Space Telescope (JWST) observations. Positions of baryonic acoustic oscillations (BAOs) and correlation functions differ by about 2 per cent between the models – an effect that is not washed out by non-linearities. Both standard ΛCDM and the EDE model studied here agree well with presently available acoustic-scale observations, but the Dark Energy Spectroscopic Instrument and Euclid measurements will provide stringent new tests.

### Most cited references91

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### Planck 2018 results: VI. Cosmological parameters

(2020)
We present cosmological parameter results from the final full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction. Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to significant gains in the precision of other correlated parameters. Improved modelling of the small-scale polarization leads to more robust constraints on many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5 σ level. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ω c h 2 = 0.120 ± 0.001, baryon density Ω b h 2 = 0.0224 ± 0.0001, scalar spectral index n s = 0.965 ± 0.004, and optical depth τ = 0.054 ± 0.007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100 θ * = 1.0411 ± 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H 0 = (67.4 ± 0.5) km s −1 Mpc −1 ; matter density parameter Ω m = 0.315 ± 0.007; and matter fluctuation amplitude σ 8 = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be N eff = 2.99 ± 0.17, in agreement with the Standard Model prediction N eff = 3.046, and find that the neutrino mass is tightly constrained to ∑ m ν < 0.12 eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2 σ , which pulls some parameters that affect the lensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, Ω K = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w 0 = −1.03 ± 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r 0.002 < 0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6 σ , tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by the Planck data.
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### The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the Data Release 9 spectroscopic galaxy sample

(2013)
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### Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛCDM

(2019)
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### Author and article information

###### Contributors
(View ORCID Profile)
(View ORCID Profile)
###### Journal
Monthly Notices of the Royal Astronomical Society
Oxford University Press (OUP)
0035-8711
1365-2966
June 2021
April 21 2021
June 2021
April 21 2021
March 31 2021
: 504
: 1
: 769-781
###### Affiliations
[1 ]Department of Astronomy, New Mexico State University, Las Cruces, 88003 NM, USA
[2 ]Department of Astronomy, University of Virginia, Charlettesville, 22904 VA, USA
[3 ]Laboratoire Univers & Particules de Montpellier, CNRS & Universite de Montpellier, Montpelier, 34090, France
[4 ]Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, E-18080 Granada, Spain
[5 ]Department of Physics and SCIPP, University of California, Santa Cruz, CA 95064, USA
[6 ]Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA
[7 ]Instituto de Astronomía, Universidad Nacional Autónoma de México, A.P. 70-264, 04510 CDMX, Mexico
[8 ]Steward Observatory, University of Arizona, Tucson, 85719 AZ, USA
[9 ]Department of Physics and Astronomy, Swarthmore College, 500 College Ave., Swarthmore, PA 19081, USA
###### Article
10.1093/mnras/stab769