[Paper Review] Hot Dark Matter in Cosmology

Joel R. Primack, Michael Groß|arXiv (Cornell University)|Jul 12, 2000

Dark Matter and Cosmic Phenomena7 references4 citations

TL;DR

This paper investigates the role of hot dark matter (HDM) — primarily massive neutrinos — in cosmological structure formation, evaluating its compatibility with modern observational data. It finds that while HDM was abandoned in favor of cold dark matter (CDM) models due to small-scale power issues, adding ~0.2 in HDM (5 eV neutrinos) to CDM improves fits to galaxy and cluster distributions. However, in low-Ωm ΛCDM models, HDM's benefit is limited, with Ων ≤ 0.1 favored, and neutrino masses constrained to mν < 5.5 eV (95% C.L.).

ABSTRACT

Cosmological dark matter in the form of neutrinos with masses of up to a few electron volts is known as hot dark matter. After an historical review of the subject, this article considers constraints on hot dark matter from current data on neutrino oscillations and on cosmology. The atmospheric neutrino oscillation data imply a lower limit on the HDM contribution to the cosmological density $Ω_ν\gsim 0.001$. The possible improvement of low-$Ω_m$ flat ($Λ$CDM) cosmological models with the addition of light neutrinos appears to be rather limited, but$Λ$CDM models with $Ω_ν\lsim 0.1$ may be consistent with presently available data. Data expected soon may permit detection of such a hot dark matter contribution, or alternatively provide stronger upper limits on $Ω_ν$ and neutrino masses.

Motivation & Objective

• Assess the viability of hot dark matter (HDM) in modern cosmological models, particularly in light of new observational constraints.
• Re-evaluate the role of massive neutrinos in structure formation, especially in flat ΛCDM models with low matter density.
• Constrain the total neutrino mass and HDM contribution (Ων) using multi-probe data: CMB, APM galaxy power spectrum, Lyman-α forest, and globular cluster ages.
• Compare the performance of CHDM and ΛCHDM models against observational data, especially in fitting small-scale power and CMB anisotropies.
• Assess whether upcoming surveys (2dF, SDSS) and weak lensing data can detect or further constrain HDM signatures.

Proposed method

• Use COBE-normalized primordial power spectra with tilt (n) to model initial density fluctuations in ΛCHDM and ΛCDM models.
• Apply free-streaming suppression of small-scale power due to relativistic neutrinos to calculate the cutoff in the linear power spectrum P(k).
• Integrate observational constraints: COBE for CMB anisotropy, APM galaxy survey for P(k) at k ≈ 0.025–0.25 h/Mpc, and Lyman-α forest data at z ≈ 2.5 for high-redshift power.
• Apply age-of-the-universe constraint (≥13.2 Gyr) from globular clusters to limit model parameters.
• Use semi-analytic models and N-body simulations to compare predicted halo distributions with observations.
• Combine weak gravitational lensing data with CMB anisotropy data to improve constraints on Ων and neutrino mass.

Experimental results

Research questions

• RQ1 How does the inclusion of hot dark matter (HDM) with neutrino masses ~5 eV affect the fit of Ωm = 1 CDM models to galaxy and cluster distribution data?
• RQ2 What is the maximum allowed contribution of HDM (Ων) in low-Ωm ΛCDM models that remain consistent with current CMB, galaxy power spectrum, and Lyman-α forest data?
• RQ3 Can the addition of HDM improve the simultaneous fit of ΛCHDM models to small-scale CMB anisotropies and the APM galaxy power spectrum peak?
• RQ4 Are the current constraints on neutrino mass from Lyman-α forest and CMB data sufficient to detect or rule out HDM with mν < 1 eV?
• RQ5 Can upcoming large-scale surveys (2dF, SDSS) and weak lensing data resolve the tension between observed and predicted small-scale power in ΛCHDM and ΛCDM models?

Key findings

• CHDM models with Ων ≈ 0.2 (neutrino mass ~5 eV) provide a significantly improved fit to the nearby galaxy and cluster distribution compared to standard CDM models.
• ΛCHDM models with Ων ≤ 0.1 are consistent with current data, particularly for Ωm = 0.4–0.6, where the best fit occurs at Ων/Ωm = 0.1 and neutrino masses of 0.8–1.2 eV for h = 0.65.
• The total neutrino mass is constrained to mν < 5.5 eV at 95% confidence level across all Ωm values, with tighter limits of mν < 2.4(Ωm/0.17 − 1) eV for 0.2 ≤ Ωm ≤ 0.5.
• ΛCDM models with Ωm = 0.4–0.5 have too much small-scale power (k > 1 h⁻¹ Mpc), while ΛCHDM models may have too little, indicating a potential tension in power spectrum normalization.
• High-resolution simulations and shape statistics from 2dF and SDSS surveys are expected to distinguish between CDM and CHDM models, especially via their impact on halo and galaxy clustering.
• Lyman-α forest data at z ≈ 2.5 can detect HDM signatures even for neutrino masses as low as a fraction of an eV, and combined weak lensing + CMB data will further tighten constraints on Ων.