Inflation, cold dark matter, and the central density problem

TL;DR

This paper tackles the central density problem in LCDM by examining inflationary power spectra that depart from exact scale invariance and by considering a light neutrino component. Using COBE-normalized spectra from several inflation models (including inverted power law, running-mass, and broken-scale invariance) and a semi-analytic halo model calibrated to simulations, the authors predict halo central densities and compare them to rotation-curve–derived densities for dark-mominated galaxies. They find that standard $n=1$ LCDM remains overdense, but modest tilts and running (notably RM with $n<1$) or BSI can bring predictions into observational ranges; neutrino masses around $0.5$–$0.65$ eV can similarly alleviate the problem, albeit with tensions in $\sigma_8$ constraints. The study highlights that galaxy rotation curves may encode information about inflation and neutrinos, and emphasizes the role of the still-uncertain $\sigma_8$ value as a crucial test for these scenarios.

Abstract

A problem with high central densities in dark halos has arisen in the context of LCDM cosmologies with scale-invariant initial power spectra. Although n=1 is often justified by appealing to the inflation scenario, inflationary models with mild deviations from scale-invariance are not uncommon and models with significant running of the spectral index are plausible. Even mild deviations from scale-invariance can be important because halo collapse times and densities depend on the relative amount of small-scale power. We choose several popular models of inflation and work out the ramifications for galaxy central densities. For each model, we calculate its COBE-normalized power spectrum and deduce the implied halo densities using a semi-analytic method calibrated against N-body simulations. We compare our predictions to a sample of dark matter-dominated galaxies using a non-parametric measure of the density. While standard n=1, LCDM halos are overdense by a factor of 6, several of our example inflation+CDM models predict halo densities well within the range preferred by observations. We also show how the presence of massive (0.5 eV) neutrinos may help to alleviate the central density problem even with n=1. We conclude that galaxy central densities may not be as problematic for the CDM paradigm as is sometimes assumed: rather than telling us something about the nature of the dark matter, galaxy rotation curves may be telling us something about inflation and/or neutrinos. An important test of this idea will be an eventual consensus on the value of sigma_8, the rms overdensity on the scale 8 h^-1 Mpc. Our successful models have values of sigma_8 approximately 0.75, which is within the range of recent determinations. Finally, models with n>1 (or sigma_8 > 1) are highly disfavored.

Figures (6)

• Figure 1: The $z=0$ rms overdensity as a function of mass scale predicted by several models of inflation and normalized to COBE. The models depicted here are the running mass model with $\sigma = 0.05$ and $c = -0.001$ (RM $n>1$), the $n=1$ scale invariant Harrison-Zel'dovich spectrum ($n=1$), the broken-scale invariant model with $k_{c} = 0.9$ and $p=10$ (BSI), the inverted power law model with index $p=4$ (IPL4), and the running mass model with $\sigma = -0.31$ and $c = 0.04$ (RM $n<1$).
• Figure 2: Power spectra with massive neutrinos compared to the standard, scale invariant power spectrum with no massive neutrinos.
• Figure 3: The median $c_{\rm vir}-M_{\rm vir}$ relation predicted by several different primordial power spectra. The predictions corresponding to the different primordial power spectra are labeled in the same fashion as in Fig. \ref{['fig:spectra']}. Bullock et al.Bullock01 estimate the $1\sigma$ scatter to be $\Delta \log(c_{\rm vir}) \simeq 0.14$ while Jing argues for a smaller scatter of $\Delta \log(c_{\rm vir}) \simeq 0.08$JING. These estimates for the $1\sigma$ scatter are illustrated by the error bars in the upper right corner.
• Figure 4: The median $c_{\rm vir}-M_{\rm vir}$ relation in models with massive neutrinos.
• Figure 5: $V_{\rm max}$ vs. $\Delta_{\rm V/2}$ predictions compared with data. The filled triangles are the data points from de Blok, McGaugh, and Rubin BMR01, the gray squares are derived from the data of de Blok and Bosma BB02, and the open pentagons are points derived from the data of Swaters S99. The different theoretical predictions are labeled in the same way as Fig. \ref{['fig:cvirs']}. The error bars in the upper right corner show the expected $1\sigma$ scatter in the theoretical predictions. The smaller range corresponds to the Jing JING estimate and the larger range corresponds to the estimate of Bullock et al.Bullock01.