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Measuring the Small-Scale Power Spectrum of Cosmic Density Fluctuations Through 21 cm Tomography Prior to the Epoch of Structure Formation

Abraham Loeb, Matias Zaldarriaga

TL;DR

This work calculates the evolution of the spin temperature for this transition and the resulting anisotropies that are imprinted on the CMB sky due to linear density fluctuations during this epoch.

Abstract

The thermal evolution of the cosmic gas decoupled from that of the cosmic microwave background (CMB) at a redshift z~200. Afterwards and before the first stars had formed, the cosmic neutral hydrogen absorbed the CMB flux at its resonant 21cm spin-flip transition. We calculate the evolution of the spin temperature for this transition and the resulting anisotropies that are imprinted on the CMB sky due to linear density fluctuations during this epoch. These anisotropies at an observed wavelength of 10.56[(1+z)/50] meters, contain an amount of information that is orders of magnitude larger than any other cosmological probe. Their detection, although challenging, could tightly constrain any possible running of the spectral index from inflation (as suggested by WMAP), small deviations from Gaussianity, or any significant contribution from neutrinos or warm dark matter to the cosmic mass budget.

Measuring the Small-Scale Power Spectrum of Cosmic Density Fluctuations Through 21 cm Tomography Prior to the Epoch of Structure Formation

TL;DR

This work calculates the evolution of the spin temperature for this transition and the resulting anisotropies that are imprinted on the CMB sky due to linear density fluctuations during this epoch.

Abstract

The thermal evolution of the cosmic gas decoupled from that of the cosmic microwave background (CMB) at a redshift z~200. Afterwards and before the first stars had formed, the cosmic neutral hydrogen absorbed the CMB flux at its resonant 21cm spin-flip transition. We calculate the evolution of the spin temperature for this transition and the resulting anisotropies that are imprinted on the CMB sky due to linear density fluctuations during this epoch. These anisotropies at an observed wavelength of 10.56[(1+z)/50] meters, contain an amount of information that is orders of magnitude larger than any other cosmological probe. Their detection, although challenging, could tightly constrain any possible running of the spectral index from inflation (as suggested by WMAP), small deviations from Gaussianity, or any significant contribution from neutrinos or warm dark matter to the cosmic mass budget.

Paper Structure

This paper contains 7 sections, 11 equations, 3 figures.

Table of Contents

  1. Introduction.
  2. Spin temperature history.
  3. The small scale power spectrum.
  4. Unprecedented information.
  5. Detectability of signal.
  6. Final comments.
  7. Acknowledgments.

Figures (3)

  • Figure 1: Upper panel: Evolution of the gas, CMB and spin temperatures with redshift [4]. Lower panel:${dT_b/d{\delta_{H}}}$ as function of redshift. The separate contributions from fluctuations in the density and the spin temperature are depicted. We also show ${dT_b/d{\delta_{H}}} a \propto {dT_b/d{\delta_{H}}} \times {\delta_{H}}$, with an arbitrary normalization. Throughout this Letter, we assume the standard set of cosmological parameters for a universe dominated by cold dark matter and a cosmological constant ($\Lambda$CDM) [6].
  • Figure 2: Angular power spectrum of 21cm anisotropies on the sky at various redshifts. From top to bottom, $z=55,40,80,30,120,25,170$.
  • Figure 3: Upper panel: Power spectrum of 21cm anisotropies at $z=55$ for a $\Lambda$CDM scale-invariant power spectrum, a model with $n=0.98$, a model with $n=0.98$ and $\alpha_r\equiv {1\over 2} (d^2\ln P/d\ln k^2)=-0.07$, a model of warm dark matter particles with a mass of 1 keV, and a model in which $f_\nu=10\%$ of the matter density is in three species of massive neutrinos with a mass of $0.4~{\rm eV}$ each. Lower panel: Ratios between the different power spectra and the scale-invariant spectrum.