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Why is the CMB fluctuation level 10^{-5}?

Max Tegmark, Martin Rees

TL;DR

The paper investigates why the CMB fluctuation amplitude is $Q\sim 10^{-5}$ and explores the consequences if $Q$ were anthropically or physically different. Using Planck-scale microphysics, it derives a lower bound $Q_{min}\sim 10^{-6}$ set by hydrogen line cooling and an upper bound $Q_{max}\sim 10^{-4.5}$ set by Compton cooling from CMB photons, showing that both extremes can suppress galaxy formation or habitability. It discusses implications for inflation/defect models and how varying $Q$ interacts with anthropic bounds on $\Lambda$ and curvature, noting potential loopholes when multiple parameters vary. The work emphasizes that counterfactual universes provide a valuable testing ground for simulations and for understanding how fundamental constants shape structure formation and the prospects for observers.

Abstract

We explore the qualitative changes that would occur if the amplitude Q ~ 10^{-5} of cosmological density fluctuations were different. If is less than about 10^{-6}, the cosmological objects that form would have so low virial temperatures that they may be unable to cool and form stars, and would be so loosely bound that even if they could produce a supernova explosion, they might be unable to retain the heavy elements necessary for planetary life. If Q is greater than about 10^{-4}, dense supermassive galaxies would form, and biological evolution could be marred by short disruption timescales for planetary orbits. If Q were still larger, most bound systems would collapse directly to supermassive black holes. These constraints on Q can be expressed in terms of fundamental constants alone, and depend only on the electromagnetic and gravitational coupling constants, the electron-proton mass ratio and the matter-to-photon ratio. We discuss the implications for inflation and defect models, and note that the recent anthropic upper bounds on the cosmological constant Lambda would be invalid if both Q and Lambda could vary and there were no anthropic constraints on Q. The same applies to anthropic bounds on the curvature parameter Omega.

Why is the CMB fluctuation level 10^{-5}?

TL;DR

The paper investigates why the CMB fluctuation amplitude is and explores the consequences if were anthropically or physically different. Using Planck-scale microphysics, it derives a lower bound set by hydrogen line cooling and an upper bound set by Compton cooling from CMB photons, showing that both extremes can suppress galaxy formation or habitability. It discusses implications for inflation/defect models and how varying interacts with anthropic bounds on and curvature, noting potential loopholes when multiple parameters vary. The work emphasizes that counterfactual universes provide a valuable testing ground for simulations and for understanding how fundamental constants shape structure formation and the prospects for observers.

Abstract

We explore the qualitative changes that would occur if the amplitude Q ~ 10^{-5} of cosmological density fluctuations were different. If is less than about 10^{-6}, the cosmological objects that form would have so low virial temperatures that they may be unable to cool and form stars, and would be so loosely bound that even if they could produce a supernova explosion, they might be unable to retain the heavy elements necessary for planetary life. If Q is greater than about 10^{-4}, dense supermassive galaxies would form, and biological evolution could be marred by short disruption timescales for planetary orbits. If Q were still larger, most bound systems would collapse directly to supermassive black holes. These constraints on Q can be expressed in terms of fundamental constants alone, and depend only on the electromagnetic and gravitational coupling constants, the electron-proton mass ratio and the matter-to-photon ratio. We discuss the implications for inflation and defect models, and note that the recent anthropic upper bounds on the cosmological constant Lambda would be invalid if both Q and Lambda could vary and there were no anthropic constraints on Q. The same applies to anthropic bounds on the curvature parameter Omega.

Paper Structure

This paper contains 14 sections, 24 equations, 1 figure.

Table of Contents

  1. INTRODUCTION
  2. Inflationary predictions
  3. The cosmological constant puzzle
  4. Simulation-testing
  5. GALAXY FORMATION AND COOLING
  6. Notation
  7. When non-linear structures form
  8. Their virial temperature
  9. WHAT IF $Q\ll 10^{-5}$?
  10. WHAT IF $Q\gg 10^{-5}$?
  11. Disruption of planetary orbits
  12. Black hole domination
  13. What if $\Lambda$ and $\Omega$ were different?
  14. DISCUSSION

Figures (1)

  • Figure 1: The nine rising curves show the largest virialized mass scale as a function of time for different values of $Q$. Structures with $M\mathrel{\hbox{$\mathchar"218$} \hbox{$\mathchar"13C$}} M_{eq}$ (horizontal line) are seen to all virialize about a factor $Q^{-3/2}$ after the end of the radiation-dominated epoch (shaded, left), whereas for later times, the virialized mass scale asymptotes to about $Q^{3/2}$ times the horizon mass (shaded, upper left). Cooling is inefficient in the remaining shaded region (right). The star corresponds to the Milky Way.