Boltzmann babies in the proper time measure

TL;DR

This paper tackles the cosmological measure problem by adopting a phenomenological, simplicity-driven approach and analyzes the proper time cutoff as a concrete measure. It shows that the proper time measure produces a strong youngness paradox: typical observers are early-time Boltzmann fluctuations, making a 2.7 K CMB observation highly improbable. Through both square-bubble and exact-bubble analyses, the authors demonstrate that allowing for bubble expansion and open geometry does not remove the paradox. They systematically test several modifications (e.g., don’t-ask-don’t-tell, spatial averaging, waiting for the first time, growing together, and anticipation) and conclude that none succeeds in reconciling the measure with observation, effectively ruling out the proper time measure as a viable cosmological gauge.

Abstract

After commenting briefly on the role of the typicality assumption in science, we advocate a phenomenological approach to the cosmological measure problem. Like any other theory, a measure should be simple, general, well-defined, and consistent with observation. This allows us to proceed by elimination. As an example, we consider the proper time cutoff on a geodesic congruence. It predicts that typical observers are quantum fluctuations in the early universe, or Boltzmann babies. We sharpen this well-known youngness problem by taking into account the expansion and open spatial geometry of pocket universes. Moreover, we relate the youngness problem directly to the probability distribution for observables, such as the temperature of the cosmic background radiation. We consider a number of modifications of the proper time measure, but find none that would make it compatible with observation.

Figures (2)

• Figure 1: The relative probability of making different observations, for example two different CMB temperatures (red disks or blue boxes), is determined by simple counting in the finite region between $\Sigma_0$ and $\Sigma_t$. The ratio tends to a finite limit as $t\rightarrow\infty$. The youngness problem is the fact that anomalous early fluctuations producing either observation (Boltzmann babies) turn out to dominate the count. To show this correctly in the figure, one would need to draw an exponentially large number of "young bubbles", like the one on the right, in which only the Boltzmann babies contribute.
• Figure 2: The top figure shows slices of constant FRW time, $\tau$ (red, light) and slices of constant geodesic time $t$ (blue, dark) in the vicinity of a bubble wall (green, thick) with initial size $r_0=0.1\, H_{\rm out}^{-1}$. Note that the constant $t$ slices are not defined for geodesics passing through the nucleation region of the bubble. The lower figure shows that geodesics of the congruence (blue, dark) eventually asymptote to comoving FRW worldlines (red, light).