Dimensionless constants, cosmology and other dark matters

TL;DR

The authors address why the 31 dimensionless constants of particle physics and cosmology take their observed values by coupling inflationary landscape priors with astrophysical selection effects in a Bayesian framework. They develop a calculable axion prior $f_{\rm prior}(\xi_c) \propto \xi_c^{-1/2}$ and model selection via halo formation, cooling, star formation, and solar-system stability, revealing a robust banana-shaped region in halo properties whose viability is truncated by $\rho_\Lambda$. Their axion-case analysis shows the predicted prior combined with selection effects yields a DM-density distribution peaking near the observed value, supporting axions as a viable DM component; they also discuss a WIMP scenario and the possibility of multiple DM components yielding comparable densities. Marginalizing over $\rho_\Lambda$ produces a robust prediction for $R=\rho_\Lambda/(\xi^4 Q^3)$, while joint predictions in $(\rho_\Lambda,\xi,Q)$ hinge on the unknown $Q$ prior, underscoring the need to model selection effects carefully when testing ensemble theories of constants. Altogether, the work illustrates how anthropic and landscape considerations can render otherwise arbitrary constants testable by exposing how priors and astrophysical selection collapse the viable parameter space and yield predictions testable by upcoming DM searches and cosmological observations.

Abstract

We identify 31 dimensionless physical constants required by particle physics and cosmology, and emphasize that both microphysical constraints and selection effects might help elucidate their origin. Axion cosmology provides an instructive example, in which these two kinds of arguments must both be taken into account, and work well together. If a Peccei-Quinn phase transition occurred before or during inflation, then the axion dark matter density will vary from place to place with a probability distribution. By calculating the net dark matter halo formation rate as a function of all four relevant cosmological parameters and assessing other constraints, we find that this probability distribution, computed at stable solar systems, is arguably peaked near the observed dark matter density. If cosmologically relevant WIMP dark matter is discovered, then one naturally expects comparable densities of WIMPs and axions, making it important to follow up with precision measurements to determine whether WIMPs account for all of the dark matter or merely part of it.

Figures (13)

• Figure 1: The shifting boundary (horizontal lines) between fundamental laws and environmental laws/effective laws/initial conditions. Whereas Ptolemy and others sought to explain roughly spherical planets and circular orbits as fundamental laws of nature, Kepler and Newton reclassified such properties as initial conditions which we now understand as a combination of dynamical mechanisms and selection effects. Classical physics removed from the fundamental law category also the initial conditions for the electromagnetic field and all other forms of matter and energy (responsible for almost all the complexity we observe), leaving the fundamental laws quite simple. A prospective theory of everything (TOE) incorporating a landscape of solutions populated by inflation reclassifies important aspects of the remaining "laws" as initial conditions. Indeed, those laws can differ from one post-inflationary region to another, and since inflation generically makes each such region enormous, its inhabitants might be fooled into misinterpreting regularities holding within their particular region as Universal (that is, multiversal) laws. Finally, if the Level IV multiverse of all mathematical structures toe exists, then even the "theory of everything" equations that physicists are seeking are merely local bylaws in Rees' terminology ReesHabitat, that vary across a wider ensemble. Despite such retreats from ab initio explanations of certain phenomena, physics has progressed enormously in explanatory power.
• Figure 2: Many selection effects that we discuss are conveniently summarized in the plane tracking the virial temperatures and densities in dark matter halos. The gas cooling requirement prevents halos below the heavy black curve from forming galaxies. Close encounters make stable solar systems unlikely above the downward-sloping line. Other dangers include collapse into black holes and disruption of galaxies by supernova explosions. The location and shape of the small remaining region (unshaded) is independent of all cosmological parameters except the baryon fraction.
• Figure 3: Same as the previous figure, but including the banana-shaped contours showing the the halo formation/destruction rate. Solid/greenish contours correspond to positive net rates (halo production) at 0.5, 0.3, 0,2, 0.1, 0.03 and 0.01 of maximum, whereas dashed/reddish contours correspond to negative net rates (halo destruction from merging) at -0.3, -0,2, -0.1, -0.03 and -0.01 of maximum, respectively. The heavy black contour corresponds to zero net formation rate. The cosmological parameters $(\xi_{\rm b},\xi_{\rm c},\xi_\nu,,Q,\rho_\Lambda)$ have a strong effect on this banana: $\xi_{\rm b}$ and $\xi_{\rm c}$ shift this banana-shape vertically, $Q$ shifts if along the parallel diagonal lines and $\rho_\Lambda$ cuts it off below $16\rho_\Lambda$ (see the next figure). Roughly speaking, there are stable habitable planetary systems only for cosmological parameters where a greenish part of the banana falls within the allowed white region from Figure \ref{['Tn5Fig']}.
• Figure 4: Same as Figure \ref{['TnFig']}, but showing effect of changing the cosmological parameters. Increasing the matter density parameter $\xi$ shifts the banana up by a factor $\xi^4$ (top left panel), increasing the fluctuation level $Q$ shifts the banana up by a factor $Q^3$ and to the right by a factor $Q$ (top right panel), increasing the baryon fraction $f_{\rm b}=\xi_{\rm b}/\xi$ shifts the banana up by a factor $f_{\rm b}$ and affects the cooling and 2nd generation constraints (bottom left panel), and increasing the dark energy density $\rho_\Lambda$ bites off the banana below $\rho_{\rm vir}=16\rho_\Lambda$ (bottom right panel). In these these four panels, the parameters have been scaled relative to their observed values as follows: up by $1/4$, $2/4$,...,$9/4$ orders of magnitude ($\xi$), up by $1/3$, $2/3$,...,$9/3$ orders of magnitude ($Q$), down by $1$ and $2$ orders of magnitude ($f_{\rm b}$), and down by $0$, $7$, $12$ and $\infty$ orders of magnitude ($\rho_\Lambda$; other panels have $\rho_\Lambda=0$).
• Figure 5: Halo density distribution for various values of $\hat{\rho}_*/\rho_\Lambda$, where $\hat{\rho}_*\equiv[s(\mu)/A]^3\rho_*\sim Q^3\xi^4$. The dashed curves show the cumulative distribution $F = {\mathrm{erfc}}\left[{(\rho_\Lambda/\hat{\rho}_*)^{1/3}/{G_\Lambda}(x[\rho_{\rm vir}])}\right]$ and the solid curves show the probability distribution $-\partial F/\partial\lg\rho_{\rm vir}$ for (peaking from right to left) $\hat{\rho}_*/\rho_\Lambda=10^5$, $10^4$, $10^3$, $10^2$, $10$, $1$ (heavy curves), $0.1$ and $0.05$. Note that no halos with $\rho_{\rm vir}<16\rho_\Lambda$ are formed.