Predictions of the causal entropic principle for environmental conditions of the universe

The causal entropic principle has been proposed as an alternative to the anthropic principle for understanding the magnitude of the cosmological constant. In this approach, the probability to create observers is assumed to be proportional to the entropy production $\Delta S$ in a maximal causally connected region—the causal diamond. We improve on the original treatment by better quantifying the entropy production due to stars, using an analytic model for the star formation history which accurately accounts for changes in cosmological parameters. We calculate the dependence of $\Delta S$ on the density contrast $Q=\delta \rho /\rho$, and find that our universe is much closer to the most probable value of $Q$ than in the usual anthropic approach and that probabilities are relatively weakly dependent on this amplitude. In addition, we make first estimates of the dependence of $\Delta S$ on the baryon fraction and overall matter abundance. Finally, we also explore the possibility that decays of dark matter, suggested by various observed gamma ray excesses, might produce a comparable amount of entropy to stars.

Figure 1

The causal diamond.

Figure 2

Unnormalized probability distributions for $\Lambda$ using different star formation rates [24, 25, 26]. The vertical line indicates the observed value of $\Lambda$.

Figure 3

Solid lines: the star formation rate used in this paper, for several values of ${\rho }_{\Lambda }$. Dashed lines are the approximation (9). Common proportionality constants have been omitted.

Figure 4

Asymptotic value of the star formation rate at large times, as a function of $\Lambda /M_P^2$.

Figure 5

Unnormalized probability distributions for $\Lambda$ at different values of $Q=Q_s{Q}_{\mathrm{obs}}$.

Figure 6

Unnormalized probability distribution for $Q$ at fixed $\Lambda ={\Lambda }_{\mathrm{obs}}$.

Figure 7

Contours of the probability distribution $dP/d\log \Lambda$, varying $Q$ and $\Lambda$.

Figure 8

Unnormalized probability distribution for relative baryon fraction $r_b=6f_b$ at fixed $\Lambda ={\Lambda }_{\mathrm{obs}}$.

Figure 9

Unnormalized probability distribution for relative matter abundance $r_m$ at fixed $\Lambda ={\Lambda }_{\mathrm{obs}}$.

Figure 10

Entropy produced by dark matter decays as a function of the dimensionless combination $\Gamma t_{\Lambda }$ (up to an overall proportionality).