The impact of the cosmological constant on past and future star formation

TL;DR

This paper models how varying the cosmological constant affects star formation history, revealing that the observed value of the cosmological constant is surprisingly small compared to predictions, challenging anthropic explanations.

Contribution

It introduces an extended analytic model for cosmic star formation across a range of cosmological constants within the $ m extLambda$CDM framework, highlighting the impact on star formation efficiency and anthropic reasoning.

Findings

Star formation efficiency peaks at 27% for certain $ m extLambda$ values.

The probability of observing the actual $ m extLambda$ is only 0.5%.

Predictions challenge the anthropic explanation for the cosmological constant.

Abstract

We present an extended analytic model for cosmic star formation, with the aim of investigating the impact of cosmological parameters on the star formation history within the $\Lambda$CDM paradigm. Constructing an ensemble of flat $\Lambda$CDM models where the cosmological constant varies between $\Lambda = 0$ and $10^5$ times the observed value, $\Lambda_{\rm obs}$, we find that the fraction of cosmic baryons that are converted into stars over the entire history of the universe peaks at $\sim$27% for $0.01 \lesssim \Lambda/\Lambda_{\rm obs} \lesssim 1$. We explain, from first principles, that the decline of this asymptotic star-formation efficiency for lower and higher values of $\Lambda$ is driven respectively by the astrophysics of star formation, and by the suppression of cosmic structure formation. However, the asymptotic efficiency declines slowly as $\Lambda$ increases, falling below 5% only for $\Lambda>100 \, \Lambda_{\rm obs}$. Making the minimal assumption that the probability of generating observers is proportional to this efficiency, and following Weinberg in adopting a flat prior on $\Lambda$, the median posterior value of $\Lambda$ is $539 \, \Lambda_{\rm obs}$. Furthermore, the probability of observing $\Lambda\leq \Lambda_{\rm obs}$ is only $0.5\%$. Although this work has not considered recollapsing models with $\Lambda<0$, the indication is thus that $\Lambda_{\rm obs}$ appears to be unreasonably small compared to the predictions of the simplest multiverse ensemble. This poses a challenge for anthropic reasoning as a viable explanation for cosmic coincidences and the apparent fine-tuning of the universe: either the approach is invalid, or more parameters than $\Lambda$ alone must vary within the ensemble.