Cosmological Tests of Everpresent $\Lambda$

Everpresent $\Lambda$ is a cosmological scenario in which the observed cosmological "constant" $\Lambda$ fluctuates between positive and negative values with a vanishing mean, and with a magnitude comparable to the critical density at any epoch. In accord with a longstanding heuristic prediction of causal set theory, it postulates that $\Lambda$ is a stochastic function of cosmic time that will vary from one realization of the scenario to another. Herein, we consider two models of "dark energy" that exhibit these features. Via Monte Carlo Markov chains, we explore the space of cosmological parameters and the set of stochastic realizations of these models, finding that Everpresent $\Lambda$ can fit the current cosmological observations as well as the $\Lambda$CDM model does. Furthermore, it removes observational tensions with $\Lambda$CDM, for low redshift measurements of Hubble constant, and the Baryonic Acoustic Oscillations (BAO) in Lyman-$\alpha$ forest at $z\sim 2-3$. However, we also find that Everpresent $\Lambda$ does not significantly help with the growth of ultramassive black holes at high redshift, and the Lithium problem in Big Bang Nuclesynthesis. Future measurements of "dark energy" at high redshifts will further test the viability of Everpresent $\Lambda$ as an alternative to the $\Lambda$CDM cosmology.