This paper investigates Everpresent Λ, a stochastic dark energy model motivated by
causal set theory and unimodular gravity, and confronts it with two key observational data sets,
Supernova Ia (SN Ia) and Cosmic Microwave Background (CMB) data. A key feature of this model is
that Λ fluctuates over time and on average the magnitude of its fluctuations is of the
order of the dominant energy density (be it radiation or matter) for the given epoch. In
particular, we focus on a phenomenological implementation of Everpresent Λ known as Model
1. The random fluctuations in Everpresent Λ realizations are generated using seed numbers,
and we find that for a small fraction of seeds Model 1 is capable of producing realizations that
fit SN Ia data better than ΛCDM. We further investigate what features distinguish these
realizations from the more general behaviour, and find that the “good” realizations have
relatively small fluctuations at low redshifts (z < 1.5), which do not closely track the matter
density. We find that Model 1 struggles to improve on ΛCDM at describing the CMB data.
However, by suppressing the values of Λ near the last scattering surface, as suggested in [1], we find a large improvement in the best fit of the model, though still with a
χ
2 value much larger than that of ΛCDM. We also study the allowed variation of the
dark energy density by the CMB constraints in a more model-independent manner, and find that some
variation (especially prior to recombination) is possible and in fact can lead to improvement over
ΛCDM and reduce the Hubble tension, in line with some early dark energy proposals.
However, for the kinds of variations considered, the favoured fluctuations are smaller in
magnitude than is typical in current Everpresent Λ models.