The Fulness of Time

Robin Dienel / Carnegie Institution for Science

So if the standard model of cosmology is wrong, what alternative is there?

For the past couple of posts I’ve been talking about a new study that suggests we’ve been measuring supernova distances a bit wrong. While these new results could solve the long-standing Hubble tension problem, it does so by overturning the ΛCDM model.¹ Specifically, it would mean that dark energy cannot be due to a cosmological constant that is inherent to the structure of spacetime. What would this mean?

To begin with, much of what we know about the Universe would still hold up. The Big Bang, cosmic expansion, and general relativity are all still valid. The only thing that changes is that the Λ in ΛCDM isn’t constant. But while the ΛCDM model has stood the test of time, it’s also the simplest cosmological model. Plenty of other models have been proposed, and it’s worth looking at a few of them.

One approach is to treat dark energy as a scalar field.² Known as quintessence, or the “fifth force,” the model proposes that expansion is due to a kind of potential energy. Just as the Big Bang created protons, electrons, and neutrinos, maybe it also created a potential field. The simplest version of quintessence allows for a uniform energy density that is greater or less than the cosmological constant, which is fixed at a value of w_q = -1. What this means is that you could tweak the model to fit what we observe.

For example, the amount of matter and dark matter we observe in the cosmos isn’t nearly enough to slow down the rate of cosmic expansion. As the Universe expands, the mass density of the Universe decreases, meaning that eventually dark energy dominates cosmic evolution. If you tweak dark energy to be weaker, then there could be enough matter and dark matter to slow down cosmic expansion. The authors of the supernova paper looked at this kind of idea, referring to it as the Flat wCDM model. They found that while it fits the data better than the standard model in some ways, overall it isn’t a particularly good match.

Another approach is what’s known as a variable dark energy model. The approach here is to describe dark energy as an equation of state rather than a specific physical phenomenon. This allows the density of dark energy to vary both in space and time. The most popular approach is known as the Chevallier–Polarski–Linder model (CPL),³ and it gained popularity when we could use the scale of galactic clustering at different cosmological distances to test whether dark energy changed over time.

Son, et al

The supernova authors also look at this approach, specifically the Flat w₀w_aCDM model, which is the simplest CPL model. In it, w₀ represents an initial dark energy density, similar to Λ, which w_a is a scale factor that can vary in time. In this way you can have dark energy start out strong in the early Universe, but weaken over time. The team found that this model fits their data quite well. The correlation is even stronger when their data is combined with Baryon Accousing Oscillation (BAO) and Cosmic Microwave Background (CMB) data. Based on their study alone, this seems to be the best model. Of course, as noted before, their data set is small, with only about 300 supernovae.

When Rubin Observatory starts gathering supernova data in the near future, we’ll be able to determine whether this new study holds up. Perhaps the Flat w₀w_aCDM model will become the new standard model. Or maybe we’ll find even stranger results and we’ll have to look to things such as modified gravity or some interacting process that combines both dark energy and dark matter. Whatever we find, we will have a better understanding of the cosmos in the fulness of time.