Delving Deep on Dynamical Dark Energy: Can we find signs of a different cosmology with the Integrated Sachs-Wolfe effect? 

Title: Structure Formation in Various Dynamical Dark Energy Scenarios 

Authors: Masoume Reyhani, Mahdi Najafi, Javad T. Firouzjaee, and Eleonora Di Valentino

First Author’s Institution: K.N. Toosi University of Technology, Tehran, Iran

Status: Submitted to Arxiv [open access]

If you go and crack open almost any paper about cosmology on arXiv, they almost all start the exact same way: “the ΛCDM model is extremely successful at describing the universe but it has some major problems.” This is definitely a good way to start a paper, as cosmology is going through some crises right now. The most famous of these is the Hubble Tension, where different methods of measuring the Hubble constant are returning strongly disagreeing results. However, there is a smattering of other issues, such as the Sigma 8 Tension and the missing satellite problem. Many of these could be explained by systematic errors in our experiments, but new physics is always an exciting possibility! One really interesting idea is to mess with the Λ of ΛCDM. Λ (Lambda) represents dark energy, the mysterious force that causes the universe to accelerate in its expansion. ΛCDM model suggests we live in a universe where 70% of all of the energy is in the form of dark energy. But what if that number was changing throughout cosmic history? This suggestion is called dynamical dark energy, and today’s authors put this theory through its paces!

ISW Effect: A User’s Guide

Ok, sure, maybe dark energy has changed in strength in the past. But how would we ever know? We can’t take a time machine to the earlier universe. Instead, we must try to spot the fingerprints of changing dark energy in the modern universe. One promising method is by studying the Integrated Sachs-Wolfe (ISW) effect. We are constantly bathed in light that is just now reaching us from the Big Bang, called the Cosmic Microwave Background (CMB). The useful thing about the CMB is that the colors of light that make it up are very predictable, and any small deviations from these predictions can tell us a lot about the history of the universe. For example, light from the Big Bang had to travel through the universe to reach us, and the universe has stuff in it [citation needed].

Fig. 1: This video provides an animation of redshifting of light by the Integrated Sachs-Wolfe Effect. Video Credit: Swinburne Animation Productions

Light’s interaction with intervening material can change the signal we receive here on Earth. The ISW is one specific example. When a photon heads into a large dense region of space, like a galaxy cluster, it is pulled in by gravity. We sometimes say that the photon has entered the “gravity well” of the cluster. As the photon enters the gravity well it gains energy, similarly to a ball speeding up as it rolls down a hill. In a static universe, the photon would have to spend all the energy it gained entering the gravity well to exit the gravity well, and leave the cluster with no change in energy. However, our universe is not static! In the time it takes for the photon to cross the cluster, the universe has spread out thanks to its constant expansion. Therefore, the force of gravity has become weaker, or the gravity well has become “shallower”.  The photon doesn’t have to spend as much energy to leave the well; it has now gained energy overall! (See an animated example of this in Figure 1.) This results in a photon with a little more energy than we would typically expect from a photon in the CMB, we say this photon makes a “hot spot” on the CMB. Similarly, if a photon were to enter a region of space that was less dense than average, (a gravitational “hill”, I guess, but I’ve never seen anyone call it that) it spends energy to do so, then as the universe expands the under-density decreases, so it regains less energy on the way out, resulting in a net loss of energy. This results in a cold spot on the CMB. To sum up: the ISW effect is the phenomenon that photons moving through an expanding universe tend to lose or gain energy depending on what they travel through, an effect we can measure by looking for cold or hot spots on the CMB. Since the ISW effect directly depends on the rate of the expansion of the universe, it is an ideal candidate for measuring the possible effects of Dynamical Dark Energy.

A Changing Dark Energy

In order to understand how exactly the existence of changing dark energy would affect the ISW effect, the authors need to choose exactly how dark energy is changing. Thus, the authors consider a few options for potential models of dynamical dark energy. These models essentially boil down to equations that describe the equation of state parameter, w,  of dark energy as a function of the age of the universe. This equation of state parameter describes the fluid-like behavior of dark energy, but all that we need to worry about here is that w is directly related to the amount of dark energy in the universe.

The authors cover 5 cases: the classic ΛCDM where w is -1, wCDM where w is constant but not necessarily -1, a linear increase in w, (the Chevallier-Polarski-Linder or CPL model) a quadratic curve (Jassal-Bagla-Padmanabhan or JBP model) and a rational expression (the Barboza-Alcaniz or BA model). If you don’t want to remember all those acronyms, just remember that we’re testing 5 models and each one is a slightly more complicated expression than the last. 

Fig. 2: In this figure we see the intensity of the ISW signal, and the rate of change of this intensity, at different epochs in cosmic history. a = 0 represents the big bang, while a = 1 is now. Note that all of the models predict slightly different values, making them potentially observationally distinct! Figure 4 in the Paper.

The authors look at two methods to examine the possible effects of changing dark energy on the universe, but we will focus on their approach that uses the ISW effect because it is the majority of the paper and, more importantly, I have a word count limit on this article. The authors first calculate the effect on the CMB that the ISW effect will have. This essentially amounts to adding up all of the gravitational wells and hills between us and where the photon traveled from along the path it took to get here. Since as we look further away in the universe we are looking back in time, this means we are adding up contributions from throughout cosmic history, so if dark energy has been changing it should affect the result of this calculation. The authors define a parameter, F, that describes how strong the ISW effect is throughout the “adding up” process, called the ISW source term. Performing the nasty calculations for each model, the authors plot the strength of the ISW effect throughout the history of the universe in Figure 2. The fact that each model gives such a different result is a good sign, it means we could potentially distinguish these cases through observation!

What do we see?

This is all well and good, but can we actually see any of these effects? The problem is that the ISW effect is quite weak – so weak, in fact, that it has yet to be significantly detected alone in observational data.  The keyword there is “alone.” The ISW effect is relatively minor on small scales,  but when photons pass through galaxy-sized gravitational wells, then we’re in business. With this idea in mind, the authors choose to consider how the distribution of the ISW effect overlaps with the distribution of galaxies, looking at what’s called a “cross correlation function.”  (If we were looking for just the ISW effect on its own, we might look at the auto-correlation function.) By measuring the overlap between the ISW and galaxy locations, we have essentially forced ourselves to pay attention to where the signal should be the strongest, which allows us to get a statistically significant measurement. Thankfully, large scale surveys of galaxies are so hot right now, so the authors have plenty to choose from. Choosing different surveys is important, as different surveys will be sensitive to different cosmological redshifts, and hence different times in cosmological history. Since we are adding up the contributions to a possibly changing dark energy throughout cosmic time, the varying sensitivity of these surveys could affect results. The authors consider the Dark Universe Explorer (DUNE), The National Radio Astronomy Observatory (NRAO) Very Large Array (VLA) Sky Survey (NVSS), The Sloan Digital Sky Survey (SDSS), and a survey similar to the Euclid Mission. The authors then calculate what we would expect to see for the ISW and galaxy distribution cross correlation function, taking into account the different sensitivities at different redshifts that these surveys have. What they find is shown in Figure 3.

Fig. 3: In the y axis of this figure the authors show the ISW-galaxy cross correlation signal as compared to expectation from ΛCDM. The x axis is in what is called CMB multipoles, and essentially corresponds to different size scales on the CMB. Low l means we are comparing points that are far apart, while high l means we are comparing points close together. Note that all of the models predict more intense signals than what ΛCDM predicts! Figure 7 in the Paper.

Their results show that the models for different dynamical dark energy scenarios yield different ISW cross correlation functions than the standard ΛCDM model. Furthermore, the different models are distinct from each other depending on the survey used. This means measurements of the ISW-galaxy cross correlation could be used to determine if dark energy has changed throughout cosmic history!

Measurement of this cross correlation is difficult, but not impossible. The author’s of today’s paper come to the important conclusion that all of the dynamical models result in higher ISW-galaxy cross correlations than the ΛCDM model alone. Therefore, we don’t have to perfectly measure the signal, only show that it’s higher than expected. Has anyone been able to do this? Actually, yes! Some studies have found measurements of this cross correlation are up to 2 sigma higher than what is predicted by ΛCDM. (Here, sigma is a statistical measurement, with higher sigma representing increased confidence in the detection being real. 3 sigma is a common cutoff for a discovery, while 5 sigma is the gold standard.) However, other studies have found signals consistent with ΛCDM. With new survey instruments and CMB telescopes coming online in the next decade, only further observation will show if dark energy is even more mysterious than previously thought!

Featured Image Credit: Wikimedia Commons

Astrobite Edited By: Alexandra Masegian

About Cole Meldorf

I am a PhD student at the University of Pennsylvania studying Astrophysics, specifically observational and theoretical cosmology. I also do some research with the Dark Energy Survey on galaxy evolution and supernova cosmology. When I'm not dying under the crushing weight of finals, I play the violin, do a little theater, and like to cook!

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