Research Highlight
March 14, 2007
A Walk Through the Dark Energy Forest: Dynamical Behavior of Generic Dark Energy Models
by Dragan Huterer and Hiranya Peiris

Much theoretical and experimental effort is currently being devoted to investigating ''dark energy'', a mysterious component that contributes about 75% of the total energy density in the universe and causes its expansion to accelerate. Virtually nothing is known about the nature of dark energy -- it could be simply the energy of empty space (Einstein's cosmological constant), a clumpy component that varies with time known as a scalar field, or something even more exotic. Working in the context of a given theoretical paradigm, it is often unclear exactly what range of observational signatures this paradigm predicts as a <i>class</i>, because particular <i>examples</i> (specific models) of that class predict only a subset of the signatures the whole class can predict. This is analogous to trying to learn about the important characteristics of a forest by studying only a selection of trees. In order to address this problem, KICP fellows Dragan Huter and Hiranya Peiris have proposed an efficient algorithm to rigorously and exhaustively sift through all of the possible evolution histories of the universe predicted by a particular paradigm of dark energy models. These histories are then compared with cosmological data (e.g. distances to supernovae, and the cosmic microwave background) to find the subset of models that look like our Universe. This is much like revealing a short walking path through the forest which efficiently leads you to representative examples of all the types of trees in it. As a by-product, the analysis also yields answers to many interesting questions one can ask about dark energy.

<i><b>Figure 1.</b> Equation of state (pressure to energy density ratio) of dark energy, the function that determines the evolution of the universe, shown between redshift zero (the present) and redshift three (when the universe was 15% of its current age). Each curve uniquely specifies the expansion history of the universe for that particular model. The proposed algorithm enables efficient exploration of millions of such models (only about 50 are shown).</i>

Once a <i>class</i> of dark energy models is chosen, what observations does it predict? This simple-sounding question becomes rather difficult to answer when one takes into account pesky details regarding the parameters describing the model. Huterer and Peiris have proposed a method similar to the highly successful one previously applied to ''inflation'' -- a near-exponential growth spurt in the very early universe -- to scan through all the models within the class and obtain the full set of evolution histories they predict. As an illustrative example, they picked the class of models to be time-varying dark energy described by a scalar field rolling down a potential. This is analogous to a ball (scalar field) rolling down a hill (the potential), slowed down by friction. Just like the slope of the hill and the initial speed of the ball determine how fast the ball is rolling down at any given time, the slope of the potential and speed of the scalar field determine the evolution of the universe. Measuring the shape of the potential (the hill) therefore allows us to gain insight to the physical mechanism that drives dark energy.

<i><b>Figure 2.</b> Same as Figure 1, except leaving only the models that are consistent with the current cosmological data. Note that data are strongest at low redshift (z<1, i.e. when the universe was more than about half its present age), and in this epoch the equation of state is constrained to be close to the cosmological constant value, -1.</i>

The key ingredients of the algorithm are a ''potential generator'' to systematically draw random examples of dynamical dark energy models, and a highly efficient statistical technique to compare these examples with the data. The details of the algorithm, however, are more complex than in the inflationary case because dark energy does not necessarily behave like a cosmological constant - the energy density of empty space, which is constant in time. A further complication is that dark energy shares its dominance with dark matter (about 25% of the total) which, unlike the former, tends to make the expansion of the universe slow down.

Applying this algorithm to scalar field models of dark energy, Huterer and Peiris have constrained these models both with current data and data expected from future experiments. The results show that future data will be capable of pinning down parameters describing dark energy with much greater precision than is possible at present. Furthermore, the analysis shows which physical aspects of the theoretical models can or cannot be determined better in the future. For example, future constraints on the speed of the scalar field and the energy density in dark energy will show a significant improvement over current constraints, whereas future constraints on the shape of the scalar field potential do not show such a great improvement. This is because dark energy has started dominating the evolution of the universe only recently, and therefore the data only samples only a small part of the potential, which is insufficient to give much information about details of its shape.

<i><b>Figure 3.</b> Constraints on the present-day value (w<sub>0</sub>) and the time variation (w<sub>a</sub>) of the dark energy equation of state from current data (blue contours) and data expected in the future (red contours). The inner and outer contours contain 68% and 95% of the total probability, showing which models are favored by the respective data sets. Individual points represent models generated by our algorithm; each point represents one model and, as in Figure 1, only a tiny fraction of the models actually explored are shown in this Figure.</i>

Particularly interesting is the fact that current data do not constrain the slope of the potential to be purely up or down, thus allowing for complex time-evolution of the equation of state. This has important implications for a recently proposed classification of dark energy potentials, either that they are ''freezing'' towards a cosmological constant-like state at the present epoch, or ''thawing'' from being in such a state in the past. The present study shows that generic scalar field models do not necessarily fall neatly in one of these classes. Nevertheless this classification is still useful, because if future data were to show that the constraints lie purely within one of these classes, it would mean that we can obtain a lot of information about the scalar field dynamics.

<i><b>Figure 4.</b> Another view of the evolution of dark energy, where the x-axis shows the equation of state, and the y-axis its rate of change. Each dark energy model creates a path in this space. The two triangular regions show regions allegedly populated by ''thawing'' (top) and ''freezing'' (bottom) models. The actual paths from our algorithm are represented by the curves, and it is clear that realistic models do not necessarily fall neatly in one of these classes.</i>

This study can be extended and generalized in a straightforward way to answer other questions about dark energy which are well worth exploring. Restricting the physical behavior of dark energy scalar field models early in the history of the universe could change the observational signatures expected today. Moreover, models other than scalar field dark energy can easily be explored. Furthermore, the present study only employed probes of the background expansion of the Universe. The next step would involve incorporating information on the growth rate of structures in the universe. It is also straightforward in this framework to study whether one can ever obtain useful information about the dark energy from the effects of its clumping, or to investigate the possible existence of interactions between dark energy and dark matter. One can sincerely hope, perhaps even expect, that these efforts will lead to important hints about the nature and the origin of dark energy.

<b>Reference:</b><br /> D. Huterer and H. Peiris, <a target='_blank' href=''>Dynamical behavior of generic quintessence potentials: constraints on key dark energy observables</a>, Phys. Rev. D 75, 083503 (2007).

Related Links:
KICP Members: Dragan Huterer; Hiranya V. Peiris