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# 4.2 Quintessence models

Another family of dark energy models are those in which the equation of state evolves, i.e. changes with time. These are known as quintessence models, and provide a slightly different explanation for why is unimportant in the early Universe, but dominates at late times.

In this model, can be written as a function of the scale factor, , as follows:

Equation label:(4)

where is a constant and is a coefficient that determines how changes with . The scale factor itself is simply a mathematical quantity that describes the changing separation of two points in space as the Universe expands.

Measuring the parameters in Equation 4 is a key aim of many observational surveys to study dark energy. This can be done, for example, by targeting observations of Type Ia supernovae at redshifts corresponding to the epochs when the Universe changed from being matter-dominated to -dominated under different theories, and through observations of the evolution of large-scale structure.

Figure 6 illustrates the constraints on and obtained by combining the Planck (2018) CMB angular power spectrum data with Type Ia supernovae (SNe), weak gravitational lensing (WL), baryon acoustic oscillation (BAO) measurements and an additional method using galaxy statistics called redshift space distortions (RSD).

Figure 6 The measured constraints on an evolving dark energy equation of state. The 2018 Planck data (blue shaded regions) are further constrained by BAO and SNe measurements (cyan shading) and by BAO, RSD and weak lensing (WL) measurements (red shading). Darker and lighter shading within each data set indicate greater and lesser degrees of certainty, respectively.

- All of the observational constraints agree with the values at the intersection of the dashed lines. Which of the models discussed in this section does that position correspond to?

- The point at the intersection of the dashed lines is and . This coordinate corresponds to a cosmological constant model.

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