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I got the basic ideas quintessence (minimally coupled) and derived the KG equation for scalar field:

$$ \ddot{\phi} + 3 H \dot{\phi} + \frac{\partial V(\phi)}{\partial \phi} = 0 $$

where $$H=\frac{\dot{a}}{a}$$ and $\phi$ is the scalar field.

There are various models depending on the choice of potential of the field, however I do not understand how to construct cosmological model from these potentials? Obviously, there is an differential equation that must be solved but does it even have an analytical solution?

P.S: I am open your resource suggestions.

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# A Exact solutions of quintessence models of dark energy

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