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A Exact solutions of quintessence models of dark energy

  1. Aug 27, 2016 #1
    Hi everyone,

    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.
    Last edited: Aug 27, 2016
  2. jcsd
  3. Aug 27, 2016 #2


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    Have you looked at the Friedmann Equations with the scalar field as the energy source?
  4. Aug 28, 2016 #3
    Dear bapowell,

    It is possible to use the energy density of the scalar field (## \rho_\phi ##) in Friedmann equations, the problem is that we don't know the exact form of the scalar field ## \phi(t) ##, therefore integration can't be accomplished. There must be some other constrains on ## \phi(t) ##
  5. Aug 28, 2016 #4


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    For a given [itex]V(\phi)[/itex], you must specify [itex]\phi(t_0)[/itex] and [itex]\dot{\phi}(t_0)[/itex]. Then you can solve the Klein-Gordon and Friedmann equations together to obtain your cosmology.
  6. Aug 28, 2016 #5
    So there are "special" solutions depending on the behaviour of scalar field like slow-roll approximation in the inflationary cosmology. In fact, tracker quintessence models propose some solutions to cosmological constant problems. Maybe I should examine these fields.
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