Beta function quintessence cosmological parameters and fundamental constants – I. Power and inverse power law dark energy potentials
AuthorThompson, Rodger I
AffiliationUniv Arizona, Steward Observ
MetadataShow full item record
PublisherOXFORD UNIV PRESS
CitationRodger I Thompson; Beta function quintessence cosmological parameters and fundamental constants – I. Power and inverse power law dark energy potentials, Monthly Notices of the Royal Astronomical Society, Volume 477, Issue 3, 1 July 2018, Pages 4104–4115, https://doi.org/10.1093/mnras/sty927
Rights© 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society
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AbstractThis investigation explores using the beta function formalism to calculate analytic solutions for the observable parameters in rolling scalar field cosmologies. The beta function in this case is the derivative of the scalar phi with respect to the natural log of the scale factor alpha, beta(phi) = d phi/d ln(a) Once the beta function is specified, modulo a boundary condition, the evolution of the scalar phi as a function of the scale factor is completely determined. A rolling scalar field cosmology is defined by its action which can contain a range of physically motivated dark energy potentials. The beta function is chosen so that the associated 'beta potential' is an accurate, but not exact, representation of the appropriate dark energy model potential. The basic concept is that the action with the beta potential is so similar to the action with the model potential that solutions using the beta action are accurate representations of solutions using the model action. The beta function provides an extra equation to calculate analytic functions of the cosmologies parameters as a function of the scale factor that are not calculable using only the model action. As an example, this investigation uses a quintessence cosmology to demonstrate the method for power and inverse power law dark energy potentials. An interesting result of the investigation is that the Hubble parameter H is almost completely insensitive to the power of the potentials and that A cold dark matter is part of the family of quintessence cosmology power-law potentials with a power of zero.
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