Abstract
We utilise a form for the Hubble parameter to generate a number of solutions to the Einstein field equations with variable cosmological constant and variable gravitational constant. The Hubble law utilised yields a constant value for the deceleration parameter. A variety of solutions is presented in the Robertson-Walker spacetimes. A generalisation of the cosmic scale factor is utilised in the anisotropic Bianchi I spacetime to illustrate that new solutions may also be found in spacetimes with less symmetry than Robertson-Walker. We also show that the constant deceleration parameter used is consistent with alternate theories of gravity by considering the scalar-tensor theory of Lau and Prokhovnik with ak = 0 Robertson-Walker background.
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Maharaj, S.D., Naidoo, R. Solutions to the field equations and the deceleration parameter. Astrophys Space Sci 208, 261–276 (1993). https://doi.org/10.1007/BF00657941
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DOI: https://doi.org/10.1007/BF00657941