Similarity solutions for the Wheeler-DeWitt equation in $f\left(R\right)$-cosmology

Abstract

In the case of a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker universe in $f\left(R\right)$-gravity we write the Wheeler-DeWitt equation of quantum cosmology. The equation depends on the functional form of $f\left(R\right)$. We select to work with four specific functions of $f\left(R\right)$, in which the field equations for the classical models are integrable and solvable through quadratures. For these models, we determine similarity solutions for the Wheeler-DeWitt equation by determine Lie-Bäcklund transformations. In addition we show how the classical limit is recovered by the similarity solutions of the Wheeler-DeWitt equation.

18 pages, 4 figures, to appear in EPJC

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• Minisuperspace Quantization of $f\left(T,B\right)$ Cosmology
• Quantum potentiality in Inhomogeneous Cosmology
• Generalized Hidden Conformal Symmetry in Quadratic $f(T)$ Gravity
• New Rotating Black Hole Solutions With Imperfect Fluid Energy-Momentum Tensor In $f(R)$ Gravity
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