On analytical solutions of f(R) modified gravity theories in FLRW cosmologies

Abstract

A novel analytical method for f(R) modified theories without matter in Friedmann-Lemaitre-Robertson-Walker spacetimes is introduced. The equation of motion for the scale factor in terms of cosmic time is reduced to the equation for the evolution of the Ricci scalar R with the Hubble parameter H. The solution of equation of motion for actions of the form of power law in Ricci scalar R, is presented with a detailed elaboration of the action quadratic in R. The reverse use of the introduced method is exemplified in finding functional forms f(R) which lead to specified scale factor functions. The analytical solutions are corroborated by numerical calculations with excellent agreement. Possible further applications to the phases of inflationary expansion and late-time acceleration as well as f(R) theories with radiation are outlined.

16 pages, 6 figures. v2: minor changes, references added. v3: minor changes, more references added. v4: version to appear in IJMPD. v5: DOI and journal reference added

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Cited by in corpus (2)

• Similarity solutions for the Wheeler-DeWitt equation in $f\left(R\right)$-cosmology
• Cosmological wheel or the arrow of time: A classical versus quantum perspective of gravity