Reconciling dark energy models with f(R) theories

By Salvatore Capozziello, Vincenzo F. Cardone, Antonio Troisi. 2005

386 citations recorded by the source corpus.

Higher-order theories of gravity have recently attracted a lot of interest as alternative candidates to explain the observed cosmic acceleration without the need of introducing any scalar field. A critical ingredient is the choice of the function $f(R)$ of the Ricci scalar curvature entering the gravity Lagrangian and determining the dynamics of the Universe. We describe an efficient procedure to reconstruct $f(R)$ from the Hubble parameter $H$ depending on the redshift $z$. Using the metric formulation of $f(R)$ theories, we derive a third order linear differential equation for $f[R(z)]$ which can be numerically solved after setting the boundary conditions on the basis of physical considerations. Since $H(z)$ can be reconstructed from the astrophysical data, the method we present makes it possible to determine, in principle, what is the $f(R)$ theory which best reproduces the observed cosmological dynamics. Moreover, the method allows to reconcile dark energy models with $f(R)$ theories finding out what is the expression of $f(R)$ which leads to the same $H(z)$ of the given quintessence model. As interesting examples, we consider ``quiessence'' (dark energy with constant equation of state) and the Chaplygin gas.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c1fb4f578edec76b994614b355e5b09bfa11dc9e

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Citations in the corpus

Modified Gravity and Cosmology (2011, background): “Observations of these quantities allow the form of a(t) to be constrained, but due to the freedom in the choice of f(R) are not able to falsify the most general form of these theories directly [240, 929, 242, 376, 973, 496, 251, 980].”
A Bird's Eye View of f (R)-Gravity (2009, background): “In the approach dubbed “designer ) (R f gravity” in [74], the desired expansion history of the universe can be obtained by specifying the desired scale factor ) (t a and integrating an ordinary differential equation for the function ) (R f that produces the chosen ) (t a [79].”
f(R) Theories (2010, methodology): “There are some works that try to reconstruct the forms of f (R) by using some desired form for the evolution of the scale factor a(t) or the observational data of SN Ia [117, 130, 442, 191, 621, 252].”