Positive running of the spectral index is achievable in Einstein-Gauss-Bonnet gravity with viable inflation, unlike standard scalar field and F(R) models which face challenges.
Reconciling dark energy models with f(R) theories
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abstract
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.
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representative citing papers
In ghost-free two-scalar f(R) thick branes, internal structure produces no narrow real-axis tensor resonances; quasinormal modes are broad with quality factors 0.9-1.9.
Ghost-free non-local gravity fits Pantheon+, DESI, and H(z) data but fails with added CMB, while generalized exponential F(R) gravity outperforms Lambda CDM across all datasets including CMB.
Modified gravity theories supply viable mathematical frameworks for inflation, bounces, and dark energy eras that match observational data.
A comprehensive review of modified gravity theories and their cosmological consequences, including a parameterized post-Friedmannian formalism for constraining deviations from General Relativity.
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Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
Modified gravity theories supply viable mathematical frameworks for inflation, bounces, and dark energy eras that match observational data.