Lectures on Cosmology

Volume 800 of the series Lecture Notes in Physics pp 99-145


Modified Gravity Models of Dark Energy

  • S. TsujikawaAffiliated withDepartment of Physics, Faculty of Science, Tokyo University of Science Email author 

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We review the recent progress for modified gravity models of dark energy – including f(R) gravity, scalar-tensor theories, and braneworld models.

In f(R) gravity, where the Lagrangian density f is a function of the Ricci scalar R, the coupling strength between dark energy and non-relativistic matter is of order 1 (\(Q = -1/\sqrt{6}\)) in the Einstein frame. Even in this situation it is possible for f(R) models to be consistent with local gravity constraints under the chameleon mechanism, while at the same time satisfying conditions for the cosmological viability. We present a number of viable f(R) models that satisfy cosmological and local gravity constraints.

We also study a class of scalar-tensor dark energy models based on Brans–Dicke theory with a scalar-field potential. The action in the Einstein frame can be viewed as a coupled quintessence scenario with a constant coupling Q that is related to a Brans–Dicke parameter \(\omega_{\mathrm{BD}}\) via \(3+2\omega_{\mathrm{BD}}=1/2Q^2\). We show that, even when \(|Q|\) is of the order of 1, it is possible for these models to be consistent with cosmological and local gravity constraints as long as the field potential is designed in a suitable way.

We investigate the evolution of matter density perturbations for f(R) and scalar-tensor models and show that model parameters as well as the strength of the coupling Q can be constrained from matter/CMB power spectra due to the enhanced growth rate of perturbations compared to the ΛCDM model.

Finally, we discuss the DGP braneworld model as a candidate for dark energy. While the late-time cosmic acceleration is possible, this model is under strong pressure from joint constraints using the data of SNLS, BAO, and the CMB shift parameter. Moreover, a ghost mode is present for such a self-accelerating universe. Thus the original DGP model is effectively ruled out from observational constraints as well as from the ghost problem.