We show that, in the context of brane-world scenarios with low tension tau=f(4), massive brane fluctuations (branons) are natural dark matter candidates. We calculate the present abundances for both hot (warm) and cold branons in terms of the branon mass M and the tension scale f. The results are compared with the current experimental bounds on these parameters. We also study the prospects for their detection in direct search experiments and comment on their characteristic signals in the indirect ones.

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We study the possible effects of classical gravitational backgrounds on the Higgs field through the modifications induced in the one-loop effective potential and the vacuum expectation value of the energy-momentum tensor. We concentrate our study on the Higgs self-interaction contribution in a perturbed FRW metric. For weak and slowly varying gravitational fields, a complete set of mode solutions for the Klein-Gordon equation is obtained to leading order in the adiabatic approximation. Dimensional regularization has been used in the integral evaluation and a detailed study of the integration of nonrational functions in this formalism has been presented. As expected, the regularized effective potential contains the same divergences as in flat spacetime, which can be renormalized without the need of additional counterterms. We find that, in contrast with other regularization methods, even though metric perturbations affect the mode solutions, they do not contribute to the leading adiabatic order of the potential. We also obtain explicit expressions of the complete energy-momentum tensor for general nonminimal coupling in terms of the perturbed modes. The corresponding leading adiabatic contributions are also obtained.

In the context of f (R) theories of gravity, we study the evolution of scalar cosmological perturbations in the metric formalism. Using a completely general procedure, we find the exact fourth-order differential equation for the matter density perturbations in the longitudinal gauge. In the case of sub-Hubble modes, the expression reduces to a second-order equation which is compared with the standard (quasi-static) equation used in the literature. We show that for general f (R) functions the quasi-static approximation is not justified. However, for those functions adequately describing the present phase of accelerated expansion and satisfying local gravity tests, it provides a correct description for the evolution of perturbations.

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