In this paper we place observational constraints on the well-known γ-gravity f (R) model using the latest cosmological data, namely we use the latest growth rate, Cosmic Microwave Background, Baryon Acoustic Oscillations, Supernovae type Ia and Hubble parameter data. Performing a joint likelihood analysis we find that the γ-gravity model is in very good agreement with observations. Utilizing the AIC statistical test we statistically compare the current f (R) model with ΛCDM cosmology and find that they are statistically equivalent. Therefore, γ-gravity can be seen as a useful scenario toward testing deviations from General Relativity. Finally, we note that we find somewhat higher values for the f (R) best-fit values compared to those mentioned in the past in the literature and we argue that this could potential alleviate the halo-mass function problem. PACS numbers: 95.36.+x, 04.50.Kd, 98.80.Es

Dark matter could be made up of dark photons, massive but very light particles whose interactions with matter resemble those of usual photons but suppressed by a small mixing parameter. We analyze the main approaches to dark photon interactions and how they can be applied to direct detection experiments which test different ranges of masses and mixings. A new experiment based on counting dark photons from induced atomic transitions in a target material is proposed. This approach appears to be particularly appropriate for dark photon detection in the meV mass range, extending the constraints in the mixing parameter by up to eight orders of magnitude with respect to previous experiments.

The Coleman-Weinberg mechanism provides a procedure by which a scalar field, which initially has no mass parameters, acquires a mass due to the anomalous nature of scale symmetry. Loop corrections trigger a spontaneous symmetry breaking and the appearance of a non-trivial vacuum. We first review the basic example of the Coleman-Weinberg mechanism, scalar Quantum Electrodynamics, in a perturbative regime where the scalar particle becomes massive through photon loops. We then present the main results of this article, what we name the gravitational Coleman-Weinberg mechanism: we analyse the same effect in a gravitational theory without explicit energy scales at tree-level. Finally, we also study the mechanism for two scalar fields in the mentioned gravitational theory. We will derive the gravitational Coleman-Weinberg potentials, analyse the parameter space where we have a symmetry breaking, and obtain the value of the corresponding scalar masses.

We provide a simple computation in order to estimate the probability of a given hierarchy between two scales. In particular, we work in a model provided with a gauge symmetry, with two scalar doublets. We start from a scale-invariant classical Lagrangian, but by taking into account the Coleman–Weinberg mechanism, we obtain masses for the gauge bosons and the scalars. This approach typically provides a light (L) and a heavy (H) sector related to the two different vacuum expectation values of the two scalars. We compute the size of the hypervolume of the parameter space of the model associated with an interval of mass ratios between these two sectors. We define the probability as proportional to this size and conclude that probabilities of very large hierarchies are not negligible in the type of models studied in this work.

We thank F. J. Llanes-Estrada and V. Sanz for useful comments.