We investigate f (R) theories of gravity within the Palatini approach and show how one can determine the expansion history, H(a), for an arbitrary choice of f (R). As an example, we consider cosmological constraints on such theories arising from the supernova type Ia, large-scale structure formation, and cosmic microwave background observations. We find that the best fit to the data is a nonnull leading order correction to the Einstein gravity. However, the current data exhibits no significant trend toward such corrections compared to the concordance ΛCDM model. Our results show that the oft-considered 1/R models are not compatible with the data. The results demonstrate that background expansion alone can act as a good discriminator between modified gravity models when multiple data sets are used.

We present results for the 3 P 2 -3 F 2 pairing gap in neutron matter with several realistic nucleon-nucleon potentials, in particular with recent, phase-shift equivalent potentials. We find that their predictions for the gap cannot be trusted at densities above ρ ≈ 1.7ρ 0 , where ρ 0 is the saturation density for symmetric nuclear matter. In order to make predictions above that density, potential models which fit the nucleon-nucleon phase shifts up to about 1 GeV are required.

There is a renewed interest in constraining the sum of the masses of the three neutrino flavours by using cosmological measurements. Solar, atmospheric, reactor and accelerator neutrino experiments have confirmed neutrino oscillations, implying that neutrinos have non-zero mass, but without pinning down their absolute masses. While it is established that the effect of light neutrinos on the evolution of cosmic structure is small, the upper limits derived from large-scale structure could help significantly to constrain the absolute scale of the neutrino masses. It is also important to know the sum of neutrino masses as it is degenerate with the values of other cosmological parameters, e.g. the amplitude of fluctuations and the primordial spectral index. A summary of cosmological neutrino mass limits is given. Current results from cosmology set an upper limit on the sum of the neutrino masses of ∼ 1 eV, somewhat depending on the data sets used in the analyses and assumed priors on cosmological parameters. It is important to emphasize that the total neutrino mass ('hot dark matter') is derived assuming that the other components in the universe are baryons, cold dark matter and dark energy. We assess the impact of neutrino masses on the matter power spectrum, the cosmic microwave background, peculiar velocities and gravitational lensing. We also discuss future methods to improve the mass upper limits by an order of magnitude.

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Context. The so-called shift parameter is related to the position of the first acoustic peak in the power spectrum of the temperature anisotropies of the cosmic microwave background (CMB). It is an often used quantity in simple tests of dark energy models. However, the shift parameter is not directly measurable from the cosmic microwave background, and its value is usually derived from the data assuming a spatially flat cosmology with dark matter and a cosmological constant. Aims. To evaluate the effectiveness of the shift parameter as a constraint on dark energy models. Methods. We discuss the potential pitfalls in using the shift parameter as a test of non-standard dark energy models. Results. By comparing to full CMB fits, we show that combining the shift parameter with the position of the first acoustic peak in the CMB power spectrum improves the accuracy of the test considerably.