Abstract: A class of well-behaved modified gravity models with long enough matter domination epoch and a late-time accelerated expansion is confronted with SNIa, CMB, SDSS, BAO and H(z) galaxy ages data, as well as current measurements of the linear growth of structure. We show that the combination of geometrical probes and growth data exploited here allows to rule out f(R) gravity models, in particular, the logarithmic of curvature model. We also apply solar system tests to the models in agreement with the cosmological data. We find that the exponential of the inverse of the curvature model satisfies all the observational tests considered and we derive the allowed range of parameters. Current data still allows for small deviations of Einstein gravity. Future, high precision growth data, in combination with expansion history data, will be able to distinguish tiny modifications of standard gravity from the Lambda CDM model.

Abstract: Using the Fenchel-Eggleston theorem for convex hulls (an extension of the Caratheodory theorem), we prove that any likelihood can be maximized by either a dark matter 1-speed distribution F(v) in Earth's frame or 2-Galactic velocity distribution f(gal) ((u) over right arrow), consisting of a sum of delta functions. The former case applies only to time-averaged rate measurements and the maximum number of delta functions is (N-1), where N is the total number of data entries. The second case applies to any harmonic expansion coefficient of the time-dependent rate and the maximum number of terms is N. Using time-averaged rates, the aforementioned form of F(v) results in a piecewise constant unmodulated halo function (eta) over tilde (BF)-B-0 (v(min)) (which is an integral of the speed distribution) with at most (N-1) downward steps. The authors had previously proven this result for likelihoods comprised of at least one extended likelihood, and found the best-fit halo function to be unique. This uniqueness, however, cannot be guaranteed in the more general analysis applied to arbitrary likelihoods. Thus we introduce a method for determining whether there exists a unique best-fit halo function, and provide a procedure for constructing either a pointwise con fi dence band, if the best-fit halo function is unique, or a degeneracy band, if it is not. Using measurements of modulation amplitudes, the aforementioned form of f(gal) ((u) over right arrow), which is a sum of Galactic streams, yields a periodic time-dependent halo function (eta) over right arrow BF (v(min); t) which at any fixed time is a piecewise constant function of v(min) with at most N downward steps. In this case, we explain how to construct pointwise confidence and degeneracy bands from the time-averaged halo function. Finally, we show that requiring an isotropic Galactic velocity distribution leads to a Galactic speed distribution F(u)that is once again a sum of delta functions, and produces a time-dependent (eta) over tilde BF (v(min); t) function (and a time-averaged (eta) over tilde (0) BF (v(min))) that is piecewise linear, di ff ering significantly from best-fit halo functions obtained without the assumption of isotropy.

Abstract: Deviations from unitarity in the three-neutrino mixing canonical picture are expected in many physics scenarios beyond the Standard Model. The mixing of new heavy neutral leptons with the three light neutrinos would in principle modify the strength and flavour structure of charged-current and neutral-current interactions with matter. Non-unitarity effects would therefore have an impact on the neutrino decoupling processes in the early Universe and on the value of the effective number of neutrinos, Neff. We calculate the cosmological energy density in the form of radiation with a non-unitary neutrino mixing matrix, addressing the possible interplay between parameters. Highly accurate measurements of Neff from forthcoming cosmological observations can provide independent and complementary limits on the departures from unitarity. For completeness, we relate the scenario of small deviations from unitarity to non-standard neutrino interactions and compare the forecasted constraints to other existing limits in the literature.