Abstract: Attractor solutions that give dynamical reasons for dark energy to act like the cosmological constant, or behavior close to it, are interesting possibilities to explain cosmic acceleration. Coupling the scalar field to matter or to gravity enlarges the dynamical behavior; we consider both couplings together, which can ameliorate some problems for each individually. Such theories have also been proposed in a Higgs-like fashion to induce gravity and unify dark energy and dark matter origins. We explore restrictions on such theories due to their dynamical behavior compared to observations of the cosmic expansion. Quartic potentials in particular have viable stability properties and asymptotically approach general relativity.

Abstract: The cosmic energy density in the form of radiation before and during Big Bang Nucleosynthesis (BBN) is typically parameterized in terms of the effective number of neutrinos N-eff. This quantity, in case of no extra degrees of freedom, depends upon the chemical potential and the temperature characterizing the three active neutrino distributions, as well as by their possible non-thermal features. In the present analysis we determine the upper bounds that BBN places on N-eff from primordial neutrino-antineutrino asymmetries, with a careful treatment of the dynamics of neutrino oscillations. We consider quite a wide range for the total lepton number in the neutrino sector, eta(nu) = eta(nu e) + eta(nu mu) + eta(nu tau) and the initial electron neutrino asymmetry eta(in)(nu e), solving the corresponding kinetic equations which rule the dynamics of neutrino (antineutrino) distributions in phase space due to collisions, pair processes and flavor oscillations. New bounds on both the total lepton number in the neutrino sector and the nu(e)-(nu) over bar (e) asymmetry at the onset of BBN are obtained fully exploiting the time evolution of neutrino distributions, as well as the most recent determinations of primordial H-2/H density ratio and He-4 mass fraction. Note that taking the baryon fraction as measured by WMAP, the H-2/H abundance plays a relevant role in constraining the allowed regions in the eta(nu)-eta(in)(nu e) plane. These bounds fix the maximum contribution of neutrinos with primordial asymmetries to N-eff as a function of the mixing parameter theta(13), and point out the upper bound N-eff less than or similar to 3.4. Comparing these results with the forthcoming measurement of N-eff by the Planck satellite will likely provide insight on the nature of the radiation content of the universe.