We study the energy-momentum tensor and helicity of gauge fields coupled through g ϕ F ˜ F / 4 to a pseudoscalar field ϕ driving inflation. Under the assumption of a constant time derivative of the ...background inflaton, we compute analytically divergent and finite terms of the energy density and helicity of gauge fields for any value of the coupling g . We introduce a suitable adiabatic expansion for mode functions of physical states of the gauge fields which correctly reproduces ultraviolet divergences in average quantities and identifies corresponding counterterms. Our calculations shed light on the accuracy and the range of validity of approximated analytic estimates of the energy density and helicity terms previously existed in the literature in the strongly coupled regime only, i.e., for g ˙ ϕ / ( 2 H ) ≫ 1 . We discuss the implications of our analytic calculations for the backreaction of quantum fluctuations onto the inflaton evolution.
The effect of a stochastic background of cosmological perturbations on the luminosity-redshift relation is computed to second order through a recently proposed covariant and gauge-invariant ...light-cone averaging procedure. The resulting expressions are free from both ultraviolet and infrared divergences, implying that such perturbations cannot mimic a sizable fraction of dark energy. Different averages are estimated and depend on the particular function of the luminosity distance being averaged. The energy flux being minimally affected by perturbations at large z is proposed as the best choice for precision estimates of dark-energy parameters. Nonetheless, its irreducible (stochastic) variance induces statistical errors on Ω(Λ)(z) typically lying in the few-percent range.
Including the metric fluctuations of a realistic cosmological geometry we reconsider an earlier suggestion that measuring the relative time-of-flight of ultra-relativistic particles can provide ...interesting constraints on fundamental cosmological and/or particle parameters. Using convenient properties of the geodetic light-cone coordinates we first compute, to leading order in the Lorentz factor and for a generic (inhomogeneous, anisotropic) space–time, the relative arrival times of two ultra-relativistic particles as a function of their masses and energies as well as of the details of the large-scale geometry. Remarkably, the result can be written as an integral over the unperturbed line-of-sight of a simple function of the local, inhomogeneous redshift. We then evaluate the irreducible scatter of the expected data-points due to first-order metric perturbations, and discuss, for an ideal source of ultra-relativistic particles, the resulting attainable precision on the determination of different physical parameters.
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