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In this work, we analyze two possible alternative and model-independent approaches to describe the inflationary period. The first one assumes a general equation of state during inflation due to Mukhanov, while the second one is based on the slow-roll hierarchy suggested by Hoffman and Turner. We find that, remarkably, the two approaches are equivalent from the observational viewpoint, as they single out the same areas in the parameter space, and agree with the inflationary attractors where successful inflation occurs. Rephrased in terms of the familiar picture of a slowly rolling, canonically normalized scalar field, the resulting inflaton excursions in these two approaches are almost identical. Furthermore, once the Galactic dust polarization data from Planck are included in the numerical fits, inflaton excursions can safely take sub-Planckian values.
We show in detail that the recently derived expression for evaluating the integrated Sachs-Wolfe (ISW) temperature shift in the cosmic microwave background (CMB) caused by individual embedded (compensated) lenses is equivalent to the conventional app
We constrain cosmological models where the primordial perturbations have both an adiabatic and a (possibly correlated) cold dark matter (CDM) or baryon isocurvature component. We use both a phenomenological approach, where the primordial power spectr
In the era of precision cosmology, even percentage level effects are significant on cosmological observables. The recent tension between the local and global values of $H_0$ is much more significant than this, and any possible solution might rely on
Methods based on the use of Greens functions or the Jost functions and the Fock-Krylov method are apparently very different approaches to understand the time evolution of unstable states. We show that the two former methods are equivalent up to some
The complexity of equivalence relations has received much attention in the recent literature. The main tool for such endeavour is the following reducibility: given equivalence relations $R$ and $S$ on natural numbers, $R$ is computably reducible to $