Phenomenological approaches of inflation and their equivalence

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.Comment: Revtex, 8 pages, 4 figures. References updated. Matches published version in PR

Probing Gravitational Lensing of the CMB with SDSS-IV Quasars

We study the cross-correlation between the Planck CMB lensing convergence map and the eBOSS quasar overdensity obtained from the Sloan Digital Sky Survey (SDSS) IV, in the redshift range $0.9 < z < 2.2$. We detect the CMB lensing convergence-quasar cross power spectrum at $5.4 \sigma$ significance. The cross power spectrum provides a quasar clustering bias measurement that is expected to be particularly robust against systematic effects. The redshift distribution of the quasar sample has a median redshift $z \approx 1.55$, and an effective redshift about $1.51$. The best fit bias of the quasar sample is $b_q = 2.43 \pm 0.45$, corresponding to a host halo mass of $\log_{10}\left( \frac{M}{h^{-1} M_\odot} \right) = 12.54^{+0.25}_{-0.36}$. This is broadly consistent with the previous literature on quasars with a similar redshift range and selection. Since our constraint on the bias comes from the cross-correlation between quasars and CMB lensing, we expect it to be robust to a wide range of possible systematic effects that may contaminate the auto correlation of quasars. We checked for a number of systematic effects from both CMB lensing and quasar overdensity, and found that all systematics are consistent with null within $2 \sigma$. The data is not sensitive to a possible scale dependence of the bias at present, but we expect that as the number of quasars increases (in future surveys such as DESI), it is likely that strong constraints on the scale dependence of the bias can be obtained.Comment: 8 pages, 6 figures, 1 table; matches published version on MNRA

Cosmological limits on neutrino unknowns versus low redshift priors

Recent Cosmic Microwave Background (CMB) temperature and polarization anisotropy measurements from the Planck mission have significantly improved previous constraints on the neutrino masses as well as the bounds on extended models with massless or massive sterile neutrino states. However, due to parameter degeneracies, additional low redshift priors are mandatory in order to sharpen the CMB neutrino bounds. We explore here the role of different priors on low redshift quantities, such as the Hubble constant, the cluster mass bias, and the reionization optical depth $\tau$. Concerning current priors on the Hubble constant and the cluster mass bias, the bounds on the neutrino parameters may differ appreciably depending on the choices adopted in the analyses. With regard to future improvements in the priors on the reionization optical depth, a value of $\tau=0.05\pm 0.01$, motivated by astrophysical estimates of the reionization redshift, would lead to $\sum m_\nu<0.0926$~eV at $90\%$~CL, when combining the full \textit{Planck} measurements, Baryon Acoustic Oscillation and Planck clusters data, thereby opening the window to unravel the neutrino mass hierarchy with existing cosmological probes.Comment: 12 pages, 5 figure

Dark Radiation and Inflationary Freedom after Planck 2015

The simplest inflationary models predict a primordial power spectrum (PPS) of the curvature fluctuations that can be described by a power-law function that is nearly scale-invariant. It has been shown, however, that the low-multipole spectrum of the CMB anisotropies may hint the presence of some features in the shape of the scalar PPS, which could deviate from its canonical power-law form. We study the possible degeneracies of this non-standard PPS with the neutrino anisotropies, the neutrino masses, the effective number of relativistic species and a sterile neutrino or a thermal axion mass. The limits on these additional parameters are less constraining in a model with a non-standard PPS when only including the temperature auto-correlation spectrum measurements in the data analyses. The inclusion of the polarization spectra noticeably helps in reducing the degeneracies, leading to results that typically show no deviation from the $\Lambda$CDM model with a standard power-law PPS.Comment: 22 pages, 17 figures, 11 tables. Updated to match the published version. Text abridged upon the referee's request

Constraints on the early and late integrated Sachs-Wolfe effects from the Planck 2015 cosmic microwave background anisotropies in the angular power spectra

The Integrated Sachs-Wolfe (ISW) effect predicts additional anisotropies in the Cosmic MicrowaveBackground due to time variation of the gravitational potential when the expansion of the universeis not matter dominated. The ISW effect is therefore expected in the early universe, due to thepresence of relativistic particles at recombination, and in the late universe, when dark energy startsto dominate the expansion. Deviations from the standard picture can be parameterized byAeISWandAlISW, which rescale the overall amplitude of the early and late ISW effects. Analyzing themost recent CMB temperature spectra from the Planck 2015 release, we detect the presence of theearly ISW at high significance withAeISW= 1.06±0.04 at 68% CL and an upper limit for thelate ISW ofAlISW<1.1 at 95% CL. The inclusion of the recent polarization data from the Planckexperiment erases such 1.5σhint forAeISW6= 1. When considering the recent detections of the lateISW coming from correlations between CMB temperature anisotropies and weak lensing, a value ofAlISW= 0.85±0.21 is predicted at 68% CL, showing a 4σevidence. We discuss the stability of ourresult in the case of an extra relativistic energy component parametrized by the effective neutrinonumberNeffand of a CMB lensing amplitudeA

Constraints on massive sterile plus active neutrino species in non minimal cosmologies

Cosmological measurements are affected by the energy density of both active and sterile massive neutrinos. We extend here a recent analysis of current cosmological data to non minimal cosmologies. Several possible scenarios are examined: a constant w \neq -1 dark energy equation of state, a non flat universe, a time varying dark energy component and coupled dark matter dark energy universes or modified gravity scenarios. When considering cosmological data only, (3+2) massive neutrino models with ~0.5 eV sterile species are allowed at 95% CL. This scenario has been shown to reconcile reactor, LSND and MiniBooNE positive signals with null results from other searches. Big Bang Nucleosynthesis bounds could compromise the viability of (3+2) models if the two sterile species are fully thermalized states at decoupling.Comment: 8 pages, 5 figure