Boundary Conditions for Topological Quantum Field Theories, Anomalies and Projective Modular Functors

We study boundary conditions for extended topological quantum field theories (TQFTs) and their relation to topological anomalies. We introduce the notion of TQFTs with moduli level $m$, and describe extended anomalous theories as natural transformations of invertible field theories of this type. We show how in such a framework anomalous theories give rise naturally to homotopy fixed points for $n$-characters on $\infty$-groups. By using dimensional reduction on manifolds with boundaries, we show how boundary conditions for $n+1$-dimensional TQFTs produce $n$-dimensional anomalous field theories. Finally, we analyse the case of fully extended TQFTs, and show that any fully extended anomalous theory produces a suitable boundary condition for the anomaly field theory.Comment: 26 pages, 6 figures. Exposition improved, bibliography updated. Final version, to appear in Comm. Math. Phy

Planck constraints on neutrino isocurvature density perturbations

The recent Cosmic Microwave Background data from the Planck satellite experiment, when combined with HST determinations of the Hubble constant, are compatible with a larger, non-standard, number of relativistic degrees of freedom at recombination, parametrized by the neutrino effective number $N_{eff}$. In the curvaton scenario, a larger value for $N_{eff}$ could arise from a non-zero neutrino chemical potential connected to residual neutrino isocurvature density (NID) perturbations after the decay of the curvaton field, parametrized by the amplitude $\alpha^{NID}$. Here we present new constraints on $N_{eff}$ and $\alpha^{NID}$ from an analysis of recent cosmological data. We found that the Planck+WP dataset does not show any indication for a neutrino isocurvature component, severly constraining its amplitude, and that current indications for a non-standard $N_{eff}$ are further relaxed.Comment: 5 pages, 3 figure

First cosmological constraints combining Planck with the recent gravitational-wave standard siren measurement of the Hubble constant

The recent observations of gravitational-wave and electromagnetic emission produced by the merger of the binary neutron-star system GW170817 have opened the possibility of using standard sirens to constrain the value of the Hubble constant. While the reported bound of $H_0=70_{-8}^{+12}$ at $68 \%$ C.L. is significantly weaker than those recently derived by observations of Cepheid variables, it does not require any form of cosmic distance ladder and can be considered as complementary and, in principle, more conservative. Here we combine, for the first time, the new measurement with the Planck Cosmic Microwave Background observations in a $12$ parameters extended $\Lambda$CDM scenario, where the Hubble constant is weakly constrained from CMB data alone and bound to a low value $H_0=55^{+7}_{-20}$ km/s/Mpc at $68 \%$ C.L. We point out that the non-Gaussian shape of the GW170817 bound makes lower values of the Hubble constant in worst agreement with observations than what expected from a Gaussian form. The inclusion of the new GW170817 Hubble constant measurement therefore significantly reduces the allowed parameter space, improving the cosmological bounds on several parameters as the neutrino mass, curvature and the dark energy equation of state.Comment: 5 pages, 4 Figures, few typos correcte

Frobenius algebras and homotopy fixed points of group actions on bicategories

We explicitly show that symmetric Frobenius structures on a finite-dimensional, semi-simple algebra stand in bijection to homotopy fixed points of the trivial SO(2)-action on the bicategory of finite-dimensional, semi-simple algebras, bimodules and intertwiners. The results are motivated by the 2-dimensional Cobordism Hypothesis for oriented manifolds, and can hence be interpreted in the realm of Topological Quantum Field Theory.Comment: 19 pages, published in TA

Can interacting dark energy solve the H0H_0 tension?

The answer is Yes! We indeed find that interacting dark energy can alleviate the current tension on the value of the Hubble constant $H_0$ between the Cosmic Microwave Background anisotropies constraints obtained from the Planck satellite and the recent direct measurements reported by Riess et al. 2016. The combination of these two datasets points towards an evidence for a non-zero dark matter-dark energy coupling $\xi$ at more than two standard deviations, with $\xi=-0.26_{-0.12}^{+0.16}$ at $95\%$ CL. However the $H_0$ tension is better solved when the equation of state of the interacting dark energy component is allowed to freely vary, with a phantom-like equation of state $w=-1.184\pm0.064$ (at $68 \%$ CL), ruling out the pure cosmological constant case, $w=-1$, again at more than two standard deviations. When Planck data are combined with external datasets, as BAO, JLA Supernovae Ia luminosity distances, cosmic shear or lensing data, we find good consistency with the cosmological constant scenario and no compelling evidence for a dark matter-dark energy coupling.Comment: 10 pages, 6 figure

Reconciling Planck with the local value of H0H_0 in extended parameter space

The recent determination of the local value of the Hubble constant by Riess et al, 2016 (hereafter R16) is now 3.3 sigma higher than the value derived from the most recent CMB anisotropy data provided by the Planck satellite in a LCDM model. Here we perform a combined analysis of the Planck and R16 results in an extended parameter space, varying simultaneously 12 cosmological parameters instead of the usual 6. We find that a phantom-like dark energy component, with effective equation of state $w=-1.29_{-0.12}^{+0.15}$ at 68 % c.l. can solve the current tension between the Planck dataset and the R16 prior in an extended $\Lambda$CDM scenario. On the other hand, the neutrino effective number is fully compatible with standard expectations. This result is confirmed when including cosmic shear data from the CFHTLenS survey and CMB lensing constraints from Planck. However, when BAO measurements are included we find that some of the tension with R16 remains, as also is the case when we include the supernova type Ia luminosity distances from the JLA catalog.Comment: 6 pages, 1 figur