Abstract: We extend an alternative, phenomenological approach to inflation by means of an equation of state and a sound speed, both of them functions of the number of e-folds and four phenomenological parameters. This approach captures a number of possible inflationary models, including those with non-canonical kinetic terms or scale-dependent non-gaussianities. We perform Markov Chain Monte Carlo analyses using the latest cosmological publicly available measurements, which include Cosmic Microwave Background (CMB) data from the Planck satellite. Within this parameterization, we discard scale invariance with a significance of about 10 sigma, and the running of the spectral index is constrained as alpha(s) = -0.60(-0.10)(+0.08) x 10(-3) (68% CL errors). The limit on the tensor-to-scalar ratio is r < 0.005 at 95% CL from CMB data alone. We find no significant evidence for this alternative parameterization with present cosmological observations. The maximum amplitude of the equilateral non-gaussianity that we obtain, vertical bar f(NL)(equil)vertical bar < 1, is much smaller than the current Planck mission errors, strengthening the case for future high-redshift, all-sky surveys, which could reach the required accuracy on equilateral non-gaussianities.

Abstract: Using the Fenchel-Eggleston theorem for convex hulls (an extension of the Caratheodory theorem), we prove that any likelihood can be maximized by either a dark matter 1-speed distribution F(v) in Earth's frame or 2-Galactic velocity distribution f(gal) ((u) over right arrow), consisting of a sum of delta functions. The former case applies only to time-averaged rate measurements and the maximum number of delta functions is (N-1), where N is the total number of data entries. The second case applies to any harmonic expansion coefficient of the time-dependent rate and the maximum number of terms is N. Using time-averaged rates, the aforementioned form of F(v) results in a piecewise constant unmodulated halo function (eta) over tilde (BF)-B-0 (v(min)) (which is an integral of the speed distribution) with at most (N-1) downward steps. The authors had previously proven this result for likelihoods comprised of at least one extended likelihood, and found the best-fit halo function to be unique. This uniqueness, however, cannot be guaranteed in the more general analysis applied to arbitrary likelihoods. Thus we introduce a method for determining whether there exists a unique best-fit halo function, and provide a procedure for constructing either a pointwise con fi dence band, if the best-fit halo function is unique, or a degeneracy band, if it is not. Using measurements of modulation amplitudes, the aforementioned form of f(gal) ((u) over right arrow), which is a sum of Galactic streams, yields a periodic time-dependent halo function (eta) over right arrow BF (v(min); t) which at any fixed time is a piecewise constant function of v(min) with at most N downward steps. In this case, we explain how to construct pointwise confidence and degeneracy bands from the time-averaged halo function. Finally, we show that requiring an isotropic Galactic velocity distribution leads to a Galactic speed distribution F(u)that is once again a sum of delta functions, and produces a time-dependent (eta) over tilde BF (v(min); t) function (and a time-averaged (eta) over tilde (0) BF (v(min))) that is piecewise linear, di ff ering significantly from best-fit halo functions obtained without the assumption of isotropy.

Abstract: The Fermi Collaboration has recently updated their analysis of gamma rays from the center of the Galaxy. They reconfirm the presence of an unexplained emission feature which is most prominent in the region of 1-10 GeV, known as the Galactic Center GeV excess (GCE). Although the GCE is now fi rmly detected, an interpretation of this emission as a signal of self-annihilating dark matter (DM) particles is not unambiguously possible due to systematic effects in the gamma-ray modeling estimated in the Galactic Plane. In this paper we build a covariance matrix, collecting different systematic uncertainties investigated in the Fermi Collaboration's paper that affect the GCE spectrum. We show that models where part of the GCE is due to annihilating DM is still consistent with the new data. We also re-evaluate the parameter space regions of the minimal supersymmetric Standard Model (MSSM) that can contribute dominantly to the GCE via neutralino DM annihilation. All recent constraints from DM direct detection experiments such as PICO, LUX, PandaX and Xenon1T, limits on the annihilation cross section from dwarf spheroidal galaxies and the Large Hadron Collider limits are considered in this analysis. Due to a slight shift in the energy spectrum of the GC excess with respect to the previous Fermi analysis, and the recent limits from direct detection experiments, we find a slightly shifted parameter region of the MSSM, compared to our previous analysis, that is consistent with the GCE. Neutralinos with a mass between 85-220 GeV can describe the excess via annihilation into a pair of W-bosons or top quarks. Remarkably, there are models with low fine-tuning among the regions that we have found. The complete set of solutions will be probed by upcoming direct detection experiments and with dedicated searches in the upcoming data of the Large Hadron Collider.