In this paper we operate under the assumption that no tensors from inflation will be measured in the future by the dedicated experiments and argue that, while for single-field slow-roll models of inflation the running of the spectral index will be ha
rd to be detected, in multi-field models the running can be large due to its strong correlation with non-Gaussianity. A detection of the running might therefore be related to the presence of more than one active scalar degree of freedom during inflation.
The AMS-02 collaboration has recently released data on the positron fraction $e^+/(e^-+e^+)$ up to energies of about 350 GeV. If one insists on interpreting the observed excess as a dark matter signal, then we find it is best described by a TeV-scale
dark matter annihilating into $tau^+tau^-$, although this situation is already severely constrained by gamma-ray measurements. The annihilation into $mu^+mu^-$ is allowed by gamma-rays more than $tau^+tau^-$, but it gives a poorer fit to textsc{AMS-02} data. Moreover, since electroweak corrections induce correlations among the fluxes of stable particles from dark matter annihilations, the recent AMS-02 data imply a well-defined prediction for the correlated flux of antiprotons. Under the assumption that their future measurements will not show any antiproton excess above the background, the dark matter interpretation of the positron rise will possibly be ruled out by only making use of data from a single experiment. This work is the first of a program where we emphasize the role of correlations among dark matter signals.
We propose that the Standard Model (SM) Higgs is responsible for generating the cosmological perturbations of the universe by acting as an isocurvature mode during a de Sitter inflationary stage. In view of the recent ATLAS and CMS results for the Hi
ggs mass, this can happen if the Hubble rate during inflation is in the range $(10^{10}- 10^{14})$ GeV (depending on the SM parameters). Implications for the detection of primordial tensor perturbations through the $B$-mode of CMB polarization via the PLANCK satellite are discussed. For example, if the Higgs mass value is confirmed to be $m_h=125.5$ GeV and $m_t, alpha_s$ are at their central values, our mechanism predicts tensor perturbations too small to be detected in the near future. On the other hand, if tensor perturbations will be detected by PLANCK through the $B$-mode of CMB, then there is a definite relation between the Higgs and top masses, making the mechanism predictive and falsifiable.
A sizeable level of non-Gaussianity in the primordial cosmological perturbations may be induced by a large trispectrum, i.e. by a large connected four-point correlation function. We compute the effect of a primordial non-Gaussian trispectrum on the h
alo mass function, within excursion set theory. We use the formalism that we have developed in a previous series of papers and which allows us to take into account the fact that, in the presence of non-Gaussianity, the stochastic evolution of the smoothed density field, as a function of the smoothing scale, is non-markovian. In the large mass limit, the leading-order term that we find agrees with the leading-order term of the results found in the literature using a more heuristic Press-Schecther (PS)-type approach. Our approach however also allows us to evaluate consistently the subleading terms, which depend not only on the four-point cumulant but also on derivatives of the four-point correlator, and which cannot be obtained within non-Gaussian extensions of PS theory. We perform explicitly the computation up to next-to-leading order.
We compute the effect of primordial non-Gaussianity on the halo mass function, using excursion set theory. In the presence of non-Gaussianity the stochastic evolution of the smoothed density field, as a function of the smoothing scale, is non-markovi
an and beside local terms that generalize Press-Schechter (PS) theory, there are also memory terms, whose effect on the mass function can be computed using the formalism developed in the first paper of this series. We find that, when computing the effect of the three-point correlator on the mass function, a PS-like approach which consists in neglecting the cloud-in-cloud problem and in multiplying the final result by a fudge factor close to 2, is in principle not justified. When computed correctly in the framework of excursion set theory, in fact, the local contribution vanishes (for all odd-point correlators the contribution of the image gaussian cancels the Press-Schechter contribution rather than adding up), and the result comes entirely from non-trivial memory terms which are absent in PS theory. However it turns out that, in the limit of large halo masses, where the effect of non-Gaussianity is more relevant, these memory terms give a contribution which is the the same as that computed naively with PS theory, plus subleading terms depending on derivatives of the three-point correlator. We finally combine these results with the diffusive barrier model developed in the second paper of this series, and we find that the resulting mass function reproduces recent N-body simulations with non-Gaussian initial conditions, without the introduction of any ad hoc parameter.
A classic method for computing the mass function of dark matter halos is provided by excursion set theory, where density perturbations evolve stochastically with the smoothing scale, and the problem of computing the probability of halo formation is m
apped into the so-called first-passage time problem in the presence of a barrier. While the full dynamical complexity of halo formation can only be revealed through N-body simulations, excursion set theory provides a simple analytic framework for understanding various aspects of this complex process. In this series of paper we propose improvements of both technical and conceptual aspects of excursion set theory, and we explore up to which point the method can reproduce quantitatively the data from N-body simulations. In paper I of the series we show how to derive excursion set theory from a path integral formulation. This allows us both to derive rigorously the absorbing barrier boundary condition, that in the usual formulation is just postulated, and to deal analytically with the non-markovian nature of the random walk. Such a non-markovian dynamics inevitably enters when either the density is smoothed with filters such as the top-hat filter in coordinate space (which is the only filter associated to a well defined halo mass) or when one considers non-Gaussian fluctuations. In these cases, beside ``markovian terms, we find ``memory terms that reflect the non-markovianity of the evolution with the smoothing scale. We develop a general formalism for evaluating perturbatively these non-markovian corrections, and in this paper we perform explicitly the computation of the halo mass function for gaussian fluctuations, to first order in the non-markovian corrections due to the use of a tophat filter in coordinate space.
In excursion set theory the computation of the halo mass function is mapped into a first-passage time process in the presence of a barrier, which in the spherical collapse model is a constant and in the ellipsoidal collapse model is a fixed function
of the variance of the smoothed density field. However, N-body simulations show that dark matter halos grow through a mixture of smooth accretion, violent encounters and fragmentations, and modeling halo collapse as spherical, or even as ellipsoidal, is a significant oversimplification. We propose that some of the physical complications inherent to a realistic description of halo formation can be included in the excursion set theory framework, at least at an effective level, by taking into account that the critical value for collapse is not a fixed constant $delta_c$, as in the spherical collapse model, nor a fixed function of the variance $sigma$ of the smoothed density field, as in the ellipsoidal collapse model, but rather is itself a stochastic variable, whose scatter reflects a number of complicated aspects of the underlying dynamics. Solving the first-passage time problem in the presence of a diffusing barrier we find that the exponential factor in the Press-Schechter mass function changes from $exp{-delta_c^2/2sigma^2}$ to $exp{-adelta_c^2/2sigma^2}$, where $a=1/(1+D_B)$ and $D_B$ is the diffusion coefficient of the barrier. The numerical value of $D_B$, and therefore the corresponding value of $a$, depends among other things on the algorithm used for identifying halos. We discuss the physical origin of the stochasticity of the barrier and we compare with the mass function found in N-body simulations, for the same halo definition.[Abridged]
It has been recently shown that the quantum Boltzmann equations may be relevant for the leptogenesis scenario. In particular, they lead to a time-dependent CP asymmetry which depends upon the previous dynamics of the system. This memory effect in the
CP asymmetry is particularly important in resonant leptogenesis where the asymmetry is generated by the decays of nearly mass-degenerate right-handed neutrinos. We study the impact of the nontrivial time evolution of the CP asymmetry in resonant leptogenesis, both in the one-flavour case and with flavour effects included. We show that significant qualitative and quantitative differences arise with respect to the case in which the time dependence of the CP asymmetry is neglected.
