We explore the correlations between correlation functions of the primordial curvature perturbation produced during inflation. We find that for general single field inflation, other than the source terms which depend on the model details, higher order correlation functions are characterized by the power spectrum, its spectral index and running. The correlation between the bispectrum and power spectrum is presented as an explicit example of our systematic approach.

The AMS-02 Collaboration has recently presented high-quality measurements of the cosmic electron and positron fluxes as well as the positron fraction. We use the measurements of the positron flux to derive, for the first time, limits on the dark matter annihilation cross section and lifetime for various final states. Working under the well-motivated assumption that a background positron flux exists from spallations of cosmic rays with the interstellar medium and from astrophysical sources, we find strong limits on the dark matter properties which are competitive, although slightly weaker, than those derived from the positron fraction. Specifically, for dark matter particles annihilating only into $e^{+}{e}^{-}$ or into ${\mu }^{+}{\mu }^{-}$, our limits on the annihilation cross section are stronger than the thermal value when the dark matter mass is smaller than 100 GeV or 60 GeV, respectively.

The effective anisotropic stress or gravitational slip $\eta =-\mathrm{\Phi }/\mathrm{\Psi }$ is a key variable in the characterization of the physical origin of the dark energy, as it allows us to test for a nonminimal coupling of the dark sector to gravity in the Jordan frame. It is however important to use a fully model-independent approach when measuring $\eta$ to avoid introducing a theoretical bias into the results. In this paper we forecast the precision with which future large surveys can determine $\eta$ in a way that only relies on directly observable quantities. In particular, we do not assume anything concerning the initial spectrum of perturbations, nor on its evolution outside the observed redshift range, nor on the galaxy bias. We first leave $\eta$ free to vary in space and time and then we model it as suggested in Horndeski models of dark energy. Among our results, we find that a future large scale lensing and clustering survey can constrain $\eta$ to within 10% if $k$-independent, and to within 60% or better at $k=0.1h/\mathrm{Mpc}$ if it is restricted to follow the Horndeski model.

In this second of two papers we apply our recently developed code to search for resonance features in the Planck CMB temperature data. We search both for log-spaced oscillations or linear-spaced oscillations and compare our findings with results of our WMAP9 analysis and the Planck team analysis [P. A. R. Ade et al. (Planck Collaboration), arXiv:1303.5082]. While there are hints of log-spaced resonant features present in the WMAP9 data, the significance of these features weaken with more data. With more accurate small scale measurements, we also find that the best-fit frequency has shifted and the amplitude has been reduced. We confirm the presence of a several low frequency peaks, earlier identified by the Planck team, but with a better improvement of fit ($\mathrm{\Delta }{\chi }_{\text{eff}}^2\sim 12$). We further investigate this improvement by allowing the lensing potential to vary as well, showing mild correlation between the amplitude of the oscillations and the lensing amplitude. We find that the improvement of the fit increases even more ($\mathrm{\Delta }{\chi }_{\text{eff}}^2\sim 14$) for the low frequencies that modify the spectrum in a way that mimics the lensing effect. Since these features were not present in the WMAP data, they are primarily due to better measurements of Planck at small angular scales. For linear-spaced oscillations we find a maximum $\mathrm{\Delta }{\chi }_{\text{eff}}^2\sim 13$ scanning two orders of magnitude in frequency space, and the biggest improvements are at extremely high frequencies. Again, we recover a best-fit frequency very close to the one found in WMAP9, which confirms that the fit improvement is driven by low $\ell$. Further comparisons with WMAP9 show Planck contains many more features, both for linear- and log-spaced oscillations, but with a smaller improvement of fit. We discuss the improvement as a function of the number of modes and study the effect of the 217 GHz map, which appears to drive most of the improvement for log-spaced oscillations. Two points strongly suggest that the detected features are fitting a combination of the noise and the dip at $\ell \sim 1800$ in the 217 GHz map: the fit improvement mostly comes from a small range of $\ell$, and comparison with simulations shows that the fit improvement is consistent with a statistical fluctuation. We conclude that none of the detected features are statistically significant.

In this first of two papers, we present a new method for searching for oscillatory features in the primordial power spectrum. A wide variety of models predict these features in one of two different flavors: logarithmically spaced oscillations and linearly spaced oscillations. The proposed method treats the oscillations as perturbations on top of the scale-invariant power spectrum, allowing us to vary all cosmological parameters. This perturbative approach reduces the computational requirements for the search as the transfer functions and their derivatives can be precomputed. We show that the most significant degeneracy in the analysis is between the distance to last scattering and the overall amplitude at low frequencies. For models with logarithmic oscillations, this degeneracy leads to an uncertainty in the phase. For linear-spaced oscillations, it affects the frequency of the oscillations. In this first of two papers, we test our code on simulated Planck-like data and show that we are able to recover fiducial input oscillations with an amplitude of a few times $\mathcal{O}({10}^{-2})$. We apply the code to WMAP9-year data and confirm the existence of two intriguing resonant frequencies for log-spaced oscillations. For linear-spaced oscillations, we find a single resonance peak. We use numerical simulations to assess the significance of these features and conclude that the data do not provide compelling evidence for the existence of oscillatory features in the primordial spectrum.

We study the exotic $bc\overline{q}\overline{q}$, $bc\overline{s}\overline{s}$ and $qc\overline{q}\overline{b}$, $sc\overline{s}\overline{b}$ systems by constructing the corresponding tetraquark currents with $J^P=0^{+}$ and $1^{+}$. After investigating the two-point correlation functions and the spectral densities, we perform QCD sum rule analysis and extract the masses of these open-flavor tetraquark states. Our results indicate that the masses of both the scalar and axial vector tetraquark states are about 7.1–7.2 GeV for the $bc\overline{q}\overline{q}$ system and 7.2–7.3 GeV for the $bc\overline{s}\overline{s}$ system. For the $qc\overline{q}\overline{b}$ tetraquark states with $J^P=0^{+}$ and $1^{+}$, their masses are extracted to be around 7.1 GeV. The masses for the scalar and axial vector $sc\overline{s}\overline{b}$ states are 7.1 and 6.9–7.1 GeV, respectively. The tetraquark states $qc\overline{q}\overline{b}$ and $sc\overline{s}\overline{b}$ lie below the thresholds of $D^{(*)}{B}^{(*)}$ and $D_s^{(*)}{B}_s^{(*)}$ respectively, but they can decay into $B_c$ plus a light meson. However, the tetraquark states $bc\overline{q}\overline{q}$ and $bc\overline{s}\overline{s}$ lie below the $D^{(*)}{\overline{B}}^{(*)}$ and $D_s^{(*)}{\overline{B}}_s^{(*)}$ thresholds, suggesting dominantly weak decay mechanisms.

Using spectral data from nonstrange and strange hadronic $\tau$ decays, flavor-breaking chiral sum rules involving the flavor $ud$ and $us$ current-current two-point functions are constructed and used to determine the $SU(3)$ next-to-next-to-leading order (NNLO) low-energy constant combinations $C_{61}^r$, $C_{12}^r+C_{61}^r+C_{80}^r$ and $C_{12}^r-C_{61}^r+C_{80}^r$. The first of these determinations updates the results of an earlier analysis by Dürr and Kambor, while the latter two are new. The error on $C_{12}^r+C_{61}^r+C_{80}^r$ is particularly small. Comparisons are made to model estimates for these quantities. The role of the third combination in significantly improving the determination of the next-to-leading order low-energy constant $L_{10}^r$ from NNLO analyses of the flavor $ud$ $V-A$ correlator is also highlighted.

The Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ is not well determined yet. It can be extracted from both inclusive or exclusive decays, like $B\to \pi (\rho )l{\overline{\nu }}_l$. However, the exclusive determination from $B\to \rho l{\overline{\nu }}_l$, in particular, suffers from a large model dependence. In this paper, we propose to extract $|V_{ub}|$ from the four-body semileptonic decay $B\to \pi \pi l{\overline{\nu }}_l$, where the form factors for the pion-pion system are treated in dispersion theory. This is a model-independent approach that takes into account the $\pi \pi$ rescattering effects, as well as the effect of the $\rho$ meson. We demonstrate that both finite-width effects of the $\rho$ meson as well as scalar $\pi \pi$ contributions can be considered completely in this way.

The geomagnetic field causes not only the east-west effect on primary cosmic rays but also affects the trajectories of the secondary charged particles in the shower, causing their lateral distribution to be stretched. Thus, both the density of the secondaries near the shower axis and the trigger efficiency of detector arrays decrease. The effect depends on the direction of the showers, thus, introducing a modulation in the measured azimuthal distribution. The azimuthal distribution of the events collected by the ARGO-YBJ detector is deeply investigated for different zenith angles in light of this effect.

We report a measurement of the branching fraction $B(D^{+}\to {\mu }^{+}{\nu }_{\mu })=[3.71\pm 0.19(\text{stat})\pm 0.06(\text{sys})]\times {10}^{-4}$ based on $2.92{\mathrm{fb}}^{-1}$ of data accumulated at $\sqrt{s}=3.773\mathrm{GeV}$ with the BESIII detector at the BEPCII collider. This measurement, in conjunction with the Cabibbo-Kobayashi-Maskawa matrix element $|V_{\mathrm{cd}}|$ determined from a global Standard Model fit, implies a value for the weak decay constant $f_{D^{+}}=(203.2\pm 5.3\pm 1.8)\mathrm{MeV}$. Additionally, using this branching fraction measurement together with a lattice QCD prediction for $f_{D^{+}}$, we find $|V_{\mathrm{cd}}|=0.2210\pm 0.0058\pm 0.0047$. In either case, these are the most precise results for these quantities to date.

The Comment [J. T. Firouzjaee, preceding Comment, Phys. Rev. D 89, 068301 (2014)] raises two points in regard to our paper [S. K. Modak and D. Singleton, Phys. Rev. D 86, 123515 (2012)]. The first is that one cannot use the tunneling picture to obtain the temperature and particle production rate in the Friedman-Robertson-Walker space-time. The second comment raised by Firouzjaee is that the Hawking-like radiation model for inflation presented in [Modak and Singleton; S. K. Modak and D. Singleton, Int. J. Mod. Phys. D 21, 1242020 (2012)] is inconsistent with the observed scalar and tensor perturbation spectrum. We show that the first comment is beside the point—we do not use the tunneling method in our papers [Modak and Singleton; Modak and Singleton]. The second criticism by Firouzjaee comes from the author evaluating quantities at different times—he evaluates the parameters of our model at the beginning of inflation and then compares this with the scalar and tensor perturbations evaluated at the horizon exit point.

Modak and Singleton [Phys. Rev. D 86, 123515 (2012)] have presented Hawking-like radiation for cosmological inflation which has a natural “turn on” and a natural “turn off” mechanism. This Hawking-like radiation results in an effective negative pressure “fluid” which leads to a rapid period of expansion in the very early Universe. We discuss that the turn on mechanism cannot happen for the Friedmann-Robertson-Walker model in the early Universe because its horizon is an apparent horizon not an event horizon. Hence, we cannot apply geometric optic approximation which is a necessary condition for the tunneling method. It was shown that this model predicts a value for $\frac{\rho }{m_{\mathrm{pl}}^4}$ which is bigger than the COBE normalization constraint in the cosmic microwave background at the horizon exit. The authors of the paper offer a Reply.

We introduce the exceptional field theory for the group ${\mathrm{E}}_{7(7)}$, based on a $(4+56)$-dimensional spacetime subject to a covariant section condition. The “internal” generalized diffeomorphisms of the coordinates in the fundamental representation of ${\mathrm{E}}_{7(7)}$ are governed by a covariant “E-bracket,” which is gauged by 56 vector fields. We construct the complete and unique set of field equations that is gauge invariant under generalized diffeomorphisms in the internal and external coordinates. Among them are featured the non-Abelian twisted self-duality equations for the 56 gauge vectors. We discuss the explicit solutions of the section condition describing the embedding of the full, untruncated 11-dimensional and type IIB supergravity, respectively. As a new feature compared to the previously constructed $E_{6(6)}$ formulation, some components among the 56 gauge vectors descend from the 11-dimensional dual graviton but nevertheless allow for a consistent coupling by virtue of a covariantly constrained compensating 2-form gauge field.

We present the details of the recently constructed ${\mathrm{E}}_{6(6)}$-covariant extension of 11-dimensional supergravity. This theory requires a $5+27$-dimensional spacetime in which the “internal” coordinates transform in the $\overline{\mathbf{27}}$ of ${\mathrm{E}}_{6(6)}$. All fields are ${\mathrm{E}}_{6(6)}$ tensors and transform under (gauged) internal generalized diffeomorphisms. The “Kaluza-Klein” vector field acts as a gauge field for the ${\mathrm{E}}_{6(6)}$-covariant “E-bracket” rather than a Lie bracket, requiring the presence of 2-forms akin to the tensor hierarchy of gauged supergravity. We construct the complete and unique action that is gauge invariant under generalized diffeomorphisms in the internal and external coordinates. The theory is subject to covariant section constraints on the derivatives, implying that only a subset of the extra 27 coordinates is physical. We give two solutions of the section constraints: the first preserves GL(6) and embeds the action of the complete (i.e. untruncated) 11-dimensional supergravity; the second preserves $\text{GL}(5)\times \text{SL}(2)$ and embeds complete type IIB supergravity. As a byproduct, we thus obtain an off-shell action for type IIB supergravity.

We extend the analytical determination of the main radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies beyond the fourth post-Newtonian approximation recently obtained by us. This extension is done to linear order in the mass ratio by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler’s gauge-invariant redshift variable. By using the version of black hole perturbation theory developed by Mano, Suzuki and Takasugi, we have pushed the analytical determination of the (linear in mass ratio) radial potential to the sixth post-Newtonian order (passing through 5 and 5.5 post-Newtonian terms). In principle, our analytical method can be extended to arbitrarily high post-Newtonian orders.

We study the impact of perturbative reheating on primordial observables in models of multiple-field inflation. By performing a sudden decay calculation, we derive analytic expressions for the local-type nonlinearity parameter $f_{\text{NL}}^{\text{local}}$, the scalar spectral index $n_{\zeta }$, and the tensor-to-scalar ratio $r_T$ as functions of the decay rates of the inflationary fields. We compare our analytic results to a fully numerical classical field theory simulation, finding excellent agreement. We find that the sensitivity of $f_{\text{NL}}$, $n_{\zeta }$, and $r_T$ to the reheating phase depends heavily on the underlying inflationary model. We quantify this sensitivity, and discuss conditions that must be satisfied if observable predictions are to be insensitive to the dynamics of reheating. We demonstrate that upon completion of reheating, all observable quantities take values within finite ranges, the limits of which are determined completely by the conditions during inflation. Furthermore, fluctuations in both fields play an important role in determining the full dependence of the observables on the dynamics of reheating. By applying our formalism to two concrete examples, we demonstrate that variations in $f_{\text{NL}}$, $n_{\zeta }$, and $r_T$ caused by changes in reheating dynamics are well within the sensitivity of Planck, and as such the impact of reheating must be accounted for when making predictions for models of multiple-field inflation. Our final expressions are very general, encompassing a wide range of two-field inflationary models, including the standard curvaton scenario. We show that the curvaton scenario is a limiting case of two-field inflation, and recover the standard curvaton results in the appropriate limit. Our results allow a much more unified approach to studying two-field inflation including the effects of perturbative reheating. As such, entire classes of models can be studied together, allowing a more systematic approach to gaining insight into the physics of the early universe through observation.

The dark matter halo profile in the inner Galaxy is very uncertain. Yet its radial dependence toward the Galactic Center is of crucial importance for the determination of the gamma-ray and radio fluxes originating from dark matter annihilations. Here we use synchrotron emission to probe the dark matter energy distribution in the inner Galaxy. We first solve the problem of the cosmic ray diffusion on very small scales, typically smaller than ${10}^{-3}\mathrm{pc}$, by using a Green’s function approach and use this technique to quantify the effect of a spiky profile [$\rho (r)\propto r^{-7/3}$] on the morphology and intensity of the synchrotron emission expected from dark matter. We illustrate our results using 10 and 800 GeV candidate weakly interacting dark matter particles annihilating directly into $e^{+}{e}^{-}$. Our most critical assumptions are that the dark matter is heavier than a few GeV and directly produces a reasonable amount of electrons and positrons in the Galaxy. We conclude that dark matter indirect detection techniques (including the Planck experiment) could be used to shed light on the dark matter halo profile on scales that lie beyond the capability of any current numerical simulations.

If the large-scale anomalies in the temperature power spectrum of the cosmic microwave background are of primordial origin, they may herald modifications to the slow-roll inflationary paradigm on the largest scales. We study the possibility that the origin of the large-scale power suppression is a modification of initial conditions during slow roll as a result of a pre-slow-roll phase during which the inflaton evolves rapidly. This stage is manifest in a potential in the equations for the Gaussian fluctuations during slow roll and modifies the power spectra of scalar perturbations via an initial condition transfer function $\mathcal{T}(k)$. We provide a general analytical study of its large- and small-scale properties and analyze the impact of these initial conditions on the infrared aspects of typical test scalar fields. The infrared behavior of massless minimally coupled test scalar field theories leads to the dynamical generation of mass and anomalous dimensions, both depending nonanalytically on $\mathcal{T}(0)$. During inflation, all quanta decay into many quanta even of the same field because of the lack of kinematic thresholds. The decay leads to a quantum entangled state of subhorizon and superhorizon quanta with correlations across the horizon. We find the modifications of the decay width and the entanglement entropy from the initial conditions. In all cases, initial conditions from a “fast-roll” stage that lead to a suppression in the scalar power spectrum at large scales also result in a suppression of the dynamically generated masses, anomalous dimensions and decay widths.

Dark matter (DM) direct detection experiments usually assume the simplest possible “standard halo model” for the Milky Way (MW) halo in which the velocity distribution is Maxwellian. This model assumes that the MW halo is an isotropic, isothermal sphere, a hypothesis that is unlikely to be valid in reality. An alternative approach is to derive a self-consistent solution for a particular mass model of the MW (i.e. obtained from its gravitational potential) using the Eddington formalism, which assumes isotropy. In this paper we extend this approach to incorporate an anisotropic phase-space distribution function. We perform Bayesian scans over the parameters defining the mass model of the MW and parametrizing the phase-space density, implementing constraints from a wide range of astronomical observations. The scans allow us to estimate the precision reached in the reconstruction of the velocity distribution (for different DM halo profiles). As expected, allowing for an anisotropic velocity tensor increases the uncertainty in the reconstruction of $f(\mathbf{v})$, but the distribution can still be determined with a precision of a factor of 4-5. The mean velocity distribution resembles the isotropic case; however, the amplitude of the high-velocity tail is up to a factor of 2 larger. Our results agree with the phenomenological parametrization proposed in Mao et al. (2013) as a good fit to $N$-body simulations (with or without baryons), since their velocity distribution is contained in our 68% credible interval.

We propose new predictions from grand unified theories (GUTs) [applicable to both supersymmetric (SUSY) and non-SUSY models] for the ratios of quark and lepton Yukawa couplings. These new predictions arise from splitting the masses of the messenger fields for the GUT-scale Yukawa operators by Clebsch-Gordan factors from GUT symmetry breaking. This has the effect that these factors enter inversely in the predicted quark-lepton Yukawa coupling ratios, leading to new possible GUT predictions. We systematically construct the new predictions that can be realized in this way in SU(5) GUTs and Pati-Salam unified theories and discuss model building applications.