In a wide class of new physics models, there exist scalar fields that obtain vacuum expectation values of high energy scales. We study the possibility that the standard model Higgs field has experienced first order phase transition at the high energy scale due to the couplings with these scalar fields. We estimate the amount of gravitational waves produced by the phase transition, and discuss observational consequences.

With continuous advances in technology, future satellite gradiometry missions will be capable of performing precision relativistic experiments and imposing constraints on modern gravity theories. To this end, the full first-order post-Newtonian tidal tensor under inertially guided and Earth-pointing local frames along post-Newtonian orbits is worked out. The physical picture behind the “Mashhoon-Theiss anomaly” is explained at the post-Newtonian level. The relativistic precession of the local frame with respect to the sidereal frame will produce modulations of Newtonian tidal forces along certain bases, which gives rise to two different kinds of secular tidal tensors. The measurements of the secular tidal force from the frame-dragging effect is also discussed.

We establish a correspondence between general relativity with diffeomorphism invariance and scalar field theories with Galilean invariance: notions such as the Levi-Civita connection and the Riemann tensor have a Galilean counterpart. This suggests Galilean theories as the unique nontrivial alternative to gauge theories (including general relativity). Moreover, it is shown that the requirement of first-order Palatini formalism uniquely determines the Galileon models with second-order field equations, similar to the Lovelock gravity theories. Possible extensions are discussed.

We consider observational effects of a running effective Planck mass in the scalar-tensor gravity theory. At the background level, an increasing effective Planck mass allows a larger Hubble constant $H_0$, which is more compatible with the local direct measurements. At the perturbative level, for cosmic microwave background (CMB) anisotropies, an increasing effective Planck mass (i) suppresses the unlensed CMB power at $\ell \lesssim 30$ via the integrated Sachs-Wolfe effect and (ii) enhances CMB lensing power. Both effects slightly relax the tension between the current CMB data from the Planck satellite and the standard $\mathrm{\Lambda }\mathrm{CDM}$ model predictions. However, these impacts on the CMB secondary anisotropies are subdominant, and the overall constraints are driven by the background measurements. Combining CMB data from the Planck satellite and an $H_0$ prior from Riess et al., we find a $\sim 2\sigma$ hint of a positive running of the effective Planck mass. However, the hint goes away when we add other low-redshift observational data including type Ia supernovae, baryon acoustic oscillations, and an estimation of the age of the Universe using the old stars.

We explore the observational adequacy of a class of unified dark energy and dark matter (UDE/M) models with a fast transition. Our constraints are set using a combination of geometric probes—some low redshift ones and some high redshift ones (CMB-related included). The transition is phenomenologically modeled by two different transition functions corresponding to a fast and to an ultrafast transition, respectively. We find that the key parameters governing the transition can be well constrained, and from the statistical point of view it follows that the models cannot be discarded when compared to LCDM. We find the intriguing result that standard or input parameters such as ${\mathrm{\Omega }}_m$ and ${\mathrm{\Omega }}_b$ are far better constrained than in LCDM, and this is the case for the derived or output parameter measuring the deceleration value at present, $q_0$.

We develop the tools necessary to assess the statistical significance of resonant features in the CMB correlation functions, combining power spectrum and bispectrum measurements. This significance is typically addressed by running a large number of simulations to derive the probability density function (PDF) of the feature-amplitude in the Gaussian case. Although these simulations are tractable for the power spectrum, for the bispectrum they require significant computational resources. We show that, by assuming that the PDF is given by a multivariate Gaussian where the covariance is determined by the Fisher matrix of the sine and cosine terms, we can efficiently produce spectra that are statistically close to those derived from full simulations. By drawing a large number of spectra from this PDF, both for the power spectrum and the bispectrum, we can quickly determine the statistical significance of candidate signatures in the CMB, considering both single frequency and multifrequency estimators. We show that for resonance models, cosmology and foreground parameters have little influence on the estimated amplitude, which allows us to simplify the analysis considerably. A more precise likelihood treatment can then be applied to candidate signatures only. We also discuss a modal expansion approach for the power spectrum, aimed at quickly scanning through large families of oscillating models.

The c.m. energy in a collisional Penrose process—a collision taking place within the ergosphere of a Kerr black hole—can diverge under suitable extreme conditions (maximal Kerr, near horizon collision and suitable impact parameters). We present an analytic expression for the c.m. energy, refining expressions given in the literature. Even though the c.m. energy diverges, we show that the maximal energy attained by a particle that escapes the black hole’s gravitational pull and reaches infinity is modest. We obtain an analytic expression for the energy of an escaping particle resulting from a collisional Penrose process, and apply it to derive the maximal energy and the maximal efficiency for several physical scenarios: pair annihilation, Compton scattering, and the elastic scattering of two massive particles. In all physically reasonable cases (in which the incident particles initially fall from infinity towards the black hole), the maximal energy (and the corresponding efficiency) are only 1 order of magnitude larger than the rest mass energy of the incident particles. The maximal efficiency found is $\approx 13.92$ and it is obtained for the scattering of an outgoing massless particle by a massive particle.

We apply two methods, i.e., the Gaussian processes and the nonparametric smoothing procedure, to reconstruct the Hubble parameter $H(z)$ as a function of redshift from 15 measurements of the expansion rate obtained from age estimates of passively evolving galaxies. These reconstructions enable us to derive the luminosity distance to a certain redshift $z$, calibrate the light-curve fitting parameters accounting for the (unknown) intrinsic magnitude of type Ia supernova (SNe Ia), and construct cosmological model-independent Hubble diagrams of SNe Ia. In order to test the compatibility between the reconstructed functions of $H(z)$, we perform a statistical analysis considering the latest SNe Ia sample, the so-called joint light-curve compilation. We find that, for the Gaussian processes, the reconstructed functions of Hubble parameter versus redshift, and thus the following analysis on SNe Ia calibrations and cosmological implications, are sensitive to prior mean functions. However, for the nonparametric smoothing method, the reconstructed functions are not dependent on initial guess models, and consistently require high values of $H_0$, which are in excellent agreement with recent measurements of this quantity from Cepheids and other local distance indicators.

Beginning from the Ashtekar formulation of general relativity, we derive a physical Hamiltonian written in terms of (classical) loop gravity variables. This is done by defining the gravitational fields within a complex of three-dimensional cells and imposing that curvature and torsion vanish within each cell. The resulting theory is holographic, with the bulk dynamics being captured completely by degrees of freedom living on cell boundaries. Quantization is readily obtainable by existing methods.

Considering the constraints on the lepton flavor violating (LFV) couplings of the new gauge boson $Z^{\prime }$ to ordinary leptons from the experimental upper limit for the LFV process $\ell \to 3{\ell }^{\prime }$, we calculate the contributions of $Z^{\prime }$ to the LFV decays $V\to {\ell }_i{\ell }_j$ with $V\in \{\varphi ,J/\mathrm{\Psi },\mathrm{\Psi }(2S),{\mathrm{\Upsilon }}^{(n)}\}$ and $\tau \to \mu (e)\varphi$ in the context of several $Z^{\prime }$ models. We find that all $Z^{\prime }$ models considered in this paper can produce significant contributions to these decay processes and make the value of the branching ratio $\mathrm{Br}(\tau \to e\varphi )$ above its experimental upper limit. The experimental upper limit of $\tau \to e\varphi$ can give more severe constraints on these $Z^{\prime }$ models than those given by the rare decay process $\tau \to 3e$.

With the heavy quark symmetry and spin rearrangement scheme, we study the strong decay behavior of the hidden-charm pentaquark states with $J^P={\frac{3}{2}}^{\pm }$, ${\frac{5}{2}}^{\pm }$ assuming they are molecular candidates composed of ${\overline{D}}^{(*)}$ and ${\mathrm{\Sigma }}_c^{(*)}$. We obtain several typical ratios of the partial decay widths of the hidden-charm pentaquarks. For the three S-wave ($\overline{D}{\mathrm{\Sigma }}_c^{*}$), (${\overline{D}}^{*}{\mathrm{\Sigma }}_c$), and (${\overline{D}}^{*}{\mathrm{\Sigma }}_c^{*}$) molecular pentaquarks with $J^P={3/2}^{-}$, we have obtained the ratio of their $J/\psi N$ decay widths: $\mathrm{\Gamma }[(\overline{D}{\mathrm{\Sigma }}_c^{*})]:\mathrm{\Gamma }[({\overline{D}}^{*}{\mathrm{\Sigma }}_c)]:\mathrm{\Gamma }[({\overline{D}}^{*}{\mathrm{\Sigma }}_c^{*})]=2.7:1.0:5.4$, which may be useful to further test the possible molecular assignment of the $P_c$ states.

Neutrino oscillations are now a well-established and deeply studied phenomena. Their mixing parameters, except for the $CP$ phase, are measured with good accuracy. The three-neutrino oscillation picture in matter is currently of great interest due to the different long-baseline neutrino experiments that are already running or under construction. In this work, we reanalyze the exact expression for the neutrino probabilities (in a constant density medium) and introduce an approximate formula. Our results are shown in a formulation that is independent of the parametrization and could be useful for unitary tests of the leptonic mixing matrix. We illustrate how the approximation, besides being simple, can reproduce the neutrino probabilities with good accuracy.

We report the first measurement of the lepton forward-backward asymmetry ${\mathcal{A}}_{\mathrm{FB}}$ as a function of the squared four-momentum of the dilepton system, $q^2$, for the electroweak penguin process $B\to X_s{\ell }^{+}{\ell }^{-}$ with a sum of exclusive final states, where $\ell$ is an electron or a muon and $X_s$ is a hadronic recoil system with an $s$ quark. The results are based on a data sample containing $772\times {10}^6$ $B\overline{B}$ pairs recorded at the $\mathrm{\Upsilon }(4S)$ resonance with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. ${\mathcal{A}}_{\mathrm{FB}}$ for the inclusive $B\to X_s{\ell }^{+}{\ell }^{-}$ is extrapolated from the sum of 10 exclusive $X_s$ states whose invariant mass is less than $2\mathrm{GeV}/c^2$. For $q^2>10.2{\mathrm{GeV}}^2/c^2$, ${\mathcal{A}}_{\mathrm{FB}}<0$ is excluded at the $2.3\sigma$ level, where $\sigma$ is the standard deviation. For $q^2<4.3{\mathrm{GeV}}^2/c^2$, the result is within $1.8\sigma$ of the standard model theoretical expectation.

We search for the process $B^0\to {\pi }^{-}{\tau }^{+}{\nu }_{\tau }$ using the full Belle data set of $711{\mathrm{fb}}^{-1}$, corresponding to $772\times {10}^{6}B\overline{B}$ pairs, collected at the $\mathrm{\Upsilon }(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We reconstruct one $B$ meson in a hadronic decay and search for the $B^0\to {\pi }^{-}{\tau }^{+}{\nu }_{\tau }$ process in the remainder of the event. No significant signal is observed and an upper limit of $\mathcal{B}(B^0\to {\pi }^{-}{\tau }^{+}{\nu }_{\tau })<2.5\times {10}^{-4}$ is obtained at the 90% confidence level.

A discovery of the flavor-violating decay $h\to \tau \mu$ at the LHC would require extra sources of electroweak symmetry breaking (EWSB) beyond the Higgs in order to reconcile it with the bounds from $\tau \to \mu \gamma$, barring fine-tuned cancellations. In fact, an $h\to \tau \mu$ decay rate at a level indicated by the CMS measurement is easily realized if the muon and electron masses are due to a new source of EWSB, while the tau mass is due to the Higgs. We illustrate this with two examples: a two Higgs doublet model, and a model in which the Higgs is partially composite, with EWSB triggered by a technicolor sector. The first- and second-generation quark masses and Cabibbo-Kobayashi-Maskawa mixing can also be assigned to the new EWSB source. Large deviations in the flavor diagonal lepton and quark Higgs Yukawa couplings are generic. If $m_{\mu }$ is due to a rank 1 mass matrix contribution, a novel Yukawa coupling sum rule holds, providing a precision test of our framework. Flavor-violating quark and lepton (pseudo)scalar couplings combine to yield a sizable $B_s\to \tau \mu$ decay rate, which could be $\mathcal{O}(100)$ times larger than the Standard Model $B_s\to \mu \mu$ decay rate.

We apply the worldline formalism to amplitudes in scalar quantum electrodynamics involving open scalar lines, with an emphasis on their nonperturbative gauge dependence. At the tree level, we study the scalar propagator interacting with any number of photons in configuration space as well as in momentum space. At one loop we rederive, in an efficient way, the off-shell vertex in an arbitrary dimension and any covariant gauge. Generalizing the Landau-Khalatnikov-Fradkin transformation for the nonperturbative propagator, we find simple nonperturbative transformation rules for arbitrary $x$-space amplitudes under a change of the covariant gauge parameter in terms of conformal cross ratios.

Amongst standard model parameters that are constrained by cosmic microwave background (CMB) observations, the optical depth $\tau$ stands out as a nuisance parameter. While $\tau$ provides some crude limits on reionization, it also degrades constraints on other cosmological parameters. Here we explore how 21 cm cosmology—as a direct probe of reionization—can be used to independently predict $\tau$ in an effort to improve CMB parameter constraints. We develop two complementary schemes for doing so. The first uses 21 cm power spectrum observations in conjunction with semianalytic simulations to predict $\tau$. The other uses global 21 cm measurements to directly constrain low redshift (post-reheating) contributions to $\tau$ in a relatively model-independent way. Forecasting the performance of the upcoming hydrogen epoch of reionization array, we find that significant reductions in the errors on $\tau$ can be achieved. These results are particularly effective at breaking the CMB degeneracy between $\tau$ and the amplitude of the primordial fluctuation spectrum $A_s$, with errors on $\ln ({10}^{10}{A}_s)$ reduced by up to a factor of 4. Stage 4 CMB constraints on the neutrino mass sum are also improved, with errors potentially reduced to 12 meV regardless of whether CMB experiments can precisely measure the reionization bump in polarization power spectra. Observations of the 21 cm line are therefore capable of improving not only our understanding of reionization astrophysics, but also of cosmology in general.

Models based on the Yang-Mills condensate (YMC) have been advocated for in the literature and claimed as successful candidates for explaining dark energy. Several variations on this simple idea have been considered, the most promising of which are reviewed here. Nevertheless, the previously attained results relied heavily on the perturbative approach to the analysis of the effective Yang-Mills action, which is only adequate in the asymptotically free limit, and were extended into a regime, the infrared limit, in which confinement is expected. We show that if a minimum of the effective Lagrangian in $\theta =-F_{\mu \nu }^a{F}^{a\mu \nu }/2$ exists, a YMC forms that drives the Universe toward an accelerated de Sitter phase. The details of the models depend weakly on the specific form of the effective Yang-Mills Lagrangian. Using nonperturbative techniques mutated from the functional renormalization-group procedure, we finally show that the minimum in $\theta$ of the effective Lagrangian exists. Thus, a YMC can actually take place. The nonperturbative model has properties similar to the ones in the perturbative model. In the early stage of the Universe, the YMC equation of state has an evolution that resembles the radiation component, i.e., $w_y\to 1/3$. However, in the late stage, $w_y$ naturally runs to the critical state with $w_y=-1$, and the Universe transitions from a matter-dominated into a dark energy dominated stage only at latest time, at a redshift whose value depends on the initial conditions that are chosen while solving the dynamical system.

We derive the limiting form of graviton radiation in gravitational scattering at trans-Planckian energies ($E\gg M_P$) and small deflection angles. We show that—owing to the graviton’s spin 2—such a limiting form unifies the soft and Regge regimes of emission, by covering a broad angular range, from forward fragmentation to the deeply central region. The single-exchange emission amplitudes have a nice expression in terms of the transformation phases of helicity amplitudes under rotations. As a result, the multiple-exchange emission amplitudes can be resummed via an impact parameter $b$-space factorization theorem that takes into account all coherence effects. We then see the emergence of an energy spectrum of the emitted radiation which, being tuned on $\hslash /R\sim M_P^2/E\ll M_P$, is reminiscent of Hawking’s radiation. Such a spectrum is much softer than the one naïvely expected for increasing input energies and neatly solves a potential energy crisis. Furthermore, by including rescattering corrections in the (quantum) factorization formula, we are able to recover the classical limit and find the corresponding quantum corrections. Perspectives for the extrapolation of such limiting radiation towards the classical collapse regime (where $b$ is of the order of the gravitational radius $R$) are also discussed.

The construction of exact linearized solutions to the Einstein equations within the Bondi-Sachs formalism is extended to the case of linearization about de Sitter spacetime. The gravitational wave field measured by distant observers is constructed, leading to a determination of the energy measured by such observers. It is found that gravitational wave energy conservation does not normally apply to inertial observers but that it can be formulated for a class of accelerated observers, i.e., with worldlines that are timelike but not geodesic.