The quantum fluctuations of the geodesic deviation equation in a flat background spacetime are discussed. We calculate the resulting mean-squared fluctuations in the relative velocity and separation of test particles. The effect of these quantum fluctuations of the spacetime geometry is given in terms of the Riemann tensor correlation function. Three different sources of the Riemann tensor fluctuations are considered: a thermal bath of gravitons, gravitons in a squeezed state, and the graviton vacuum state.

In the context of Cartan theory, we will show that the Proca action can be obtained from the Gauss-Bonnet action for a special choice of the torsion tensor. This in fact equivalent to the special case of the fourth vector Galileon Lagrangian. The theory will then be promoted to contain an axion field. It will be proved that the model admits a de Sitter expanding phase with healthy tensor and vector fluctuations. The scalar sector has 4 degrees of freedom, but only one of them remains dynamical in the limit $k\to \infty$. We will analyze the scalar fluctuations in the small scales limit and obtain the parameter space of the theory in which all the perturbations remain healthy.

The motion of test membranes on which the group $G$ of isometries of a spacetime $M$ acts has been considered in general settings. It has been shown that the configuration of Nambu-Goto membranes is described by the Nambu-Goto membranes in the quotient manifold $M/G$ with an appropriate projected metric if (i) $G$ is Abelian, (ii) $G$ is semisimple and compact, or (iii) the orthogonal distribution of the orbit of $G$ is integrable, but in general not. It has also been shown that a similar result holds when the membranes couple with scalar maps or differential form fields.

We investigate the gravitational radiation from binary systems in conformal gravity (CG) and massive conformal gravity (MCG). CG might explain observed galaxy rotation curves without dark matter, and both models are of interest in the context of quantum gravity. Here we show that gravitational radiation emitted by compact binaries allows us to strongly constrain both models. We work in Weyl gauge, which fixes the rescaling invariance of the models, and derive the linearized fourth-order equation of motion for the metric, which describes massless and massive modes of propagation. In the limit of a large graviton mass, MCG reduces to general relativity (GR), whereas CG does not. Coordinates are fixed by Teyssandier gauge to show that for a conserved energy-momentum tensor the gravitational radiation is due to the time-dependent quadrupole moment of a nonrelativistic source, and we derive the gravitational energy-momentum tensor for both models. We apply our findings to the case of close binaries on circular orbits, which have been used to indirectly infer the existence of gravitational radiation prior to the direct observation of gravitational waves. As an example, we analyze the binary system PSR $\mathrm{J}1012+5307$, chosen for its small eccentricity. When fixing the graviton mass in CG such that observed galaxy rotation curves could be explained without dark matter, the gravitational radiation from a binary system is much smaller than in GR. Thus in CG one cannot explain the orbital decay of binary systems via gravitational radiation, and replace dark matter simultaneously. In MCG with small masses of the graviton, again one cannot reproduce the orbit of binaries by the emission of gravitational waves. On the other hand, for large graviton masses, the orbital period of compact binaries is in agreement with the data, as MCG reduces to GR in this limit.

We compute the 11 lowest frequency radial oscillation modes of strange stars admixed with fermionic dark matter. In the two-fluid formalism we integrate the structure equations for hydrostatic equilibrium to compute the mass and the star of the object for three different dark matter amounts. Then we solve the Sturm-Liouville boundary value problem for the perturbations, and we compute the fundamental as well as 10 excited frequency radial modes. The large separation and the second frequency difference for all cases are shown as well.

We analyze a displaced dilepton signal expected at the LHC for a tau left sneutrino as the lightest supersymmetric particle with a mass in the range 45–100 GeV. The sneutrinos are pair produced via a virtual $W$, $Z$ or $\gamma$ in the $s$ channel and, given the large value of the tau Yukawa coupling, their decays into two dileptons or a dilepton plus missing transverse energy from neutrinos can be significant. The discussion is carried out in the framework of the $\mu \nu \mathrm{SSM}$, where the presence of $R$-parity violating couplings involving right-handed neutrinos solves the $\mu$ problem and can reproduce the neutrino data. To probe the tau left sneutrinos we compare the predictions of this scenario with the ATLAS search for long-lived particles using displaced lepton pairs in $pp$ collisions at $\sqrt{s}=8\mathrm{TeV}$, allowing us to constrain the parameter space of the model. We also consider an optimization of the trigger requirements used in existing displaced-vertex searches by means of a high level trigger that exploits tracker information. This optimization is generically useful for a light metastable particle decaying into soft charged leptons. The constraints on the sneutrino turn out to be more stringent. We finally discuss the prospects for the 13 TeV LHC searches as well as further potential optimizations.

The quantum chromodynamics (QCD) axion solves the strong $CP$ problem and represents an attractive particle candidate for cold dark matter (CDM). However, quantum fluctuations of the axion field during inflation easily result in large CDM isocurvature perturbations that are in conflict with observations of the cosmic microwave background. In this paper, we demonstrate how this problem can be solved in low-scale models of hybrid inflation that may emerge from supersymmetric grand unified theories. We consider both F-term hybrid inflation and D-term hybrid inflation in supergravity, explicitly taking into account the effect of hidden-sector supersymmetry breaking. We discuss the production of cosmic strings and show how the soft terms in the scalar potential readily allow us to achieve the correct scalar spectral index. In both cases, we are able to identify large regions in parameter space that are consistent with all constraints. In particular, we find that evading the CDM isocurvature constraint always requires a small Yukawa or gauge coupling of $\mathcal{O}({10}^{-3})$ or smaller. This translates into upper bounds on the gravitino mass of $\mathcal{O}({10}^5)\mathrm{GeV}$ in F-term hybrid inflation and $\mathcal{O}({10}^9)\mathrm{GeV}$ in D-term hybrid inflation. Our results point to interesting scenarios in well-motivated parameter regions that will be tested in future axion and cosmic microwave background experiments.

The global picture of the Higgs potential in the bottom-up approach is still unknown. A large deviation as big as $\mathcal{O}(1)$ fluctuations of the Higgs self-couplings is still a viable option for the new physics. An interesting new physics scenario that can be linked to a large Higgs self-coupling is the baryogenesis based on the strong first order phase transition. We revisit the strong first order phase transition in two classes of beyond the Standard Models, namely the Higgs portal with the singlet scalar under the Standard Model gauge group with ${\mathbb{Z}}_2$ symmetry and the effective field theory approach with higher-dimensional operators. We numerically investigate a few important issues in the validity of the effective potential, caused by the breakdown of the high-temperature approximation, and in the criteria for the strong first order phase transition. We illustrate that these issues can lead to $\mathcal{O}(1)$ uncertainties in the precision of the Higgs self-couplings, which are relevant when discussing sensitivity limits of different future colliders. We also find that the quartic coupling of the above two classes of scenarios compatible with the strong first order electroweak phase transition where the cubic coupling is not negligible can achieve a $2\sigma$ sensitivity at the 100 TeV $pp$ collider. From this novel observation, we show that the correlation between the Higgs cubic coupling and the quartic coupling will be useful for differentiating various underlying new physics scenarios and discuss its prospect for the future colliders. Throughout our numerical investigation, the contribution from the Goldstone boson is not included.

We investigate the stability of the standard model electroweak (EW) vacuum in the presence of Planck-scale suppressed operators of the type ${\varphi }^{2n}/M_{\mathrm{P}}^{2n-4}$ that involve the Higgs field $\varphi$ and could, in principle, be induced by quantum gravity effects. We show how minimal embeddings of the standard model (SM) in supergravity (SUGRA) can stabilize the EW vacuum against such operators up to very high values of the induced supersymmetry breaking scale $M_{\mathcal{S}}$, which may well be above the onset of the so-called SM metastability scale of $10^{11}\mathrm{GeV}$. In particular, we explicitly demonstrate how discrete $R$ symmetries could be invoked to suppress the occurrence of harmful Planck-scale operators of the form ${\varphi }^{2n}/M_{\mathrm{P}}^{2n-4}$ to arbitrary higher powers of $n$. We analyze different scenarios of Planck-scale gravitational physics and derive lower limits on the power $n$ that is required in order to protect our EW vacuum from dangerous rapid decay. The significance of our results for theories of low-scale quantum gravity is illustrated.

We report a lattice QCD determination of the $\pi \gamma \to \pi \pi$ transition amplitude for the $P$-wave, $I=1$ two-pion final state, as a function of the photon virtuality and $\pi \pi$ invariant mass. The calculation was performed with $2+1$ flavors of clover fermions at a pion mass of approximately 320 MeV, on a $32^3\times 96$ lattice with $L\approx 3.6\mathrm{fm}$. We construct the necessary correlation functions using a combination of smeared forward, sequential and stochastic propagators, and determine the finite-volume matrix elements for all $\pi \pi$ momenta up to $|\overrightarrow{P}|=\sqrt{3}\frac{2\pi }{L}$ and all associated irreducible representations. In the mapping of the finite-volume to infinite-volume matrix elements using the Lellouch-Lüscher factor, we consider two different parametrizations of the $\pi \pi$ scattering phase shift. We fit the $q^2$ and $s$ dependence of the infinite-volume transition amplitude in a model-independent way using series expansions, and compare multiple different truncations of this series. Through analytic continuation to the $\rho$ resonance pole, we also determine the $\pi \gamma \to \rho$ resonant transition form factor and the $\rho$ meson photocoupling, and obtain $|G_{\rho \pi \gamma }|=0.0802(32)(20)$.

The hadronic contribution to the eight forward amplitudes of light-by-light scattering (${\gamma }^{*}{\gamma }^{*}\to {\gamma }^{*}{\gamma }^{*}$) is computed in lattice QCD. Via dispersive sum rules, the amplitudes are compared to a model of the ${\gamma }^{*}{\gamma }^{*}\to \text{hadrons}$ cross sections in which the fusion process is described by hadronic resonances. Our framework can provide an important test for the model estimates of hadronic light-by-light scattering in the anomalous magnetic moment of the muon, $a_{\mu }^{\text{HLbL}}$. Using simple parametrizations of the resonance $M\to {\gamma }^{*}{\gamma }^{*}$ transition form factors, we determine the corresponding monopole and dipole masses by performing a global fit to all eight amplitudes. Together with a previous dedicated calculation of the ${\pi }^0\to {\gamma }^{*}{\gamma }^{*}$ transition form factor, our calculation provides valuable information for phenomenological estimates of $a_{\mu }^{\text{HLbL}}$. The presented calculations are performed in two-flavor QCD with pion masses extending down to 190 MeV at two different lattice spacings. In addition to the fully connected Wick contractions, on two lattice ensembles we also compute the ($2+2$) disconnected class of diagrams, and find that their overall size is compatible with a parameter-free, large-$N$ inspired prediction, where $N$ is the number of colors. Motivated by this observation, we estimate in the same way the disconnected contribution to $a_{\mu }^{\text{HLbL}}$.

In this paper, we present SGK18 FFs, a first QCD analysis of parton-to- unidentified charged hadrons fragmentation functions (FFs) at next-to-next-to-leading order (NNLO) accuracy in perturbative QCD. This analysis is based on single-inclusive charged hadron production in electron-positron ($e^{-}{e}^{+}$) annihilation. The uncertainties in the extraction of SGK18 FFs as well as the corresponding observables are estimated using the “Hessian” technique. We study the quality of the SGK18 FFs determined in this analysis by comparing with the recent results in literature. We also show how SGK18 FFs results describe the available data for single-inclusive unidentified charged hadron production in $e^{-}{e}^{+}$ annihilation. We demonstrate that the theoretical uncertainties due to the variation of the renormalization and factorization scales improve when NNLO QCD corrections are considered. We find that the resulting SGK18 FFs are in good agreement with all data analyzed and the inclusion of NNLO corrections tends to improve the data description with somewhat smaller uncertainty.

This article is devoted to the study of scalar perturbations in loop quantum cosmology. It aims at clarifying the situation with respect to the way initial conditions are set and to the specific choice of an inflaton potential. Several monomial potentials are studied. Both the dressed metric and deformed algebra approaches are considered. We show that the calculation of the ultraviolet part of the spectrum, which is the physically relevant region for most background trajectories, is reliable, whereas the infrared and intermediate parts do depend on some specific choices that are made explicit.

Quantum scale invariant regularization is a variant of dimensional regularization where the renormalization scale is treated as a dynamical field. But, rather than be regarded as a novel regularization method on par with dimensional regularization, momentum cutoff, Pauli-Villars etc., it should be understood as a way to define a subset in the infinite space of nonrenormalizable models of certain type. The subset realizes the demand that renormalization scale, along with any other dimensionful parameters, should be interpreted as a dynamical field’s homogeneous background. This restriction is most straightforwardly implemented using dimensional regularization but it can hypothetically be imposed with any regularization method. Theories that satisfy it offer a new perspective on the radiative violation of global scale symmetry associated with RG functions. As a result of the quantum scale invariant regularization being implemented, the scale symmetry is preserved at the quantum level despite the RG functions being nonzero, as can be inspected at the level of composite quantum operators that govern dilatation of Green functions. We analyze these statements in explicit detail using a specific but easily generalized toy model with scalar fields.

The direct detection of gravitational waves crowns decades of efforts in the modeling of sources and of increasing detectors’ sensitivity. With future third-generation Earth-based detectors or space-based observatories, gravitational-wave astronomy will be at its full bloom. Previously brushed-aside questions on environmental or other systematic effects in the generation and propagation of gravitational waves are now begging for a systematic treatment. Here, we study how electromagnetic and gravitational radiation is scattered by a binary system. Scattering cross sections, resonances and the effect of an impinging wave on a gravitational-bound binary are worked out for the first time. The ratio between the scattered-wave amplitude and the incident wave can be of order ${10}^{-5}$ for known pulsars, bringing this into the realm of future gravitational-wave observatories. For currently realistic distribution of compact-object binaries, the interaction cross section is too small to be of relevance.

We continue our investigation of the 4D effective field theory for closed string axions in type II compactifications with $D$-branes. The inclusion of Stückelberg couplings for the axions requires the presence of chiral fermions at $D$-brane intersections, whose interactions at strong non-Abelian gauge coupling induce mass terms for the axions and scalar chiral condensate excitations, dubbed infladrons. The setup allows for a realization of naturallike inflation with a closed string axion as inflaton and a flattened scalar potential due to the backreaction of the more massive infladrons. We further point out that this large field inflationary model is not compromised by axionic wormhole corrections.

We study a scalar particle of mas $m_1$ decaying into two particles of mass $m_2$ during the radiation and matter dominated epochs of a standard cosmological model. An adiabatic approximation is introduced that is valid for degrees of freedom (d.o.f.) with typical wavelengths much smaller than the particle horizon ($\propto$ Hubble radius) at a given time. We implement a nonperturbative method that includes the cosmological expansion and obtain a cosmological Fermi’s Golden Rule that enables one to compute the decay law of the parent particle with mass $m_1$, along with the build up of the population of daughter particles with mass $m_2$. The survival probability of the decaying particle is $P(t)=e^{-{\tilde{\mathrm{\Gamma }}}_k(t)t}$ with ${\tilde{\mathrm{\Gamma }}}_k(t)$ being an effective momentum and time dependent decay rate. It features a transition timescale $t_{\mathrm{nr}}$ between the relativistic and nonrelativistic regimes and for $k\ne 0$ is always smaller than the analogous rate in Minkowski spacetime, as a consequence of (local) time dilation and the cosmological redshift. For $t\ll t_{\mathrm{nr}}$ the decay law is a “stretched exponential” $P(t)=e^{-(t/t^{*}{)}^{3/2}}$, whereas for the nonrelativistic stage with $t\gg t_{\mathrm{nr}}$, we find $P(t)=e^{-{\mathrm{\Gamma }}_{0}t}(t/t_{\mathrm{nr}}{)}^{{\mathrm{\Gamma }}_0{t}_{\mathrm{nr}}/2}$, with ${\mathrm{\Gamma }}_0$ the Minkowski space time decay width at rest. The Hubble timescale $\propto 1/H(t)$ introduces an energy uncertainty $\mathrm{\Delta }E\sim H(t)$ which relaxes the constraints of kinematic thresholds. This opens new decay channels into heavier particles for $2\pi E_k(t)H(t)\gg 4m_2^2-m_1^2$, with $E_k(t)$ the (local) comoving energy of the decaying particle. As the expansion proceeds this channel closes and the usual two particle threshold restricts the decay kinematics.

We explore the dynamics and observational predictions of the warm little inflaton scenario, presently the simplest realization of warm inflation within a concrete quantum field theory construction. We consider three distinct types of scalar potentials for the inflaton, namely chaotic inflation with a quartic monomial potential, a Higgs-like symmetry breaking potential and a non-renormalizable plateau-like potential. In each case, we determine the parametric regimes in which the dynamical evolution is consistent for 50-60 e-folds of inflation, taking into account thermal corrections to the scalar potential and requiring, in particular, that the two fermions coupled directly to the inflaton remain relativistic and close to thermal equilibrium throughout the slow-roll regime and that the temperature is always below the underlying gauge symmetry breaking scale. We then compute the properties of the primordial spectrum of scalar curvature perturbations and the tensor-to-scalar ratio in the allowed parametric regions and compare them with Planck data, showing that this scenario is theoretically and observationally successful for a broad range of parameter values.

We explore cosmological constraints on the sum of the three active neutrino masses $M_{\nu }$ in the context of dynamical dark energy (DDE) models with equation of state (EoS) parametrized as a function of redshift $z$ by $w(z)=w_0+w_{a}z/(1+z)$, and satisfying $w(z)\ge -1$ for all $z$. We make use of cosmic microwave background data from the Planck satellite, baryon acoustic oscillation measurements, and supernovae Ia luminosity distance measurements, and perform a Bayesian analysis. We show that, within these models, the bounds on $M_{\nu }$ do not degrade with respect to those obtained in the $\mathrm{\Lambda }\mathrm{CDM}$ case; in fact, the bounds are slightly tighter, despite the enlarged parameter space. We explain our results based on the observation that, for fixed choices of $w_0$, $w_a$ such that $w(z)\ge -1$ (but not $w=-1$ for all $z$), the upper limit on $M_{\nu }$ is tighter than the $\mathrm{\Lambda }\mathrm{CDM}$ limit because of the well-known degeneracy between $w$ and $M_{\nu }$. The Bayesian analysis we have carried out then integrates over the possible values of $w_0\text{−}{w}_a$ such that $w(z)\ge -1$, all of which correspond to tighter limits on $M_{\nu }$ than the $\mathrm{\Lambda }\mathrm{CDM}$ limit. We find a 95% credible interval (C.I.) upper bound of $M_{\nu }<0.13\mathrm{eV}$. This bound can be compared with the 95% C.I. upper bounds of $M_{\nu }<0.16\mathrm{eV}$, obtained within the $\mathrm{\Lambda }\mathrm{CDM}$ model, and $M_{\nu }<0.41\mathrm{eV}$, obtained in a DDE model with arbitrary EoS (which allows values of $w<-1$). Contrary to the results derived for DDE models with arbitrary EoS, we find that a dark energy component with $w(z)\ge -1$ is unable to alleviate the tension between high-redshift observables and direct measurements of the Hubble constant $H_0$. Finally, in light of the results of this analysis, we also discuss the implications for DDE models of a possible determination of the neutrino mass ordering by laboratory searches.