The singly Cabibbo-suppressed decay ${\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Sigma }}^{-}{K}^{+}{\pi }^{+}$ is observed for the first time with a statistical significance of $5.4\sigma$ by using $4.5{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at center-of-mass energies between 4.600 and 4.699 GeV with the BESIII detector at BEPCII. The absolute branching fraction of ${\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Sigma }}^{-}{K}^{+}{\pi }^{+}$ is measured to be $(3.8\pm {1.2}_{\mathrm{stat}}\pm {0.2}_{\mathrm{syst}})\times {10}^{-4}$ in a model-independent approach. This is the first observation of a Cabibbo-suppressed ${\mathrm{\Lambda }}_c^{+}$ decay involving ${\mathrm{\Sigma }}^{-}$ in the final state. The ratio of branching fractions between ${\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Sigma }}^{-}{K}^{+}{\pi }^{+}$ and the Cabibbo-favored decay ${\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Sigma }}^{-}{\pi }^{+}{\pi }^{+}$ is observed to be $(0.4\pm 0.1)s_c^2$, where $s_c\equiv \sin {\theta }_c=0.2248$ with ${\theta }_c$ the Cabibbo mixing angle.

We consider exact Wentzel-Kramers-Brillouin analysis to a $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics defined by the potential, $V(x)={\omega }^2{x}^2+g{x}^2(ix{)}^{ϵ=2}$ with $\omega \in {\mathbb{R}}_{\ge 0}$, $g\in {\mathbb{R}}_{>0}$. We in particular aim to verify a conjecture proposed by Ai-Bender-Sarkar (ABS), that pertains to a relation between $D$-dimensional $\mathcal{P}\mathcal{T}$-symmetric theories and analytic continuation (AC) of Hermitian theories concerning the energy spectrum or Euclidean partition function. For the purpose, we construct energy quantization conditions by exact Wentzel-Kramers-Brillouin analysis and write down their transseries solution by solving the conditions. By performing alien calculus to the energy solutions, we verify validity of the ABS conjecture and seek a possibility of its alternative form by Borel resummation theory if it is violated. Our results claim that the validity of the ABS conjecture drastically changes depending on whether $\omega >0$ or $\omega =0$: If $\omega >0$, then the ABS conjecture is violated when exceeding the semiclassical level of the first nonperturbative order, but its alternative form is constructable by Borel resummation theory. The $\mathcal{P}\mathcal{T}$ and the AC energies are related to each other by a one-parameter Stokes automorphism, and a median resummed form, which corresponds to a formal exact solution, of the AC energy (resp. $\mathcal{P}\mathcal{T}$ energy) is directly obtained by acting Borel resummation to a transseries solution of the $\mathcal{P}\mathcal{T}$ energy (resp. AC energy). If $\omega =0$, then, with respect to the inverse energy level-expansion, not only perturbative/nonperturbative structures of the $\mathcal{P}\mathcal{T}$ and the AC energies but also their perturbative parts do not match with each other. These energies are independent solutions, and no alternative form of the ABS conjecture can be reformulated by Borel resummation theory.

In this article, we study the impact of self-interaction and multiparticle states on sustaining negative energies in relativistic quantum systems. For physically reasonable models, one usually requires bounds on both magnitude and duration of the accumulation of negative energy, typically given in form of a quantum energy inequality (QEI). Such bounds have applications in semiclassical gravity where they exclude exotic spacetime geometries and imply the formation of singularities. The essence of this article is a novel numerical method for determining optimal QEI bounds at the one- or two-particle level, extending previous work focused on the one-particle case and overcoming a new type of technical challenge associated with the two-particle scenario. Our method is tailored for integrable models in quantum field theory constructed via the S-matrix boostrap. Applying the method to a representative model, the sinh-Gordon model, we confirm self-interaction as the source of negative energy, with stronger interactions leading to more pronounced negativities. Moreover, we establish the validity of QEIs and the averaged weak energy condition (AWEC) at the one- and two-particle level. Lastly, we identify a constrained one-parameter class of nonminimal stress tensor expressions satisfying QEIs at both levels, with more stringent constraints emerging from the QEI bounds at the two-particle level.

We study effective dynamics of the nonsupersymmetric two-dimensional $\mathbb{CP}(N-1)$ model in the large $N$ limit. This model is deformed by a mass term $m$ preserving ${\mathbb{Z}}_N$ symmetry of the Lagrangian. At small $m$ the theory is strongly coupled and resembles the undeformed $\mathbb{CP}(N-1)$ model, while at large $m$ it is in a weakly coupled Higgs phase with spontaneously broken ${\mathbb{Z}}_N$. We find the phase transition point and discuss the fate of the kink-antikink “mesons” at strong coupling. We also resolve an issue of instability that arose in previous studies of this model.

The secondary component of GW190814 has mass in the range $2.5–2.67M_{\odot }$, placing it within the lower mass gap separating neutron stars from black holes. According to the predictions of general relativity and state-of-the-art nuclear equations of state, this object is too heavy to be a neutron star. In this work, we explore the possibility that this object is a neutron star under the hypothesis that general relativity is modified to include screening mechanisms and that the neutron star formed in an unscreened environment. We introduce a set of parametrized post-Tolman-Oppenheimer-Volkoff (post-TOV) equations appropriate for screened modified gravity whose free parameters are environment dependent. We find that it is possible that the GW190814 secondary could be a neutron star that formed in an unscreened environment for a range of reasonable post-TOV parameters.

This article presents an analysis of regular rotating black hole solutions within the framework of teleparallel equivalent to general relativity. The study evaluates the total energy and derives an analytical expression for the irreducible mass of a regular black hole. The results reveal the significance of these regular black holes as approximations of real astrophysical objects. The investigation explores the behavior of the total energy for different surfaces and its value at spatial infinity. Additionally, the article addresses the instability of the inner horizon and examines the inertial acceleration of an observer inside the inner horizon.

The primary constraints for general teleparallel quadratic gravity are presented. They provide a basic classification of teleparallel theories from the perspective of the full nonlinear theory and represent the first step towards a full-fledged Hamiltonian analysis. The results are consistent with the limit of metric and symmetric teleparallel quadratic gravity. In the latter case we also present novel results, since symmetric teleparallel theories have only been partially studied so far. Apart from the general results, we also present the special cases of teleparallel theories classically equivalent to general relativity, which differ by a boundary term from the formulation of Einstein and Hilbert. This affects the constraint algebra as the primary constraints involve a mix of torsion and nonmetricity, implying that the symmetries of general relativity are realized in a more intricate way compared to the teleparallel case. In this context, a more detailed understanding will provide insights for energy and entropy in gravity, quantum gravity, and numerical relativity of this alternative formulation of general relativity. The primary constraints are presented both in the standard formulation and in irreducible parts of torsion and nonmetricity. The special role of axial torsion and its connection to the one-parameter of viable new general relativity is confirmed. Furthermore, we find that one of the irreducible parts of nonmetricity affects the primary constraint for shift but not lapse.

In this paper we propose a new generalized mass-to-horizon relation to be used in the context of entropic cosmologies and holographic principle scenarios. We show that a general scaling of the mass with the universe horizon as $M=\gamma \frac{c^2}{G}{L}^n$ leads to a new generalized entropy $S_n=\gamma \frac{n}{1+n}\frac{2\pi k_B{c}^3}{G\hslash }{L}^{n+1}$ from which we can recover many of the recently proposed forms of entropies at cosmological and black hole scales and also establish a thermodynamically consistent relation between each of them and Hawking temperature. We analyze the consequences of introducing this new mass-to-horizon relation on cosmological scales by comparing the corresponding modified Friedmann, acceleration, and continuity equations to cosmological data. We find that when $n=3$, the entropic cosmology model is fully and totally equivalent to the standard $\mathrm{\Lambda }\mathrm{CDM}$ model, thus providing a new fundamental support for the origin and the nature of the cosmological constant. In general, if $\log \gamma <-3$, and irrespective of the value of $n$, we find a very good agreement with the data comparable with $\mathrm{\Lambda }\mathrm{CDM}$ from which, in Bayesian terms, our models are indistinguishable.

In this paper, we study the global phase space dynamics of single nonminimally coupled scalar field inflation models in the metric and Palatini formalisms. Working in the Jordan frame, we derive the scalar-tensor general field equations and flat Friedmann-Lemaître-Robertson-Walker cosmological equations and present the Palatini and metric equations in a common framework. We show that inflation is characterized by a “master” trajectory from a saddle-type de Sitter fixed point to a stable node fixed point, approximated by slow-roll conditions (presented for the first time in the Palatini formalism). We show that, despite different underlying equations, the fixed point structure and properties of many models are congruent in metric and Palatini formalisms, which explains their qualitative similarities and their suitability for driving inflation. On the other hand, the global phase portraits reveal how even models which predict the same values for observable perturbations differ, both to the extent of the phase space physically available to their trajectories, as well as their past asymptotic states. We also note how the slow-roll conditions tend to underestimate the end of inflationary accelerated expansion experienced by the true nonlinear “master” solution. The explicit examples we consider range from the metric and Palatini induced gravity quintic potential with a Coleman-Weinberg correction factor to Starobinsky, metric, and Palatini nonminimal Higgs, as well as second-order pole and several nontrivial Palatini models.

We develop the first model for extreme mass-ratio inspirals with misaligned angular momentum and primary spin, and zero eccentricity—also known as quasispherical inspirals—evolving under the influence of the first-order in mass-ratio gravitational self-force. The forcing terms are provided by an efficient spectral interpolation of the first-order gravitational self-force in the outgoing radiation gauge. In order to speed up the calculation of the inspiral, we apply a near-identity (averaging) transformation to eliminate all dependence of the orbital phases from the equations of motion while maintaining all secular effects of the first-order gravitational self-force at postadiabatic order. The resulting solutions are defined with respect to “Mino time”; thus, we perform a second averaging transformation, so the inspiral is parametrized in terms of Boyer-Lindquist time, which is more convent for LISA data analysis. We also perform a similar analysis using the two-timescale expansion and find that using either approach yields self-forced inspirals that can be evolved to subradian accuracy in less than a second. The dominant contribution to the inspiral phase comes from the adiabatic contributions, so we further refine our self-force model using information from gravitational wave flux calculations. The significant dephasing we observe between the lower and higher accuracy models highlights the importance of accurately capturing adiabatic contributions to the phase evolution.

Inflation with Weyl scaling symmetry provides a viable scenario that can generate both the nearly scaling invariant primordial density fluctuation and a dark matter candidate. Here we point out that, in addition to the primordial gravitational waves (GWs) from quantum fluctuations, the production of high-frequency GWs from preheating in such inflation models can provide another probe of the inflationary dynamics. We conduct both linear analytical analysis and nonlinear numerical lattice simulation in a typical model. We find that significant stochastic GWs can be produced, and the frequency band is located around ${10}^8\mathrm{Hz}–{10}^{10}\mathrm{Hz}$, which might be probed by future resonance-cavity experiments.

The initial density of dark matter (DM) particles, otherwise secluded from the standard model (SM), may be generated at reheating, with an initial temperature ratio for internal thermalizations, ${\xi }_i=T_{\mathrm{DM},\mathrm{i}}/T_{\mathrm{SM},\mathrm{i}}$. This scenario necessarily implies inflaton-mediated scatterings between DM and SM after reheating, with a rate fixed by the relic abundance of DM and the reheat temperature. These scatterings can be important for an inflaton mass and reheat temperature as high as $\mathcal{O}({10}^7\mathrm{GeV})$ and $\mathcal{O}({10}^9\mathrm{GeV})$, respectively, since the thermally averaged collision terms become approximately independent of the inflaton mass when the bath temperature is larger than the mass. The impact of these scatterings on DM cosmology is studied modeling the perturbative reheating physics by a gauge-invariant set of inflaton interactions up to dimension 5 with the SM gauge bosons, fermions, and the Higgs fields. It is observed that an initially lower (higher) DM temperature will rapidly increase (decrease), even with very small couplings to the inflaton. There is a sharp lower bound on the DM mass below which the relic abundance cannot be satisfied due to faster backscatterings depleting DM quanta to SM particles. For low DM masses, the cosmic microwave background constraints become stronger due to the collisions for ${\xi }_i<1$, probing values as small as $\mathcal{O}({10}^{-4})$, and weaker for ${\xi }_i>1$. The big-bang nucleosynthesis constraints become stronger due to the collisions for lower DM masses, probing ${\xi }_i$ as small as $\mathcal{O}(0.1)$, and weaker for higher DM mass. Thus inflaton-mediated collisions with predictable rates, relevant even for high-scale inflation models, can significantly impact the cosmology of light DM.

The $E_G$ statistic is a discriminating probe of gravity developed to test the prediction of general relativity (GR) for the relation between gravitational potential and clustering on the largest scales in the observable Universe. We present a novel high-precision estimator for the $E_G$ statistic using CMB lensing and galaxy clustering correlations that carefully matches the effective redshifts across the different measurement components to minimize corrections. A suite of detailed tests is performed to characterize the estimator’s accuracy, its sensitivity to assumptions and analysis choices, and the non-Gaussianity of the estimator’s uncertainty is characterized. After finalization of the estimator, it is applied to Planck CMB lensing and SDSS CMASS and LOWZ galaxy data. We report the first harmonic space measurement of $E_G$ using the LOWZ sample and CMB lensing and also updated constraints using the final CMASS sample and the latest Planck CMB lensing map. We find ${\widehat{E}}_G^{\mathrm{Planck}+\mathrm{CMASS}}=0.36_{-0.05}^{+0.06}(68.27\%)$ and ${\widehat{E}}_G^{\mathrm{Planck}+\mathrm{LOWZ}}=0.40_{-0.09}^{+0.11}(68.27\%)$, with additional subdominant systematic error budget estimates of 2% and 3%, respectively. Using ${\mathrm{\Omega }}_{\mathrm{m},0}$ constraints from Planck and SDSS BAO observations, $\mathrm{\Lambda }\mathrm{CDM}$-GR predicts $E_G^{\mathrm{GR}}(z=0.555)=0.401\pm 0.005$ and $E_G^{\mathrm{GR}}(z=0.316)=0.452\pm 0.005$ at the effective redshifts of the CMASS and LOWZ based measurements. We report the measurement to be in good statistical agreement with the $\mathrm{\Lambda }\mathrm{CDM}$-GR prediction and report that the measurement is also consistent with the more general GR prediction of scale independence for $E_G$. This work provides a carefully constructed and calibrated statistic with which $E_G$ measurements can be confidently and accurately obtained with upcoming survey data.

Current cosmological tensions show that it is crucial to test the predictions from the canonical $\mathrm{\Lambda }\mathrm{CDM}$ paradigm at different cosmic times. One very appealing test of structure formation in the Universe is the growth rate of structure in our universe $f$, usually parametrized via the growth index $\gamma$, with $f\equiv {\mathrm{\Omega }}_m(a{)}^{\gamma }$ and $\gamma \simeq 0.55$ in the standard $\mathrm{\Lambda }\mathrm{CDM}$ case. Recent studies have claimed a suppression of the growth of structure from a variety of cosmological observations, characterized by $\gamma >0.55$. By employing different self-consistent growth parametrizations schemes, we show here that $\gamma <0.55$, obtaining instead an enhanced growth of structure today. This preference reaches the $3\sigma$ significance using cosmic microwave background observations, supernova Ia and baryon acoustic oscillation measurements. The addition of cosmic microwave background lensing data relaxes such a preference to the $2\sigma$ level, since a larger lensing effect can always be compensated with a smaller structure growth, or, equivalently, with $\gamma >0.55$. We have also included the lensing amplitude $A_{\mathrm{L}}$ as a free parameter in our data analysis, showing that the preference for $A_{\mathrm{L}}>1$ still remains, except for some particular parametrizations when lensing observations are included. We also do not find any significant preference for an oscillatory dependence of $A_{\mathrm{L}}$, $A_{\mathrm{L}}+A_m\sin \ell$. To further reassess the effects of a nonstandard growth, we have computed by means of $N$-body simulations the dark matter density fields, the dark matter halo mass functions and the halo density profiles for different values of $\gamma$. Future observations from the Square Kilometer Array, reducing by a factor of 3 the current errors on the $\gamma$ parameter, further confirm or refute with a strong statistical significance the deviation of the growth index from its standard value.

We present the first simulation-based inference (SBI) of cosmological parameters from field-level analysis of galaxy clustering. Standard galaxy clustering analyses rely on analyzing summary statistics, such as the power spectrum $P_{\ell }$, with analytic models based on perturbation theory. Consequently, they do not fully exploit the nonlinear and non-Gaussian features of the galaxy distribution. To address these limitations, we use the SimBIG forward modeling framework to perform SBI using normalizing flows. We apply SimBIG to a subset of the Baryon Oscillation Spectroscopic Survey CMASS galaxy sample using a convolutional neural network with stochastic weight averaging to perform massive data compression of the galaxy field. We infer constraints on ${\mathrm{\Omega }}_m={0.267}_{-0.029}^{+0.033}$ and ${\sigma }_8={0.762}_{-0.035}^{+0.036}$. While our constraints on ${\mathrm{\Omega }}_m$ are in line with standard $P_{\ell }$ analyses, ours on ${\sigma }_8$ are $2.65\times$ tighter. Our analysis also provides constraints on the Hubble constant $H_0=64.5\pm 3.8\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ from galaxy clustering alone. This higher constraining power comes from additional non-Gaussian cosmological information, inaccessible with $P_{\ell }$. We demonstrate the robustness of our analysis by showcasing our ability to infer unbiased cosmological constraints from a series of test simulations that are constructed using different forward models than the one used in our training dataset. This work not only presents competitive cosmological constraints but also introduces novel methods for leveraging additional cosmological information in upcoming galaxy surveys like the Dark Energy Spectroscopic Instrument, Prime Focus Spectrograph, and Euclid.

The non-Gaussian spatial distribution of galaxies traces the large-scale structure of the Universe and therefore constitutes a prime observable to constrain cosmological parameters. We conduct Bayesian inference of the $\mathrm{\Lambda }\mathrm{CDM}$ parameters ${\mathrm{\Omega }}_m$, ${\mathrm{\Omega }}_b$, $h$, $n_s$, and ${\sigma }_8$ from the Baryon Oscillation Spectroscopic Survey CMASS galaxy sample by combining the wavelet scattering transform (WST) with a simulation-based inference approach enabled by the SimBIG forward model. We design a set of reduced WST statistics that leverage symmetries of redshift-space data. Posterior distributions are estimated with a conditional normalizing flow trained on 20,000 simulated SimBIG galaxy catalogs with survey realism. We assess the accuracy of the posterior estimates using simulation-based calibration and quantify generalization and robustness to the change of forward model using a suite of 2000 test simulations. When probing scales down to $k_{\max }=0.5h/\mathrm{Mpc}$, we are able to derive accurate posterior estimates that are robust to the change of forward model for all parameters, except ${\sigma }_8$. We mitigate the robustness issues with ${\sigma }_8$ by removing the WST coefficients that probe scales smaller than $k\sim 0.3h/\mathrm{Mpc}$. Applied to the Baryon Oscillation Spectroscopic Survey CMASS sample, our WST analysis yields seemingly improved constraints obtained from a standard perturbation-theory-based power spectrum analysis with $k_{\max }=0.25h/\mathrm{Mpc}$ for all parameters except $h$. However, we still raise concerns on these results. The observational predictions significantly vary across different normalizing flow architectures, which we interpret as a form of model misspecification. This highlights a key challenge for forward modeling approaches when using summary statistics that are sensitive to detailed model-specific or observational imprints on galaxy clustering.

We present the cosmological constraints from analyzing higher-order galaxy clustering on small nonlinear scales. We use SimBIG, a forward modeling framework for galaxy clustering analyses that employs simulation-based inference to perform highly efficient cosmological inference using normalizing flows. It leverages the predictive power of high-fidelity simulations and robustly extracts cosmological information from regimes inaccessible with current standard analyses. In this work, we apply SimBIG to a subset of the BOSS galaxy sample and analyze the redshift-space bispectrum monopole, $B_0(k_1,k_2,k_3)$, to $k_{\max }=0.5h/\mathrm{Mpc}$. We achieve $1\sigma$ constraints of ${\mathrm{\Omega }}_m=0.293_{-0.027}^{+0.027}$ and ${\sigma }_8=0.783_{-0.038}^{+0.040}$, which are more than 1.2 and $2.4\times$ tighter than constraints from standard power spectrum analyses of the same dataset. We also derive 1.4, 1.4, $1.7\times$ tighter constraints on ${\mathrm{\Omega }}_b$, $h$, $n_s$. This improvement comes from additional cosmological information in higher-order clustering on nonlinear scales and, for ${\sigma }_8$, is equivalent to the gain expected from a standard analysis on a $\sim 4\times$ larger galaxy sample. Even with our BOSS subsample, which only spans 10% of the full BOSS volume, we derive competitive constraints on the growth of structure: $S_8=0.774_{-0.053}^{+0.056}$. Our constraint is consistent with results from both cosmic microwave background and weak lensing. Combined with a ${\omega }_b$ prior from big bang nucleosynthesis, we also derive a constraint on $H_0={67.6}_{-1.8}^{+2.2}\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ that is consistent with early Universe constraints.

The terrestrial detection of a neutrino burst from the next galactic core-collapse supernova (CCSN) will provide profound insight into stellar astrophysics, as well as fundamental neutrino physics. Using time-of-flight (ToF) effects, a CCSN signal can be used to constrain the absolute neutrino mass. In this work, we study the case where a black hole forms during core-collapse, abruptly truncating the neutrino signal. This sharp cutoff is a feature that can be leveraged in a ToF study, enabling strict limits to be set on the neutrino mass which are largely model-independent. If supernova neutrinos are detected on Earth in liquid scintillator detectors, the exceptional energy resolution would allow an energy-dependent sampling of the ToF effects at low neutrino energies. One promising experimental program is the Jiangmen Underground Neutrino Observatory (JUNO), a next-generation liquid scintillator detector currently under construction in China. Using three-dimensional black hole-forming core-collapse supernova simulations, the sensitivity of a JUNO-like detector to the absolute neutrino mass is conservatively estimated to be $m_{\nu }<0.39_{-0.01}^{+0.06}\mathrm{eV}$ for a 95% CL bound. A future-generation liquid scintillator observatory like THEIA-100 could even achieve sub-0.2 eV sensitivity.

Certain relations among neutron-star observables that are insensitive to the underlying nuclear matter equation of state are known to exist. Such universal relations have been shown to be valid for cold and stationary neutron stars. Here, we study these relations in more dynamic scenarios: protoneutron stars and hypermassive neutron stars, allowing us to investigate the time evolution of these relations from the birth to the death of a neutron star. First, we study protoneutron stars. We use an effective equation of state, extracted from three-dimensional core-collapse supernova simulations, to obtain the structure of spherically symmetric protoneutron stars. We then consider nonradial oscillations to compute their $f$-mode frequency ($f$), as well as slow rotation and small tidal deformation, to compute their moment of inertia ($I$), spin-induced quadrupole moment ($Q$), and Love number. We find that well-established universal relations for cold neutron stars involving these observables (namely, the $I$-Love-$Q$ and $f$-Love relations) are approximately valid for protoneutron stars, with a deviation below $\approx 10\%$ for a postbounce time above $\approx 0.5\mathrm{s}$, considering eight different supernova progenitors and one equation of state (SFHo). Next, we study hypermassive neutron stars. The bulk of a neutron star is defined as the region enclosed by the isodensity surface that corresponds to the maximum compactness ($C$) inside the star. We obtain a new universal relation between the $f$-mode frequency and the compactness of cold and nonrotating neutron stars, using bulk quantities. We show that this relation has an equation-of-state-variation of $\approx 3\%$, considering a set of ten equations of state. Bulk quantities of postmerger remnants can be obtained from numerical-relativity simulations. Using results from binary neutron star merger simulations, we study the evolution of hypermassive neutron stars on the $f\text{−}C$ plane, considering two different mass ratios and one equation of state (SFHo). We find that the relation between the peak frequency of the gravitational-wave signal and the compactness from these hypermassive neutron stars deviates from the universal $f\text{−}C$ relation by $\approx 70\%–80\%$, when the peak frequency is taken directly as a proxy for the $f$-mode. As our results are limited to a single equation of state, the deviations we obtain when universal relations for cold neutron stars are used for protoneutron stars or hypermassive neutron stars can be conservatively considered as a lower limit. Finally, we discuss the reliability of the universal relations in the context of future observations of gravitational waves from remnants of core-collapse supernovae or binary neutron star mergers.

We study the supersymmetric $Q$ balls which decay at present and find that they create a distinctive spectrum of gamma rays at around O(10) MeV. The charge of the $Q$ ball is lepton numbers in order for the lifetime to be as long as the present age of the Universe, and the main decay products are light leptons. However, as the charge of the $Q$ ball decreases, the decay channel into pions becomes kinematically allowed towards the end of the decay, and the pions are produced at rest. Immediately, ${\pi }^0$ decays into two photons with the energy of 67.5 MeV, half the pion mass, which exhibits a unique emission line. In addition, ${\pi }^{\pm }$ decay into ${\mu }^{\pm }$, which further decay with emitting internal bremsstrahlung, whose spectrum has a sharp cutoff at $\sim 50\mathrm{MeV}$. If the observations find these peculiar features of the gamma-ray spectrum in the future, it could be a smoking gun of the supersymmetric $Q$-ball decay at present.