We have recently proposed a simple relativistic theory which reduces to modified Newtonian dynamics for the weak-field quasistatic situations applied to galaxies, and to cosmological behavior as in the $\mathrm{\Lambda }\mathrm{CDM}$ model, yielding a realistic cosmology in line with observations. A key requirement of any such model is that Minkowski space is stable against linear perturbations. We expand the theory action to second order in perturbations on a Minkowski background and show that it leads to healthy dispersion relations involving propagating massive modes in the vector and the scalar sector. We use Hamiltonian methods to eliminate constraints present, demonstrate that the massive modes have Hamiltonian bounded from below, and show that a nonpropagating mode with a linear time dependence may have unbounded Hamiltonian for wave numbers $k<\mu$ and bounded otherwise. The scale $\mu$ is estimated to be $\lesssim {\mathrm{Mpc}}^{-1}$ so that the low momenta instability may only play a role on cosmological scales.

We study binary black hole mergers in the extreme mass-ratio limit. We determine the energy, angular momentum, and linear momentum of the post-merger, remnant black hole. Unlike previous works, we perform our analysis directly in the test-particle limit by solving the Regge-Wheeler-Zerilli wave equation with a source that moves along a geodesic. We rely on the fact that toward the merger, small mass-ratio binary systems follow a quasiuniversal geodesic trajectory. This formalism captures the final premerger stages of small mass-ratio binaries and thus provides a straightforward universal description in a region inaccessible to numerical relativity simulations. We present a general waveform template that may be used in the search for gravitational wave bursts from small and intermediate mass-ratio binary systems. Finally, this formalism gives a formal proof that the recoil velocity is quadratic in the symmetric mass ratio $\nu$. Specifically, the velocity is given by $V/c\approx 0.0467{\nu }^2$. This result is about 4% larger than previously estimated. Most of this difference stems from the inclusion of higher multipoles in our calculation.

We provide a comprehensive study on the non-Markovian dynamics of the black hole phase transitions based on the underlying free energy landscape. In general, there are two typical timescales to characterize non-Markovian dynamics: (i) the timescale of the system represented by the intrinsic oscillating time of the black hole state at the potential well on the free energy landscape; (ii) the correlation time of the effective thermal bath. By assuming that the transition processes between different black hole states are stochastic, the non-Markovian dynamics of the black hole phase transition is governed by the generalized Langevin equation with the time-dependent friction that represents the memory effect from the effective thermal bath when the timescale of the system is comparable or shorter than the timescale of the effective thermal bath. We consider the first passage problem associated with the black hole phase transitions and derive the analytical expressions of the mean first passage time in the weak, intermediate, and large friction regimes. As the concrete examples, we study the effects of three types of time dependent friction kernel (delta function friction, exponentially decayed friction, and oscillatory friction) on the dynamics of Hawking-Page phase transition and the small/large Reissner-Nordström anti–de Sitter black hole phase transition. We found that there is a kinetic turnover point for each type of friction kernel when the friction strength varies. For the exponentially decayed friction kernel, it is shown that the non-Markovian effect slows down the phase transition dynamics in the weak friction regime and speeds up the transition process in the strong friction regime. For the oscillating decayed friction kernel, we found kinetic resonances when the oscillating frequency of the effective thermal bath is equal to the oscillating frequency of the black hole state in the initial potential well on the free energy landscape.

The origins of matter and radiation in the universe lie in a hot big bang. We present a number of well-motivated cosmologies in which the big bang occurs through a strong first-order phase transition—either at the end of inflation, after a period of kination (“kination-induced big bang”), or after a second period of vacuum domination in the early Universe (“supercooled big bang”); we also propose a “dark big bang” where only the dark matter in the Universe is created in a first-order phase transition much after inflation. In all of these scenarios, the resulting gravitational radiation can explain the tentative signals reported by the NANOGrav, Parkes, and European Pulsar Timing Array experiments if the reheating temperature of the hot big bang, and correspondingly the energy scale of the false vacuum, falls in the range $T_{*}\sim {\rho }_{\mathrm{vac}}^{1/4}=\mathrm{MeV}–100\mathrm{GeV}$. All of the same models at higher reheating temperatures will be of interest to upcoming ground- and space-based interferometer searches for gravitational waves at larger frequency.

Some cosmological models with non-negligible dark energy fractions, in particular windows of the prerecombination epoch, are capable of alleviating the Hubble tension quite efficiently, while keeping the good description of the data that are used to build the cosmic inverse distance ladder. There has been an intensive discussion in the community on whether these models enhance the power of matter fluctuations, leading de facto to a worsening of the tension with the large-scale structure measurements. We address this pivotal question in the context of several early dark energy (EDE) models, considering also in some cases a coupling between dark energy and dark matter, and the effect of massive neutrinos. We fit them using the Planck 2018 likelihoods, the supernovae of Type Ia from the Pantheon compilation, and data on baryon acoustic oscillations. We find that ultralight axion-like (ULA) EDE can actually alleviate the $H_0$ tension without increasing the values of ${\sigma }_{12}$ with respect to those found in the $\mathrm{\Lambda }\mathrm{CDM}$, whereas EDE with an exponential potential does not have any impact on the tensions. A coupling in the dark sector tends to enhance the clustering of matter, and the data limit greatly the influence of massive neutrinos, since the upper bounds on the sum of their masses are too close to those obtained in the standard model. We find that in the best case, namely ULA, the Hubble tension is reduced to $\sim 2\sigma$.

Ultralight bosonic dark matter is expected to be able to form a cloud surrounding the supermassive black hole (SMBH) in the Galactic center. With increasing precision of the observations of the stellar kinematics around the SMBH, tiny effects from such a dark matter cloud, including its gravitational perturbation and the direct coupling with the ordinary matter may be detectable. In this work, we search for possible evidence of the scalar cloud using accurate orbital measurements of the S2 star around Sgr ${\mathrm{A}}^{*}$. We solve the first order post-Newtonian equation, considering simultaneously the extended mass distribution of the scalar cloud and the frequency shift induced by the additional coupling via Higgs portal or photon portal interaction. Furthermore, we also investigate the impact of an astrophysical power-law component from the gas and stellar remnants. We find that the astrometric and spectroscopic data of the S2 star are well consistent with the scenario of a pointlike mass of Sgr ${\mathrm{A}}^{*}$. We thus derive upper limits of the coupling of the new interaction and the extended mass, with and without the contribution from the astrophysical component. The limits of the Higgs/photon coupling and the extended mass of the scalar cloud are the most stringent ones for the scalar mass window between $3.2\times {10}^{-19}\mathrm{eV}$ and $1.6\times {10}^{-18}\mathrm{eV}$.

The Taiji project is a space gravitational-wave detection mission consisting of three satellites that form a giant equilateral triangle with a side length of approximately $3\times {10}^6\mathrm{km}$ in the heliocentric orbit. The target of the mission is to detect gravitational-wave signals in the 0.1 mHz to 1 Hz band. However, its intersatellite distances are affected by celestial bodies in the solar system, introducing changes that may reach levels of 30,000 km in magnitude. Thus, it is important to investigate whether the gravitational fields of celestial bodies in the detection frequency band will have an impact on the realization of ultrahigh-sensitivity intersatellite ranging measurements. In this study, a high-precision orbit propagator with an accuracy of 0.03 pm on the 1 AU scale is developed. Based on this orbit propagator, the impact of the major large celestial bodies in the solar system on the detection sensitivity in the intersatellite measurements are analyzed. Detailed numerical studies show that the linear spectral density of the range and range acceleration are approximately $1\times {10}^{-13}\mathrm{m}/\sqrt{\mathrm{Hz}}$ and $5\times {10}^{-23}\mathrm{m}/{\mathrm{s}}^2/\sqrt{\mathrm{Hz}}$, respectively, at 0.1 mHz, indicating that the gravitational disturbance generated by the major celestial bodies in the solar system will not affect the aim of the Taiji mission to detect gravitational waves in the frequency band 0.1 mHz to 1 Hz.

The detection potential of the active neutrino magnetic moment (${\nu }_a\mathrm{MM}$) and the active sterile transition magnetic moment (${\nu }_s\mathrm{MM}$) in the solar neutrino $\mathrm{CE}\nu \mathrm{NS}$ process from future dark matter direct detection experiments is studied and compared with the respective allowed range to explain the Xenon1T excess. We find that the sensitivity to the ${\nu }_a\mathrm{MM}$ approaches to the level between ${10}^{-10}{\mu }_B$ and ${10}^{-11}{\mu }_B$, which is dominantly limited by the detection threshold. On the other hand, the future solar neutrino $\mathrm{CE}\nu \mathrm{NS}$ detection would be powerful in probing the ${\nu }_s\mathrm{MM}$ for the sterile neutrino mass below 10 MeV, which can unambiguously test the ${\nu }_s\mathrm{MM}$ explanation of the Xenon1T excess. The sensitivity in the general framework with both ${\nu }_a\mathrm{MM}$ and ${\nu }_s\mathrm{MM}$ contributions is also derived.

We study radiative plateaulike inflation and ${\mathrm{Z}}_{BL}$-portal freeze-in fermionic dark matter in a minimal $B-L$ extended model. The ${\mathrm{U}(1)}_{B-L}$ Higgs, responsible for heavy neutrino masses, also drives inflation in the early Universe, thanks to radiative corrections from the heavy neutrinos and the ${\mathrm{Z}}_{BL}$ gauge boson. In our benchmark choice for the ${\mathrm{U}(1)}_{B-L}$ gauge coupling $g_{B-L}\sim {10}^{-4}$, a light ${\mathrm{Z}}_{BL}$ boson can be explored by current and future lifetime frontier experiments, such as the Forward Search Experiment (FASER) and FASER 2 at the LHC, SHiP, Belle II, and LHCb. For the benchmark, the Hubble scale of inflation (${\mathcal{H}}_{\inf }$) is very low [${\mathcal{H}}_{\inf }=\mathcal{O}(100)\mathrm{eV}$] and the inflaton turns out to be very light with mass of $\mathcal{O}(1)\mathrm{eV}$, and consequently the decay width of the inflaton is extremely small. We investigate a two-field system with the $\mathrm{inflaton}/B-L$ Higgs and the Standard Model (SM) Higgs, and find that the reheating with a sufficiently high temperature occurs when the waterfall direction to the SM Higgs direction opens up in the trajectory of the scalar field evolution.

The scotogenic model of neutrino mass is modified so that the dark Majorana fermion singlet $S$ which makes the neutrino massive is itself generated in one loop. This is accomplished by having $Z_6$ lepton symmetry softly broken to $Z_2$ in the scalar sector by a unique quadratic term.

We determine the gluonic spectral function $SU(3)$ Yang-Mills theory as well as we found fermionic spectral functions in the strong quenched QED where we found a novel solution. Our developed technique provides solutions with the usual branch cut for propagators while not showing any pole structure at the first Riemann sheet (identical with entire complex plane) of the complex square of momentum. Implications and further utilization are briefly addressed for QCD and Standard model calculations.

We extend our study of the large-$N$ expansion of general nonequilibrium many-body systems with matrix degrees of freedom $M$, and its dual description as a sum over surface topologies in a dual string theory, to the Keldysh-rotated version of the Schwinger-Keldysh formalism. The Keldysh rotation trades the original fields $M_{\pm }$—defined as the values of $M$ on the forward and backward segments of the closed time contour—for their linear combinations $M_{\mathrm{cl}}$ and $M_{\mathrm{qu}}$, known as the “classical” and “quantum” fields. First we develop a novel “signpost” notation for nonequilibrium Feynman diagrams in the Keldysh-rotated form, which simplifies the analysis considerably. Before the Keldysh rotation, each world-sheet surface $\mathrm{\Sigma }$ in the dual string theory expansion was found to exhibit a triple decomposition into the parts ${\mathrm{\Sigma }}^{\pm }$ corresponding to the forward and backward segments of the closed time contour, and ${\mathrm{\Sigma }}^{\wedge }$ which corresponds to the instant in time where the two segments meet. After the Keldysh rotation, we find that the world-sheet surface $\mathrm{\Sigma }$ of the dual string theory undergoes a very different natural decomposition: $\mathrm{\Sigma }$ consists of a “classical” part ${\mathrm{\Sigma }}^{\mathrm{cl}}$ and a “quantum embellishment” part ${\mathrm{\Sigma }}^{\mathrm{qu}}$. We show that both parts of $\mathrm{\Sigma }$ carry their own independent genus expansion. The nonequilibrium sum over world-sheet topologies is naturally refined into a sum over the double decomposition of each $\mathrm{\Sigma }$ into its classical and quantum part. We apply this picture to the classical limits of the quantum nonequilibrium system (with or without interactions with a thermal bath), and find that in these limits, the dual string perturbation theory expansion reduces to its appropriately defined classical limit.

We analyze the large-$N$ expansion of general nonequilibrium systems with fluctuating matrix degrees of freedom and $SU(N)$ symmetry, using the Schwinger-Keldysh formalism and its closed real-time contour with a forward and backward component. In equilibrium, the large-$N$ expansion of such systems leads to a sum over topologies of two-dimensional surfaces of increasing topological complexity, predicting the possibility of a dual description in terms of string theory. We extend this argument away from equilibrium and study the universal features of the topological expansion in the dual string theory. We conclude that in nonequilibrium string perturbation theory, the sum over world sheet topologies is further refined: Each world sheet surface $\mathrm{\Sigma }$ undergoes a triple decomposition into the part ${\mathrm{\Sigma }}^{+}$ corresponding to the forward branch of the time contour, the part ${\mathrm{\Sigma }}^{-}$ on the backward branch, and the part ${\mathrm{\Sigma }}^{\wedge }$ that corresponds to the instant in the far future where the two branches of the time contour meet. The sum over topologies becomes a sum over the triple decompositions. We generalize our findings to the Kadanoff-Baym time contour relevant for systems at finite temperature and to the case of closed and open, oriented or unoriented strings. Our results are universal and follow solely from the features of the large-$N$ expansion without any assumptions about the world sheet dynamics.

The Chern-Simons-Kodama (CSK) state is an exact, nonperturbative wave function in the Ashtekar formulation of classical general relativity. In this work, we find a generalized fermionic CSK state by solving the extended gravitational and fermionic Hamiltonian constraints of the Wheeler-DeWitt equation exactly. We show that this new state reduces to the original Kodama state upon symmetry reduction to Friedmann-Lematre-Robertson-Walker (FLRW) coordinates with perturbative fermionic corrections, making contact with the Hartle-Hawking and Vilenkin wave functions of the universe in cosmology. We also find that when both torsion and fermions are nonvanishing, the wave function possesses a finite amplitude to evade the big bang curvature singularity.

Modular fluctuations have previously been shown to obey an area law $⟨\mathrm{\Delta }{K}^2⟩=⟨K⟩=A/4G_N$. Furthermore, modular fluctuations generate fluctuations in the spacetime geometry of empty causal diamonds. Here we demonstrate the physical origin of these fluctuations, showing that the modular area law, in $d$-dimensionsal Minkowski space, can be reproduced from shockwaves arising from vacuum fluctuations. The size of the vacuum fluctuations is fixed by commutation relations in light-ray operators, of the same form postulated by ’t Hooft in the context of black hole horizons.

We show that a non-Hermitian two coupled Sachdev-Ye-Kitaev (SYK) model can provide thermodynamic structure equivalent to a Hermitian two coupled SYK model. The energy spectrum, the entanglement degree of the ground states and the low energy effective action of this model are not influenced by the non-Hermiticity. The novel biorthogonal ground states demonstrates that two SYK sites, one of which can be in the ground state and the other in the Schwarzian excited state by tuning the non-Hermiticity. We find evidence that the free energy is independent of the non-Hermiticity.

From statistical mechanics the trace of the thermal average of any energy-momentum tensor is $⟨{T^{\mu }}_{\mu }⟩=T\partial P/\partial T-4P$. The renormalization group formula $⟨{T^{\mu }}_{\mu }⟩=\beta (g_M)\partial P/\partial g_M$ for QCD with massless fermions requires the pressure to have the structure, $P=T^4\sum _{n=0}^{\infty }{\varphi }_n(g_M)[\ln (\frac{M}{4\pi T}){]}^n,$ where the factor $4\pi$ is for later convenience. The functions ${\varphi }_n(g_M)$ for $n\ge 1$ may be calculated from ${\varphi }_0(g_M)$ using the recursion relation $n{\varphi }_n(g_M)=-\beta (g_M)d{\varphi }_{n-1}/d{g}_M$. This is checked against known perturbation theory results by using the terms of order $(g_M{)}^2$, $(g_M{)}^3$, $(g_M{)}^4$ in ${\varphi }_0(g_M)$ to obtain the known terms of order $(g_M{)}^4$, $(g_M{)}^5$, $(g_M{)}^6$ in ${\varphi }_1(g_M)$ and the known term of order $(g_M{)}^6$ in ${\varphi }_2(g_M)$. The above series may be summed and gives the same result as choosing $M=4\pi T$, viz. $T^4{\varphi }_0(g_{4\pi T})$.

Here we look at an application of the Hartle metric to describe a rotating version of the spherical string cloud/global monopole solution. While rotating versions of this solution have previously been constructed via the Newman-Janis algorithm, that process does not preserve the equation of state. The Hartle method allows for preservation of equation of state, at least in the sense of a slowly rotating perturbative solution. In addition to the direct utility of generating equations which could be used to model a region of a rotating string cloud or similar system, this work shows that it is possible to adapt the Hartle metric to slowly rotating anisotropic systems with Segre type [(11)(1,1)] following an equation of state between the distinct eigenvalues.