We motivate a minimal realization of slow-roll $k$-inflation by incorporating the local conformal symmetry and the broken global SO(1,1) symmetry in the metric-affine geometry. With use of the metric-affine geometry where both the metric and the affine connection are treated as independent variables, the local conformal symmetry can be preserved in each term of the Lagrangian and thus higher derivatives of scalar fields can be easily added in a conformally invariant way. Predictions of this minimal slow-roll $k$-inflation, $n_{\mathrm{s}}\sim 0.96$, $r\sim 0.005$, and $c_{\mathrm{s}}\sim 0.03$, are not only consistent with current observational data but also have a prospect to be tested by forthcoming observations.

We use numerical methods to obtain moduli-dependent Calabi-Yau metrics, and from them, the moduli-dependent massive tower of Kaluza-Klein states for the one-parameter family of quintic Calabi-Yau manifolds. We then compute geodesic distances in their Kähler and complex structure moduli space using exact expressions from mirror symmetry, approximate expressions, and numerical methods, and we compare the results. Finally, we fit the moduli dependence of the massive spectrum to the geodesic distance to obtain the rate at which states become exponentially light. The result is indeed of order 1, as suggested by the swampland distance conjecture. We also observe level crossing in the eigenvalue spectrum and find that states in small irreducible representations of the symmetry group tend to become lighter than states in larger irreducible representations.

The mass spectra of isovector $\mathrm{\Upsilon }$, $\psi$, $\varphi$, and $\omega$ meson resonances are investigated, in the AdS/QCD and information entropy setups. The differential configurational entropy is employed to obtain the mass spectra of radial $S$-wave resonances, with higher excitation levels, in each one of these meson families, whose respective first undisclosed states are discussed and matched up to candidates in the Particle Data Group.

In addition to the familiar string theories with spacetime supersymmetry, there exist a number of nonsupersymmetric ten-dimensional superstrings. Nearly all of these theories have closed string tachyons, indicating a misidentification of the vacuum around which they are to be quantized. In this work, we identify (meta)stable vacua for all known tachyonic superstrings. These vacua are all lower dimensional, with most of them being familiar two-dimensional string theories. However, there are also intriguing examples of solutions in dimensions 6, 8, and 9, with respective gauge groups $E_7\times E_7$, $SU(16)$, and $E_8$. These special vacua have positive vacuum energy and no moduli.

Planck scale modified dispersion relations are one way to capture the influence of quantum gravity on the propagation of fundamental point particles effectively. We derive the time dilation between an observer’s or particle’s proper time, given by a Finslerian length measure induced from a modified dispersion relation, and a reference laboratory time. To do so, the Finsler length measure for general first order perturbations of the general relativistic dispersion relation is constructed explicitly. From this we then derive the time dilation formula for the $\kappa$-Poincaré dispersion relation in several momentum space bases, as well as for modified dispersion relations considered in the context of string theory and loop quantum gravity. Most interestingly we find that the momentum Lorentz factor in the present and future colliders can, in principle, become large enough to constrain the Finsler realization of the $\kappa$-Poincaré dispersion relation in the bicrossproduct basis as well as a string theory inspired modified dispersion relation, at Planck scale sensitivity with the help of the muon’s lifetime.

We investigate the properties of near-conformal dynamics in a sector of large charge when approaching the lower boundary of the conformal window from the chirally broken phase. To elucidate our approach we use the time-honored example of the phenomenologically relevant $SU(2)$ color theory featuring $N_f$ Dirac fermions transforming in the fundamental representation of the gauge group. In the chirally broken phase we employ the effective pion Lagrangian featuring also a pseudodilaton to capture a possible smooth conformal-to-nonconformal phase transition. We charge the baryon symmetry of the Lagrangian and study its impact on the ground state and spectrum of the theory as well as the would-be conformal dimensions of the lowest large-charge operator. We moreover study the effects of and dependence on the fermion mass term.

In this article, we analyze the fundamental global and local symmetries involved in the action for the free relativistic point particle in Minkowski space. Moreover, we identify a hidden local symmetry, whose explicit consideration and factorization utilizing of a Fujikawa prescription leads to the construction of relativistic two-point correlation functions that satisfy the Chapman-Kolmogorov identity. By means of a detailed topological analysis, we find three different relativistic correlation functions (orthochronous, spacelike, and Feynman) which are obtained from the exclusive integration of paths within different sectors in Minkowski space. Finally, the connection of this approach to the Feynman checkerboard construction is explored.

We study the properties of the spacetime around a regular nonminimal magnetic black hole (BH) together with the dynamics of the neutral, magnetized, and magnetically charged particles in its vicinity. The dependence of the values of curvature invariants and the outer event horizon corresponding to the extreme charge of the BH from the coupling parameter are studied in detail. Our study of the test particle motion shows that the innermost stable circular orbit (ISCO) radius decreases with the increase of the magnetic charge of the nonminimal regular magnetic BH. We show that the increase of the ISCO radius with the increase of the coupling parameter is due to the decrease of the extreme value of the BH charge. In particular, when the coupling parameter $q\to \infty$ the ISCO radius tends to the value $r_{\mathrm{ISCO}}=4.5M$. The effect of the magnetic charge parameter on ISCO radius can mimic the effect due to the spin parameter of the rotating Kerr BH, and the mimicking values of the spin parameter decreases with the increase of the coupling parameter. We also explore the possible mimicking of the parameters through the observations of twin-peak quasiperiodic oscillations (QPOs). Our analysis shows that the Reissner-Nordström (RN) charge can mimic the spin parameter of the Kerr BH up to $a/M\simeq 0.51$ provided that there is the same relation between the upper and lower frequencies of the twin-peak QPOs. On the other hand, the nonminimal regular magnetic BH coupling parameter may mimic the spin parameter up to $a/M\simeq 0.215$ in the relativistic precession model.

In this work we derive the junction conditions for the matching between two spacetimes at a separation hypersurface in the perfect-fluid version of $f(R,T)$ gravity, not only in the usual geometrical representation but also in a dynamically equivalent scalar-tensor representation. We start with the general case in which a thin shell separates the two spacetimes at the separation hypersurface, for which the general junction conditions are deduced, and the particular case for smooth matching is considered when the stress-energy tensor of the thin shell vanishes. The set of junction conditions is similar to the one previously obtained for $f(R)$ gravity but features also constraints in the continuity of the trace of the stress-energy tensor $T_{ab}$ and its partial derivatives, which force the thin shell to satisfy the equation of state of radiation $\sigma =2p_t$. As a consequence, a necessary and sufficient condition for spherically symmetric thin shells to satisfy all the energy conditions is the positivity of its energy density $\sigma$. For specific forms of the function $f(R,T)$, the continuity of $R$ and $T$ ceases to be mandatory but a gravitational double layer arises at the separation hypersurface. The Martinez thin-shell system and a thin shell surrounding a central black hole are provided as examples of application.

We explore the benefits of adapted gauges to small mass ratio binary black hole evolutions in the moving puncture formulation. We find expressions that approximate the late time behavior of the lapse and shift, $({\alpha }_0,{\beta }_0)$, and use them as initial values for their evolutions. We also use a position and black hole mass dependent damping term, $\eta [{\overrightarrow{x}}_1(t),{\overrightarrow{x}}_2(t),m_1,m_2]$, in the shift evolution, rather than a constant or conformal-factor dependent choice. We have found that this substantially reduces noise generation at the start of the numerical integration and keeps the numerical grid stable around both black holes, allowing for more accuracy with lower resolutions. We test our choices for this gauge in detail in a case study of a binary with a $7:1$ mass ratio, and then use $15:1$ and $32:1$ binaries for a convergence study. Finally, we apply our new gauge to a $64:1$ binary and a $128:1$ binary to well cover the comparable and small mass ratio regimes.

Studies of neutron stars are at their peak after the multimessenger observation of the binary merger event GW170817, which strongly constrains the stellar parameters like tidal deformability, masses, and radii. Although current and future observations will provide stronger limits on the neutron stars parameters, knowledge of explicit interior solutions to Einstein’s equations, which connect observed parameters with the internal structure, are crucial to have a satisfactory description of the interior of these compact objects. A well-known exact solution, which has shown a relatively good approximation to a neutron star, is the Tolman VII solution. In order to provide a better fitting for the energy density profile, with the realistic equations of state for neutron stars, recently, Jiang and Yagi proposed a modified version of this model, which introduces an additional parameter $\alpha$, reflecting the interplay of the quadratic and the newly added quartic term in the energy density profile. Here we study the dynamical stability of this modified Tolman VII solution using the theory of infinitesimal and adiabatic radial oscillations developed by Chandrasekhar. For this purpose, we determine values of the critical adiabatic index, for the onset of instability, considering configurations with varying compactness and $\alpha$. We found that the new models are stable against radial oscillations for a considerable range of values of compactness and the new parameter $\alpha$, thus supporting their applicability as a physically plausible approximation of realistic neutron stars.

Employing the Fisher information matrix analysis, we estimate parameter errors of TianQin and Laser Interferometer Space Antenna (LISA) for monochromatic gravitational waves. With the long-wavelength approximation, we derive analytical formulas for the parameter estimation errors. We separately analyze the effects of the amplitude modulation due to the changing orientation of the detector plane and the Doppler modulation due to the translational motion of the center of the detector around the Sun. We disclose that in the low-frequency regime there exist different patterns in angular resolutions and estimation errors of sources’ parameters between LISA and TianQin, the angular resolution falls off as $S_n(f)/f^2$ for TianQin but $S_n(f)$ for LISA, and the estimation errors of the other parameters fall off as $\sqrt{S_n(f)}/f$ for TianQin but $\sqrt{S_n(f)}$ for LISA. In the medium-frequency regime, we observe the same pattern where the angular resolution falls off as $S_n(f)/f^2$ and the estimation errors of the other parameters fall off as $\sqrt{S_n(f)}$ for both TianQin and LISA. In the high-frequency regime, the long-wavelength approximation fails; we numerically calculate the parameter estimation errors for LISA and TianQin and find that the parameter estimation errors measured by TianQin are smaller than those by LISA.

We naturally extend general relativity with a conformally coupled scalar field by only requiring conformal invariance of the scalar field equation of motion and not of the action. The classically extended theory incorporates a scalar-Gauss-Bonnet sector and has second-order equations of motion, belonging to the Horndeski class. Remarkably, the theory features a purely geometrical field equation that allows for closed-form black hole solutions and cosmologies to be easily found. These solutions permit investigations of in-vogue scalar-Gauss-Bonnet corrections to the gravitational action without the need of resorting to approximations or numerical methods.

We study the motion of gas clouds in the vicinity of boson stars, performing simulations with the black hole accretion code. We compare the motion of the gas clouds with particle motion along geodesics and analyze the tidal effects on the gas clouds, which leads to the disruption of the clouds. First we consider small and dense clouds associated with three different types of bound orbits close to the boson star and analyze the mechanisms of debris formation for these. We infer from the simulations that the lifetimes of these nearby clouds are longer for initially circularly orbiting clouds than for clouds on initially eccentric orbits. Next we compare the evolution of more extended and less dense clouds on initially circular orbits around a boson star and a Schwarzschild black hole and compare the motion in these two spacetimes. In particular, we observe the formation of a ringlike structure around the boson star endowed with a spiralling shock structure and a constant thermal bremsstrahlung total luminosity. This final configuration contrasts strongly with the black hole scenario where the gas is totally captured behind the event horizon.

We study the strong gravitational lensing due to the Kerr black holes with angular momentum $a$ and the Kerr-Newman black holes with additional charge $Q$. We first derive the analytical expressions of the deflection angles of light rays that particularly diverge as they travel near the photon sphere. In this strong deflection limit, the light rays can circle around the black hole multiple times before reaching the observer, giving relativistic images. The obtained analytical expressions are then applied to compute the angular positions of relativistic images due to the supermassive galactic black holes. In this work, we focus on the outermost image with reference to the optical axis. We find that its angular separation from the one closest to the optical axis increases with the increase of angular momentum $a$ of the black holes for light rays in direct orbits. Additionally, the effects of the charge $Q$ of black holes also increase the angular separation of the outermost image from the others for both direct and retrograde orbits. The potentially increasing observability of the relativistic images from the effects of angular momentum and charge of the black holes will be discussed.

The Schrödinger equation with a harmonic potential coupled to the Poisson equation, called the Schrödinger-Newton-Hooke (SNH) system, has been considered in a variety of physical contexts, ranging from quantum mechanics to general relativity. Our work is directly motivated by the fact that the SNH system describes the nonrelativistic limit of the Einstein-massive-scalar system with negative cosmological constant. With this paper we begin the investigations aiming at understanding solutions of the SNH system in the energy supercritical spatial dimensions $d\ge 7$, where we expect to observe interesting short wavelength behaviors due to the confinement of waves by the trapping potential. Here we study spherically symmetric stationary solutions and prove the existence of one-parameter families of nonlinear ground and excited states. The frequency of the ground state as the function of the central density is shown to exhibit different qualitative behaviors in dimensions $7\le d\le 15$ and $d\ge 16$, which is expected to affect the stability properties of the ground states in these dimensions. Our results bear many similarities to the analogous problem that has been studied for the Gross-Pitaevskii equation.

This paper aims at investigating the influence of space-time curvature on the uncertainty relation. In particular, relying on previous findings, we assume the quantum wave function to be confined to a geodesic ball on a given spacelike hypersurface whose radius is a measure of the position uncertainty. On the other hand, we concurrently work out a viable physical definition of the momentum operator and its standard deviation in the nonrelativistic limit of the $3+1$ formalism. Finally, we evaluate the uncertainty relation, which to second order depends on the Ricci scalar of the effective 3-metric and the corresponding covariant derivative of the shift vector. For the sake of illustration, we apply our general result to a number of examples arising in the context of both general relativity and extended theories of gravity.

Inflationary magnetogenesis has long been assumed to be the most promising mechanism for producing the large-scale magnetic fields in our universe. However, generically, such models are plagued with either backreaction or strong coupling problems within the standard framework. This paper has shown that the reheating phase can play a crucial role in alleviating those problems along with the cosmic microwave background. The electrical conductivity is assumed to be negligible during the entire period of reheating, and the classic Faraday electromagnetic induction changes the magnetic field’s dynamics drastically. Our detailed analysis reveals that this physical phenomenon not only converts a large class of magnetogenesis model observationally viable without any theoretical problem but also can uniquely fix the perturbative average inflaton equation of state, ${\omega }_{\varphi }=(p+2)/(p+2)$ during reheating given a specific value of the large scale magnetic field. This observation hints the inflaton to assume the potential of form $V(\varphi )\sim {\varphi }^p$ near its minimum with $p\gtrsim 3.5$ if one considers the limitations of the present-day strength of the large scale magnetic field to be ${\mathcal{P}}_{B0}^{\frac{1}{2}}\gtrsim {10}^{-18}\mathrm{G}$. Our analysis opens up a new avenue toward constraining the inflationary and magnetogenesis model together via reheating.

A plethora of observational data obtained over the last couple of decades has allowed cosmology to enter into a precision era and has led to the foundation of the standard cosmological constant and cold dark matter paradigm, known as the $\mathrm{\Lambda }\mathrm{CDM}$ model. Given the many possible extensions of this concordance model, we present here several novel consistency tests which could be used to probe for deviations from $\mathrm{\Lambda }\mathrm{CDM}$. First, we derive a joint consistency test for the spatial curvature ${\mathrm{\Omega }}_{k,0}$ and the matter density ${\mathrm{\Omega }}_{\mathrm{m},0}$ parameters, constructed using only the Hubble rate $H(z)$, which can be determined directly from observations. Second, we present a new test of possible deviations from homogeneity using the combination of two datasets, either the baryon acoustic oscillation (BAO) and $H(z)$ data, or the transversal and radial BAO data, while we also introduce two consistency tests for $\mathrm{\Lambda }\mathrm{CDM}$ which could be reconstructed via the transversal and radial BAO data. We then reconstruct the aforementioned tests using the currently available data in a model independent manner using a particular machine learning approach, namely the genetic algorithms. Finally, we also report on a $\sim 4\sigma$ tension on the transition redshift as determined by the $H(z)$ and radial BAO data.