We quantize super Yang-Mills action in $\mathcal{N}=3$ harmonic superspace using “Fermi-Feynman” gauge and also develop the background field formalism. This leads to simpler propagators and Feynman rules that are useful in performing explicit calculations. The superspace rules are used to show that divergences do not appear at one loop and beyond. We also compute a finite contribution to the effective action from a four-point diagram at one loop, which matches the expected covariant result.

We adopt a combination of analytical and numerical methods to study the renormalization group flow of the most general field theory with quartic interaction in $d=4-\epsilon$ with $N=3$ and $N=4$ scalars. For $N=3$, we find that it admits only three nondecomposable critical points: the Wilson-Fisher with $O(3)$ symmetry, the cubic with $H_3=({\mathbb{Z}}_2{)}^3⋊S_3$ symmetry, and the biconical with $O(2)\times {\mathbb{Z}}_2$. For $N=4$, our analysis reveals the existence of new nontrivial solutions with discrete symmetries and with up to three distinct field anomalous dimensions.

If time travel is possible, it seems to inevitably lead to paradoxes. These include consistency paradoxes, such as the famous grandfather paradox, and bootstrap paradoxes, where something is created out of nothing. One proposed class of resolutions to these paradoxes allows for multiple histories (or timelines) such that any changes to the past occur in a new history, independent of the one where the time traveler originated. We introduce a simple mathematical model for a spacetime with a time machine and suggest two possible multiple-histories models, making use of branching spacetimes and covering spaces, respectively. We use these models to construct novel and concrete examples of multiple-histories resolutions to time travel paradoxes, and we explore questions such as whether one can ever come back to a previously visited history and whether a finite or infinite number of histories is required. Interestingly, we find that the histories may be finite and cyclic under certain assumptions, in a way which extends the Novikov self-consistency conjecture to multiple histories and exhibits hybrid behavior combining the two. Investigating these cyclic histories, we rigorously determine how many histories are needed to fully resolve time travel paradoxes for particular laws of physics. Finally, we discuss how observers may experimentally distinguish between multiple histories and the Hawking and Novikov conjectures.

We propose a new derivation from full loop quantum gravity (LQG) to the loop quantum cosmology improved $\overline{\mu }$-scheme effective dynamics, based on the reduced phase-space formulation of LQG and a proposal of an effective Hamiltonian/action in full LQG. A key step of our program is an improved regularization of full LQG Hamiltonian on a cubic lattice. The improved Hamiltonian uses a set of “dressed holonomies” $h_{\mathrm{\Delta }}(\mathfrak{s})$ which depend on both the connection $A$ and the length of the curve $\mathfrak{s}$. With the improved Hamiltonian, we propose a quantum effective action and derive a new set of effective equations of motion (EOMs) for full LQG. Then, we show that these new EOMs imply the $\overline{\mu }$-scheme effective dynamics for both the homogeneous-isotropic and Bianchi-I cosmologies, and predict a bounce and Planckian critical density. As a byproduct, although the model is defined on a cubic lattice, we find that the improved effective Hamiltonian of cosmology is invariant under lattice refinement. The cosmological effective dynamics, predictions for the bounce, and critical density are results in the continuum limit.

We discuss, without assuming asymptotic flatness, a gravitational lens for an observer and source that are within a finite distance from a lens object. The proposed lens equation is consistent with the deflection angle of light that is defined for the nonasymptotic observer and source by Takizawa et al. [Phys. Rev. D 101, 104032 (2020)] based on the Gauss-Bonnet theorem with using the optical metric. This lens equation, though it is shown to be equivalent to the Bozza lens equation [Phys. Rev. D 78, 103005 (2008)], is linear in the deflection angle. Therefore, the proposed equation is more convenient for the purpose of doing an iterative analysis. As an explicit example of an asymptotically nonflat spacetime, we consider a static and spherically symmetric solution in Weyl conformal gravity, especially a case that $\gamma$ parameter in the Weyl gravity model is of the order of the inverse of the present Hubble radius. For this case, we examine iterative solutions for the finite-distance lens equation up to the third order. The effect of the Weyl gravity on the lensed image position begins at the third order, and it is linear in the impact parameter of light. The deviation of the lensed image position from the general relativistic one is $\sim {10}^{-2}\mathrm{microarcseconds}$ for the lens and source with a separation angle of $\sim 1\mathrm{arcminute}$, where we consider a cluster of galaxies with ${10}^{14}{M}_{\odot }$ at $\sim 1\mathrm{Gpc}$ for instance. The deviation becomes $\sim {10}^{-1}\mathrm{microarcseconds}$, even if the separation angle is $\sim 10\mathrm{arcminutes}$. Therefore, effects of the Weyl gravity model are negligible in current and near-future observations of gravitational lensing. On the other hand, the general relativistic corrections at the third order $\sim 0.1\mathrm{milliarcseconds}$ can be relevant with VLBI observations.

Motivated by the discrepancy in measurements of $H_0$ between local and global probes, we investigate whether teleparallel gravities could be a better model to describe the present-day observations or at least to alleviate the $H_0$ tension. Specifically, in this work we study and place constraints on three popular $f(T)$ models in light of the Planck-2018 cosmic microwave background data release. We find that the $f(T)$ power-law model can alleviate the $H_0$ tension from $4.4\sigma$ to $1.9\sigma$ level, while the $f(T)$ model of two exponentials fails to resolve this inconsistency. Moreover, for the first time, we obtain constraints on the effective number of relativistic species $N_{\mathrm{eff}}$ and on the sum of the neutrino masses $\mathrm{\Sigma }{m}_{\nu }$ in $f(T)$ gravity. We find that the constraints obtained are looser than in $\mathrm{\Lambda }\mathrm{CDM}$. However, the introduction of massive neutrinos into the cosmological model alleviates the $H_0$ tension for the power-law model. Finally, we find that whether a viable $f(T)$ theory can mitigate the $H_0$ tension depends on the mathematical structure of the distortion factor $y(z,b)$. These results could provide a clue for theoreticians to write a more physical-motivated expression of $f(T)$ function.

The baryon-antibaryon asymmetry (excess of matter over antimatter in our Universe), indicated by observational data from the cosmic microwave background anisotropies, predictions of primordial nucleosynthesis, and the absence of intense radiation from matter-antimatter annihilation, constitutes an unsolved puzzle in cosmology. Two mechanisms for baryon asymmetry have been proposed as extensions of the Standard Model of particle physics at high energies. They rely on new couplings involving the baryon number current, one with a scalar field, called spontaneous baryogenesis, and the other with space-time curvature, named gravitational baryogenesis. These two mechanisms are investigated in the context of many bouncing scenarios, either symmetric or asymmetric around the bounce. It is shown that the constraints on the free parameters of these scenarios, imposed to yield the observed baryon-to-entropy ratio, are mild, already containing the values compatible with other observational constraints coming from the features of the power spectra of cosmological perturbations. Hence, realistic bouncing models can yield the observed baryon-antibaryon asymmetry if one of the two mechanisms proposed takes place in nature.

The fundamental ($f$-) mode gravitational waves from cold low-mass neutron stars are systematically studied with various equations of state (EOSs) characterized by the nuclear saturation parameters, especially focusing on the phenomena of the avoided crossing with the first pressure ($p_1$-) mode. We find that the $f$-mode frequency and the average density for the neutron star at the avoided crossing can be expressed as a function of the parameter, $\eta$, which is the specific combination of the nuclear saturation parameters. Owing to these relations, we can derive the empirical formula expressing the $f$-mode frequency for a low-mass neutron star, whose central density is larger than that for the neutron star at the avoided crossing, as a function of $\eta$ and the square root of the stellar average density, $x$. On the other hand, we also derive the empirical formula expressing the $f$-mode frequency for a neutron star, whose central density is less than that for the neutron star at the avoided crossing, as a function of $x$ independently of the adopted EOS. Furthermore, adopting the empirical formula of $x$ as a function of $\eta$ and $u_c$, which is the ratio of the stellar central density to the saturation density, we can also rewrite our empirical formula for the $f$-mode frequency to a function of $\eta$ and $u_c$. So, by observing the $f$-mode gravitational wave from a low-mass neutron star, whose mass or gravitational redshift is known, one could evaluate the values of $\eta$ and $u_c$, which enables us to severely constrain the EOS for neutron star matter.

Preinflationary dynamics is known to have left observable imprints via the varied dynamics of the inflaton and the graviton fields during those epochs. It is highlighted here that other particle degrees of freedom, too, are capable of leaving their imprints on primordial observables if they transfer their entropies upon annihilation after becoming nonrelativistic during a preinflationary epoch. Such annihilations of other particles would result in lowering of the tensor-to-scalar ratio at the pivot scale (and at length scales larger to that) which would help bring those potentials back in accordance with current observations which are otherwise disfavored for yielding large tensor-to-scalar ratios at present.

After a quantum phase transition, the quantum vacuum can break up to form classical topological defects. We examine this process for scalar field models with $Z_2$ symmetry for different quench rates for the phase transition. We find that the number density of kinks at late times universally scales as $C{m}^{1/2}{t}^{-1/2}$, where $m$ is a mass scale in the model and $C\approx 0.22$; it does not depend on the quench timescale in contrast to the Kibble-Zurek scaling for thermal phase transitions. A subleading correction $\propto t^{-3/2}$ to the kink density depends on the details of the phase transition.

We consider a simple extension of the Standard Model (SM) by a complex scalar doublet and a singlet along with three sterile neutrinos. The sterile neutrinos mix with the SM neutrinos to produce three light neutrino states consistent with the oscillation data and three heavy sterile states. The lightest sterile neutrino has lifetime longer than the age of the Universe and can provide correct dark matter relic abundance. Utilizing tree-level flavor changing interactions of a light scalar with mass $\sim \mathcal{O}(100)\mathrm{MeV}$ along with sterile neutrinos, we can explain the anomalous magnetic moments of both muon and electron, KOTO anomalous events and the MiniBooNE excess simultaneously.

The gluon distributions of the pion obtained from various global fits exhibit large variations among them. Within the framework of the color evaporation model, we show that the existing pion-induced $J/\psi$ production data, usually not included in the global fits, can impose useful additional constraints on the pion parton distribution functions (PDFs). In particular, these data can probe the pion’s gluon densities at large $x$. Existing pion-induced $J/\psi$ data covering a broad range of beam momenta are compared with next-to-leading-order QCD calculations using various sets of pion PDFs. It is found that $J/\psi$ data measured at forward rapidity and at sufficiently high beam momentum are sensitive to the large-$x$ gluon distribution of pions. The current $J/\psi$ data favor the Sutton-Martin-Roberts-Stirling and Gluck-Reya-Vogt pion PDFs, containing significant gluon content at large $x$.

The low-lying $S$-wave $QQ\overline{s}\overline{s}$ ($Q=c$, $b$) tetraquark states with $I(J^P)=0(0^{+})$, $0(1^{+})$ and $0(2^{+})$ are systematically investigated in the framework of complex scaling range of chiral quark model. Every structure including meson-meson, diquark-antidiquark and K-type configurations, and all possible color channels in four-body sector are considered by means of a commonly extended variational approach, Gaussian expansion method. Within the studied mass region, several narrow and wide resonance states are obtained for $cc\overline{s}\overline{s}$ and $bb\overline{s}\overline{s}$ tetraquarks with $I(J^P)=0(0^{+})$ and $0(2^{+})$. Meanwhile, narrow resonances for $cb\overline{s}\overline{s}$ tetraquarks are also found in $I(J^P)=0(0^{+})$, $0(1^{+})$ and $0(2^{+})$ states. The possibility of finding tetraquark structures with masses $\sim 0.6\mathrm{GeV}$ above the non-interacting hadron-hadron thresholds (and not close to them) is a feature related with the absence of the one-pion exchange interaction in the $QQ\overline{s}\overline{s}$ sector and thus it could deserve experimental confirmation.

With the KATRIN experiment, the determination of the absolute neutrino mass scale down to cosmologically favored values has come into reach. We show that this measurement provides the missing link between the Standard Model and the dark sector in scotogenic models, where the suppression of the neutrino masses is economically explained by their only indirect coupling to the Higgs field. We determine the linear relation between the electron neutrino mass and the scalar coupling ${\lambda }_5$ associated with the dark neutral scalar mass splitting to be ${\lambda }_5=3.1\times {10}^{-9}{m}_{{\nu }_e}/\mathrm{eV}$. This relation then induces correlations among the dark matter (DM) and new scalar masses and their Yukawa couplings. Together, KATRIN and future lepton flavor violation experiments can then probe the fermion DM parameter space, irrespective of the neutrino mass hierarchy and $CP$ phase.

In this work, we study the supersymmetric warped conformal field theory in two dimensions. We show that the Hofman-Strominger theorem on symmetry enhancement could be generalized to the supersymmetric case. More precisely, we find that within a chiral superspace $(x^{+},\theta )$, a two-dimensional field theory with two translational invariance and a chiral scaling symmetry can have enhanced local symmetry, under the assumption that the dilation spectrum is discrete and non-negative. Similar to the pure bosonic case, there are two kinds of minimal models, one being $N=(1,0)$ supersymmetric conformal field theories, while the other being $N=1$ supersymmetric warped conformal field theories (SWCFT). We study the properties of SWCFT, including the representations of the algebra, the space of states, and the correlation functions of the superprimaries.

The Rezzolla-Zhidenko (RZ) framework provides an efficient approach to characterize spherically symmetric black hole spacetimes in arbitrary metric theories of gravity using a small number of variables [Rezzolla and Zhidenko, Phys. Rev. D 90, 084009 (2014)]. These variables can be obtained in principle from near-horizon measurements of various astrophysical processes, thus potentially enabling efficient tests of both black hole properties and the theory of general relativity in the strong-field regime. Here, we extend this framework to allow for the parametrization of arbitrary asymptotically flat, spherically symmetric metrics and introduce the notion of an 11-dimensional (11D) parametrization space $\mathrm{\Pi }$, on which each solution can be visualized as a curve or surface. An ${\mathcal{L}}^2$ norm on this space is used to measure the deviation of a particular compact object solution from the Schwarzschild black hole solution. We calculate various observables, related to particle and photon orbits, within this framework and demonstrate that the relative errors we obtain are low (about ${10}^{-6}$). In particular, we obtain the innermost stable circular orbit (ISCO) frequency, the unstable photon-orbit impact parameter (shadow radius), the entire orbital angular speed profile for circular Kepler observers, and the entire lensing deflection angle curve for various types of compact objects, including nonsingular and singular black holes, boson stars, and naked singularities, from various theories of gravity. Finally, we provide in a tabular form the first 11 coefficients of the fourth-order RZ parametrization needed to describe a variety of commonly used black hole spacetimes. When comparing with the first-order RZ parametrization of astrophysical observables such as the ISCO frequency, the coefficients provided here increase the accuracy by 2 orders of magnitude or more.

An investigation is undertaken into the properties and effects of a preinflationary era during at least part of which semiclassical gravity was valid. It is argued that if the Universe (or our part of it) was approximately homogeneous and isotropic during that era, then the Universe was likely to have been radiation dominated. A simple model in which the Universe contains classical radiation and a cosmological constant is used to investigate potential effects of such a preinflationary era on the cosmic microwave background. The power spectrum is computed using the mode functions of a quantized massless minimally coupled scalar field. Various choices of state for this field are considered, including adiabatic vacuum states of various orders and the vacuum state that would naturally occur if the Universe made a sudden transition from being radiation dominated to de Sitter space. In all cases investigated, there is a suppression of the power spectrum at large angles, and, when plotted as a function of the momentum parameter, there are always oscillations with state-dependent amplitudes.

New early dark energy (NEDE) is a component of vacuum energy at the electron volt scale, which decays in a first-order phase transition shortly before recombination [F. Niedermann and M. S. Sloth, New early dark energy]. The NEDE component has the potential to resolve the tension between recent local measurements of the expansion rate of the Universe using supernovae (SN) data and the expansion rate inferred from the early Universe through measurements of the cosmic microwave background (CMB) when assuming $\mathrm{\Lambda }\mathrm{CDM}$. We discuss in depth the two-scalar field model of the NEDE phase transition including the process of bubble percolation, collision, and coalescence. We also estimate the gravitational wave signal produced during the collision phase and argue that it can be searched for using pulsar timing arrays. In a second step, we construct an effective cosmological model, which describes the phase transition as an instantaneous process, and derive the covariant equations that match perturbations across the transition surface. Fitting the cosmological model to CMB, baryonic acoustic oscillations, and SN data, we report $H_0={69.6}_{-1.3}^{+1.0}\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ (68% C.L.) without the local measurement of the Hubble parameter, bringing the tension down to $2.5\sigma$. Including the local input, we find $H_0=71.4\pm 1.0\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ (68% C.L.) and strong evidence for a nonvanishing NEDE component with a $\simeq 4\sigma$ significance.