In gauge theories on a spacetime equipped with a circle, the holonomy variables, living in the Cartan torus, play special roles. With their periodic nature properly taken into account, we find that a supersymmetric gauge theory in $d$ dimensions tends to reduce in the small radius limit to a disjoint sum of multiple ($d-1$) dimensional theories at distinct holonomies, called $H$-saddles. The phenomenon occurs regardless of the spacetime dimensions, and here we explore such $H$-saddles for $d=4$ $\mathcal{N}=1$ theories on $T^2$ fibered over ${\mathrm{\Sigma }}_g$, in the limits of elongated $T^2$. This naturally generates novel relationships between 4d and 3d partition functions, including ones between 4d and 3d Witten indices, and also leads us to reexamine recent studies of the Cardy exponents and the Casimir energies and of their purported connections to the 4d anomalies.

We investigate the Schwinger pair production phenomena in spatially homogeneous strong electric fields. We first consider scalar QED in four-dimensions and discuss the potential ambiguity in the adiabatic order assignment for the electromagnetic potential required to fix the renormalization subtractions. We argue that this ambiguity can be solved by invoking the conformal anomaly when both electric and gravitational backgrounds are present. We also extend the adiabatic regularization method for spinor QED in two-dimensions and find consistency with the chiral anomaly. We focus on the issue of the renormalization of the electric current $⟨j^{\mu }⟩$ generated by the created pairs. We illustrate how to implement the renormalization of the electric current for the Sauter pulse.

The recent interest in modified theories of gravity, involving some type of non-minimal coupling to the Ricci scalar and the calculation of cosmological observables in the Einstein or the Jordan frame, motivate the formulation of these theories in terms of quantities that are invariant under frame transformations. Furthermore, in view of the description of gravity and its geometry motivated by string theory, such a formulation could be extended to include theories of extra spatial dimensions. In the present article, we generalize the construction of frame-invariant quantities, concerning a general, $D$-dimensional scalar-tensor theory. Then, we limit our scope to the five-dimensional braneworld scenario, where we study thick brane solutions that are localized on the 3-brane and extend the invariant formulation to the case of multiple scalar fields nonminimally coupled to gravity.

It is well known that global topological defects induce a repulsive gravitational potential for test particles. “What is the gravitational potential induced by black holes with a cosmological constant (Schwarzschild-de Sitter (S-dS) metric) on finite thickness global topological defects?” This is the main question addressed in the present analysis. We also discuss the validity of Derrick’s theorem when scalar field configurations are embedded in nontrivial gravitational backgrounds. In the context of the above stated question, we consider three global defect configurations: a finite thickness spherical domain wall with a central S-dS black hole, a global string loop with a S-dS black hole in the center and a global monopole near a S-dS black hole. Using an analytical model, numerical simulations of the evolving spherical wall and energetic arguments we show that the spherical wall experiences a repelling gravitational potential due to the mass of the central black hole. This potential is further amplified by the presence of a cosmological constant. For initial domain wall radius larger than a critical value, the repulsive potential dominates over the wall tension and the wall expands towards the cosmological horizon of the S-dS metric where it develops ghost instabilities (the kinetic term changes sign). For smaller initial radius, tension dominates and the wall contracts towards the black hole horizon where it also develops ghost instabilities. We also show, using the same analytical model and energetic arguments that a global monopole is gravitationally attracted by a black hole while a cosmological constant induces a repulsive gravitational potential as in the case of test particles. Finally we show that a global string loop with finite thickness experiences gravitational repulsion due to the cosmological constant which dominates over its tension for a radius larger than a critical radius leading to an expanding rather than contracting loop.

We systematically examine the compactness of neutron stars as Tolman VII solutions in scalar-tensor theory of gravity. As a result, when the coupling constant is confined to values provided by astronomical observations we show that the maximum compactness of neutron stars in general relativity is higher than that in scalar-tensor gravity. In addition, we show that although ultracompact stars, with a radius smaller than the Regge-Wheeler potential peak, can exist in general relativity (e.g., Tolman VII solution), their scalarized counterparts cannot be constructed even in the limiting case of uniform density stars.

We study relations between hydrodynamical (H) and scalar field (SF) models of the dark energy in the homogeneous isotropic universe. The focus is on the SF described by the Lagrangian with the canonical kinetic term within spatially flat cosmology. We analyze requirements that guarantee the same cosmological history for the SF and H models at least for special solutions. The differential equation for the SF potential is obtained that ensures such equivalence of the SF and H models. However, if the “equivalent” SF potential is found for a given equation of state (EOS) of the H model, this does not mean that all solutions of this SF model have corresponding H-model analogs. In this view we derived a condition that guarantees an “approximate equivalence,” when there is a small difference between energy-momentum tensors of the models. The equivalent SF potentials and corresponding SF solutions for linear EOS are found in an explicit form; we also present examples with more complicated EOS.

We present novel analytic hairy black holes with a flat base manifold in the ($3+1$)-dimensional Einstein $SU(2)$-Skyrme system with negative cosmological constant. We also construct ($3+1$)-dimensional black strings in the Einstein $SU(2)$-nonlinear sigma model theory with negative cosmological constant. The geometry of these black strings is a three-dimensional charged Bañados-Teitelboim-Zanelli black hole times a line, without any warp factor. The thermodynamics of these configurations (and its dependence on the discrete hairy parameter) is analyzed in details. A very rich phase diagram emerges.

This paper is devoted to an investigation of Euclidean wormholes made by fuzzy instantons. We investigate the Euclidean path integral in anti–de Sitter space. In Einstein gravity, we introduce a scalar field with a potential. Because of the analyticity, there is a contribution of complex-valued instantons, so-called fuzzy instantons. If we have a massless scalar field, then we obtain Euclidean wormholes, where the probabilities become smaller and smaller as the size of the throat becomes larger and larger. If we introduce a nontrivial potential, then, in order to obtain a nonzero tunneling rate, we need to tune the shape of the potential. With the $O(4)$ symmetry, after the analytic continuation to the Lorentzian time, the wormhole throat should expand to infinity. However, by adding mass, one may obtain an instant wormhole that should eventually collapse to the event horizon. The existence of Euclidean wormholes is related to the stability or unitarity issues of anti–de Sitter space. We are not conclusive yet, but we carefully comment on these physical problems.

In this paper, we investigate a new phenomenological parametrization for unified dark matter and dark energy based on the polynomial expansion of the barotropic equation of state parameter $w$. Our parametrization provides a well-behaving evolution of $w$ for both small and big redshifts as well as in the far future. The dark fluid described by our parametrization behaves for big redshifts like dark matter (DM). Therefore, one can parametrize dark energy and dark matter using a single dark fluid, like in the case of the Chaplygin gas. Within this parametrization, we consider two models: one with a dark energy (DE) barotropic parameter fixed to be $-1$ and the second one, where $w\ne -1$ is chosen to match the best fit to the data. We study the main cosmological properties of these models at the expansion and perturbation levels. Based on the Markov chain Monte Carlo method with the currently available cosmic observational data sets, we constrain these models to determine the cosmological parameters at the level of the background and clustering of matter. We consider the interaction between dark matter and dark energy which directly affects the evolution of matter and its clustering. Our model appears to be perfectly consistent with the $\mathrm{\Lambda }\mathrm{CDM}$ model, while providing unification of DE and DM.

Starting from the Gleyzes-Langlois-Piazza-Vernizzi action, we derive the most general effective theory that is invariant under internal shifts and a ${\mathbb{Z}}_2$ mirror symmetry in the scalar sector. Contrary to what one may think, this model presents a dark matter tracker previous to the dark energy domination. We show that, in an empty universe and to linear order in perturbations, the scalar mode clusters in exactly the same way as standard nonrelativistic cold dark matter. This also holds for the subsector of the theory where the speed of propagation of gravitational waves equals that of light, in agreement with the recent multimessenger observation. However, the inclusion of standard model particles introduces nontrivial couplings of the gravitational scalar mode to baryons, modifying their clustering properties. We argue that no arrangement of the parameters of the model can reduce the extra scalar to precisely behave as cold dark matter.

Recent progress in high sensitivity cosmic microwave background (CMB) polarization experiments opens up a window on large scale structure (LSS), as CMB polarization fluctuations on small angular scales can arise from a combination of LSS and ionization fluctuations in the late Universe. Gravitational lensing effects can be extracted from CMB data sets with quadratic estimators but reconstructions of electron density fluctuations (EDFs) with quadratic estimators are found to be significantly biased by the much larger lensing effects in the secondary CMB fluctuations. In this paper we establish a bispectrum formalism using tracers of LSS to extract the subdominant EDFs from CMB polarization data. We find that this bispectrum can effectively reconstruct angular band powers of cross-correlation between EDFs and LSS tracers. Next generation CMB polarization experiments in conjunction with galaxy surveys and cosmic infrared background experiments can detect signatures of EDFs with high significance.

We revisit supersymmetric hybrid inflation in the context of the flipped $SU(5)$ model. With minimal superpotential and minimal Kähler potential, and soft supersymmetry (SUSY) masses of order (1–100) TeV, compatibility with the Planck data yields a symmetry breaking scale $M$ of flipped $SU(5)$ close to $(2–4)\times {10}^{15}\mathrm{GeV}$. This disagrees with the lower limit $M\gtrsim 7\times {10}^{15}\mathrm{GeV}$ set from proton decay searches by the Super-Kamiokande collaboration. We show how $M$ close to the unification scale $2\times {10}^{16}\mathrm{GeV}$ can be reconciled with SUSY hybrid inflation by employing a nonminimal Kähler potential. Proton decays into $e^{+}{\pi }^0$ with an estimated lifetime of order $10^{36}\mathrm{years}$. The tensor to scalar ratio $r$ in this case can approach observable values $\sim {10}^{-4}–{10}^{-3}$.

If the dark-energy density asymptotically approaches a nonzero constant, ${\rho }_{\mathrm{DE}}\to {\rho }_0$, then its equation of state parameter $w$ necessarily approaches $-1$. The converse is not true; dark energy with $w\to -1$ can correspond to either ${\rho }_{\mathrm{DE}}\to {\rho }_0$ or ${\rho }_{\mathrm{DE}}\to 0$. This provides a natural division of models with $w\to -1$ into two distinct classes: asymptotic $\mathrm{\Lambda }$ (${\rho }_{\mathrm{DE}}\to {\rho }_0$) and pseudo-$\mathrm{\Lambda }$ (${\rho }_{\mathrm{DE}}\to 0$). We delineate the boundary between these two classes of models in terms of the behavior of $w(a)$, ${\rho }_{\mathrm{DE}}(a)$, and $a(t)$. We examine barotropic and quintessence realizations of both types of models. Barotropic models with positive squared sound speed and $w\to -1$ are always asymptotically $\mathrm{\Lambda }$; they can never produce pseudo-$\mathrm{\Lambda }$ behavior. Quintessence models can correspond to either asymptotic $\mathrm{\Lambda }$ or pseudo-$\mathrm{\Lambda }$ evolution, but the latter is impossible when the expansion is dominated by a background barotropic fluid. We show that the distinction between asymptotic $\mathrm{\Lambda }$ and pseudo-$\mathrm{\Lambda }$ models for $w>-1$ is mathematically dual to the distinction between pseudorip and big/little rip models when $w<-1$.

We study possible effects of a dark matter (DM) core on the maximum mass of a neutron star (NS), on the mass-radius relation and on the NS tidal deformability parameter $\mathrm{\Lambda }$. We show that all these quantities would in general be reduced in the presence of a DM core. In particular, our calculations indicate that the presence of a DM core with a mass fraction $\sim 5\%$ could affect significantly the interpretation of these NS data as constraints on the nuclear equation of state (EOS), potentially excluding some EOS models on the basis of the measured mass of PSR $\mathrm{J}0348+0432$, while allowing other EOS models to become consistent with the LIGO/Virgo upper limit on $\mathrm{\Lambda }$. Specific scenarios for generating such DM cores are explored in an Appendix.

The next generation of axion direct-detection experiments may rule out or confirm axions as the dominant source of dark matter. We develop a general likelihood-based framework for studying the time-series data at such experiments, with a focus on the role of dark matter astrophysics, to search for signatures of the QCD axion or axionlike particles. We illustrate how in the event of a detection the likelihood framework may be used to extract measures of the local dark matter phase-space distribution, accounting for effects such as annual modulation and gravitational focusing, which is the perturbation to the dark matter phase-space distribution by the gravitational field of the Sun. Moreover, we show how potential dark matter substructure, such as cold dark matter streams or a thick dark disk, could impact the signal. For example, we find that when the bulk dark matter halo is detected at $5\sigma$ global significance, the unique time-dependent features imprinted by the dark matter component of the Sagittarius stream, even if only a few percent of the local dark matter density, may be detectable at $\sim 2\sigma$ significance. A corotating dark disk, with lag speed $\sim 50\mathrm{km}/\mathrm{s}$, that is $\sim 20\%$ of the local dark matter density could dominate the signal, while colder but as-of-yet unknown substructure may be even more important. Our likelihood formalism, and the results derived with it, are generally applicable to any time-series-based approach to axion direct detection.

We perform a precise calculation of the decay rate of the electroweak vacuum in the standard model as well as in models beyond the standard model. We use a recently developed technique to calculate the decay rate of a false vacuum, which provides a gauge invariant calculation of the decay rate at the one-loop level. We give a prescription to take into account the zero modes in association with translational, dilatational, and gauge symmetries. We calculate the decay rate per unit volume, $\gamma$, by using an analytic formula. The decay rate of the electroweak vacuum in the standard model is estimated to be ${\log }_{10}\gamma \times \mathrm{Gyr}{\mathrm{Gpc}}^3=-{582}_{-45-329-218-1}^{+40+184+144+2}$, where the first, second, third, and fourth errors are due to the uncertainties of the Higgs mass, the top quark mass, the strong coupling constant and the choice of the renormalization scale, respectively. The analytic formula of the decay rate, as well as its fitting formula given in this paper, is also applicable to models that exhibit a classical scale invariance at a high energy scale. As an example, we consider extra fermions that couple to the standard model Higgs boson, and discuss their effects on the decay rate of the electroweak vacuum.

Supersymmetry breaking close to the scale of grand unification can explain cosmic inflation. As we demonstrate in this paper, this can be achieved in strongly coupled supersymmetric gauge theories, such that the energy scales of inflation and supersymmetry breaking are generated dynamically. As a consequence, both scales are related to each other and exponentially suppressed compared to the Planck scale. As an example, we consider a dynamical model in which gauging a global flavor symmetry in the supersymmetry-breaking sector gives rise to a Fayet-Iliopoulos $D$ term. This results in successful $D$-term hybrid inflation in agreement with all theoretical and phenomenological constraints. The gauged flavor symmetry can be identified with $U(1{)}_{B-L}$, where $B$ and $L$ denote baryon and lepton number, respectively. In the end, we arrive at a consistent cosmological scenario that provides a unified picture of high-scale supersymmetry breaking, viable $D$-term hybrid inflation, spontaneous $B-L$ breaking at the scale of grand unification, baryogenesis via leptogenesis, and standard model neutrino masses due to the type-I seesaw mechanism.

Towards experimental confirmations of the type-I seesaw mechanism, we explore a prospect of discovering the heavy Majorana right-handed neutrinos (RHNs) from a resonant production of a new massive gauge boson ($Z^{\prime }$) and its subsequent decay into a pair of RHNs ($Z^{\prime }\to NN$) at the future high luminosity runs at the Large Hadron Collider (LHC). Recent simulation studies have shown that the discovery of the RHNs through this process is promising in the future. However, the current LHC data very severely constrains the production cross section of the $Z^{\prime }$ boson into a dilepton final states, $pp\to Z^{\prime }\to {\ell }^{+}{\ell }^{-}$ ($\ell =e$ or $\mu$). Extrapolating the current bound to the future, we find that a significant enhancement of the branching ratio $\mathrm{BR}(Z^{\prime }\to NN)$ over $\mathrm{BR}(Z^{\prime }\to {\ell }^{+}{\ell }^{-})$ is necessary for the future discovery of RHNs. As a well-motivated simple extension of the standard model (SM) to incorporate the $Z^{\prime }$ boson and the type-I seesaw mechanism, we consider the minimal ${\mathrm{U}(1)}_X$ model, which is a generalization of the well-known minimal $B-L$ model without extending the particle content. We point out that this model can yield a significant enhancement up to $\mathrm{BR}(Z^{\prime }\to NN)/\mathrm{BR}(Z^{\prime }\to {\ell }^{+}{\ell }^{-})\simeq 5$ (per generation). This is in sharp contrast with the minimal $B-L$ model, a benchmark scenario commonly used in simulation studies, which predicts $\mathrm{BR}(Z^{\prime }\to NN)/\mathrm{BR}(Z^{\prime }\to {\ell }^{+}{\ell }^{-})\simeq 0.5$ (per generation). With such an enhancement and a realistic model-parameter choice to reproduce the neutrino oscillation data, we conclude that the possibility of discovering RHNs with, for example, a $300{\mathrm{fb}}^{-1}$ luminosity implies that the $Z^{\prime }$ boson will be discovered with a luminosity of $170.5{\mathrm{fb}}^{-1}$ ($125{\mathrm{fb}}^{-1}$) for the normal (inverted) hierarchy of the light neutrino mass pattern.

The type II seesaw model is a well-motivated new physics scenario to address the origin of the neutrino mass issue. We show that this model can easily accommodate an absolutely stable vacuum until the Planck scale, however with strong limit on the exotic scalar masses and the corresponding mixing angle. We examine the model prediction at the current and future high luminosity run of the Large Hadron Collider (LHC) for the scalar masses and mixing angles fixed at such high-scale valid region. Specifically, we device the associated and pair production of the charged scalars as a new probe of the model at the LHC. We show that for a particular signal process the model can be tested with $5\sigma$ signal significance even at the present run of the LHC.