Thermodynamics and its quantum counterpart are traditionally described with statistical ensembles. Canonical typicality has related statistical mechanics for a system to ensembles of global energy eigenstates of a system and its environment, analyzing their cardinality. We show that the canonical density for a system emerges from a maximally entangled global state of system and environment through relational complex time evolution between system and environment without the need to maximize the entropy or to count states.

Renormalization is a well-known technique to get rid of ultraviolet (UV) singularities. When relying on dimensional regularization, these become manifest as $\epsilon$ poles, allowing one to define counterterms with useful recursive properties. However, this procedure requires one to work at “integral level” and poses difficulties to achieve a smooth combination with seminumerical approaches. This article is devoted to the development of an integrand-level renormalization formalism, better suited for semi- or fully numerical calculations. Starting from the loop-tree duality, we keep the causal representations of the integrands of multiloop Feynman diagrams and explore their UV behavior. Then, we propose a strategy that allows one to build local counterterms, capable of rendering the expressions integrable in the high-energy limit and in four space-time dimensions. Our procedure was tested on diagrams up to three loops, and we found a remarkably smooth cancellation of divergences. The results of this work constitute a powerful step toward a fully local renormalization framework in quantum field theory.

The spinor-helicity representations of massive and (partially) massless particles in four-dimensional (anti–)de Sitter (A)dS spacetime are studied within the framework of the dual pair correspondence. We show that the dual groups (also known as “little groups”) of the anti–de Sitter and de Sitter groups are, respectively, $O(2N)$ and $O^{*}(2N)$. For $N=1$, the generator of the dual algebra $\mathfrak{so}(2)\cong {\mathfrak{so}}^{*}(2)\cong \mathfrak{u}(1)$ corresponds to the helicity operator, and the spinor-helicity representation describes massless particles in (A)${\text{dS}}_4$. For $N=2$, the dual algebra is composed of two ideals, $\mathfrak{s}$ and ${\mathfrak{m}}_{\mathrm{\Lambda }}$. The former ideal $\mathfrak{s}\cong \mathfrak{so}(3)$ fixes the spin of the particle, while the mass is determined by the latter ideal ${\mathfrak{m}}_{\mathrm{\Lambda }}$, which is isomorphic to $\mathfrak{so}(2,1)$, $\mathfrak{iso}(2)$, or $\mathfrak{so}(3)$ depending on the cosmological constant being positive, zero, or negative. In the case of a positive cosmological constant, namely ${\mathrm{dS}}_4$, the spinor-helicity representation contains all massive particles corresponding to the principal series representations and the partially massless particles corresponding to the discrete series representations leaving out only the light massive particles corresponding to the complementary series representations. The zero and negative cosmological constant cases, which had been addressed in earlier references, are also discussed briefly. Finally, we consider the multilinear form of helicity spinors invariant under (A)dS group, which can serve as the (A)dS counterpart of the scattering amplitude, and discuss technical differences and difficulties of the (A)dS cases compared to the flat spacetime case.

We construct, for the first time, a Bemfica-Disconzi-Noronha-Kovtun (BDNK) theory for linear stochastic fluctuations, which is proved to be mathematically consistent, causal, and covariantly stable. The Martin-Siggia-Rose action is shown to be bilocal in most cases, and the noise is not white. The presence of nonhydrodynamic modes induces long-range correlations in the primary fluid variables (temperature, chemical potential, and flow velocity). However, correlators of conserved densities remain localized in space, and coincide with those calculated within fluctuating Isreal-Stewart theory. We show that, in some cases, there is a nonlocal change of variables that maps the Israel-Stewart action into the BDNK action.

We consider rigid-body quantization of the Skyrmion in the most general four-derivative generalization of the Skyrme model with a potential giving pions a mass, as well as in a class of higher-order Skyrme models. We quantize the spin and isospin zero modes following the results of Pottinger and Rathske. Although one could hope that a one-parameter family of theories could provide a smaller spin contribution to the energy at some point in theory space—which would be welcome for Bogomol’nyi-Prasad-Sommerfield-type models, we find that the standard Skyrme model limit, with two time derivatives, gives rise to the smallest spin contribution to the energy. We speculate whether this tuning of the spin energy could be useful in the larger picture of quantizing vibrational and light massive modes of the Skyrmions. Finally, we establish a topological energy bound for the Pottinger-Rathske model with potential terms as well as new bounds for higher-order Skyrme models, with and without a potential.

We investigate the differences between a test timelike particle’s motions around scale-dependent Planck stars and its motions around renormalization group improved Schwarzschild black holes in detail. By introducing the positive or negative sign of the parameter $s$ (with $s=-1$ and $s=+1$ denoting scale-dependent Planck stars and renormalization group improved Schwarzschild black holes, respectively), we present the circular orbital characteristics of both scale-dependent Planck stars and renormalization group improved Schwarzschild black holes. This shows the existence of stable and unstable circular orbits and the dependence of the innermost stable circular orbit on a dimensionless parameter $|\tilde{\omega }|(\gamma ,{\lambda }_{\mp })$, where $|\tilde{\omega }|$ comes from the theory of nonperturbative renormalization groups, $\gamma$ is the identification of the cutoff for the distance scale, and ${\lambda }_{\mp }$ are two new dimensionless normalized parameters. In comparison to the black holes, the parameter $\gamma$ has more influence on stable and unstable circular orbits for the scale-dependent Planck stars. Specifically, we calculate the particle’s relativistic periastron advance for the two models and give a preliminary bound on scale-dependent Planck stars and the renormalization group improved Schwarzschild black holes by using the result of the S2 star’s precession with observations from GRAVITY. The bound we obtain in the present work is $s|\tilde{\omega }|=(-0.80\pm 1.53)\times {10}^{92}$. By using the shadow result from EHT, the bound on $s|\tilde{\omega }|$ is improved by up to 3 or 4 orders of magnitude, which is $-1.36\times {10}^{88}\lesssim s|\tilde{\omega }|\lesssim 2.32\times {10}^{89}$. It suggests that a primordial black hole or even a mini–black hole can give a tighter bound on two spacetimes in the future. While we need to break the parameters’ degeneracy for the two models with future observations, the negative value in our bound suggests that the existence of Planck stars may be possible. We also intensively compare the particle’s periodic orbits around Planck stars with those around the black holes. It is found that small variations in ${\lambda }_{\mp }$ make the particle’s orbits alternate back and forth from periodic to quasiperiodic orbits, or even jump to nonbound orbits in two spacetimes. We discuss briefly the gravitational waveforms generated from the periodic motions for a small body which orbits a supermassive Planck star or a supermassive black hole, which exhibit some distinct phases and amplitudes for the two models. Our results show that it might be possible to aid in the identification between two spacetimes by using the particle’s motion.

We recently hypothesized that a distortion parameter exists such that its signed sum for all images of singular gravitational lensing of a source vanishes identically [K. S. Virbhadra, Phys. Rev. D 106, 064038 (2022)]. We found a distortion parameter (the ratio of the tangential to radial magnifications) that satisfied the hypothesis for the images of Schwarzschild lensing with flying colors. We now show that another distortion parameter (the difference of tangential and radial magnifications) also magnificently supports our hypothesis when we perform computations with the primary-secondary and relativistic images. The distortion parameters, which satisfy the aesthetically appealing hypothesis, will likely aid in developing gravitational lensing theory. Finally, we discuss the conservation of distortions of images in gravitational lensing.

Extensions to general relativity allow the polarization of gravitational waves (GW) from astrophysical sources to suffer from amplitude and velocity birefringence, which respectively induce changes in the ellipticity and orientation of the polarization tensor. We introduce a multimessenger approach to test this polarization behavior of GWs during their cosmological propagation using binary sources, for which the initial polarization is determined by the inclination and orientation angles of the orbital angular momentum vector with respect to the line of sight. In particular, we use spatially resolved radio imaging of the jet from a binary neutron star (BNS) merger to constrain the orientation angle and hence the emitted polarization orientation of the GW signal at the site of the merger, and compare to that observed on Earth by GW detectors. For GW170817, using past measurements of the inclination angle, we constrain the deviation from general relativity due to amplitude birefringence to ${\kappa }_A=-0.12_{-0.61}^{+0.60}$, while the velocity birefringence parameter ${\kappa }_V$ remains unconstrained. The inability to constrain ${\kappa }_V$ is due to the low amplitude of GW170817 in the Virgo detector, and measurements of the polarization orientation require information from a combination of multiple detectors with different alignments. For this reason, we also mock future BNS mergers with resolved afterglow proper motion and project that ${\kappa }_V$ could be constrained to a precision of 5 rad (corresponding to an angular shift of the GW polarization of $\delta {\varphi }_V\approx 0.2\mathrm{rad}$ for a BNS at 100 Mpc) by a future network of third-generation ground-based GW detectors such as Cosmic Explorer and the radio High Sensitivity Array. Crucially, this velocity birefringence effect cannot be constrained with dark binary mergers as it requires polarization information at the emission time, which can be provided only by electromagnetic emission.

Disformal transformations of Friedmann-Lemaître-Robertson-Walker and Bianchi geometries are analyzed in the context of scalar-tensor gravity. Novel aspects discussed explicitly are the $3+1$ splitting, the effective fluid equivalent of the gravitational scalar, Bianchi models, stealth solutions, and de Sitter solutions with nonconstant scalar field (which are signatures of scalar-tensor gravity). Both pure disformal transformations and more general ones are discussed, including those containing higher derivatives of the scalar field recently introduced in the literature.

Scalar-tensor theories have a long history as possible phenomenological alternatives to general relativity but are known to potentially produce deviations from the (strong) equivalence principle in systems involving self-gravitating objects, as a result of the presence of an additional gravitational scalar field besides the tensor modes of general relativity. We describe here a novel mechanism whereby the equivalence principle is violated for an isolated rotating neutron star, if the gravitational scalar field is changing in time far from the system. We show that the neutron star rotational period changes due to an effective coupling (“angular momentum sensitivity”) to the gravitational scalar and compute that coupling for viable equations of state for nuclear matter. We comment on the relevance of our findings for testing scalar-tensor theories and models of ultralight dark matter with pulsar timing observations, a topic that we tackle in a companion paper.

We consider a cosmic string moving through a gas of superfluid dark matter (SFDM) particles and analyze how it affects the dark matter distribution. We look at two different cases; first, a cosmic string passing through an already condensed region, and second, through a region that is not yet condensed. In the former, the string induces a weak shock in the superfluid, and the Bose-Einstein condensate (BEC) survives. In the latter, a wake of larger density is formed behind the string, and we study under which conditions a BEC can be formed in the virialized region of the wake. By requiring the thermalization of the DM particles and the overlap of their de Broglie wavelengths inside the wake, we obtain an upper bound on the mass of the dark matter particles on the order of 10 eV, which is compatible with typical SFDM models.

We study the properties of the stochastic gravitational-wave background (SGWB) produced by domain walls (DWs) during inflation without forming a network. We numerically simulate the DW production caused by a second-order phase transition and calculate the SGWB spectrum using a $1000\times 1000\times 1000$ lattice. We show that the SGWB can be observed directly by future terrestrial and space gravitational-wave detectors and through the $B$-mode spectrum in the cosmic microwave background. With numerical simulations, we derive an empirical formula for the strength and qualitative features of the SGWB spectrum. The details of the SGWB spectrum also contain information about the later evolution of the Universe.

Recently, the EMPRESS Collaboration has included new data in the extraction of the primordial ${}^4\mathrm{He}$ abundance from big bang nucleosynthesis (BBN), resulting in a determination that differs from the previous value and from theoretical expectations. There have been several studies attempting to explain this anomaly which involve variation of fundamental constants between the time of BBN and the present. Since the Higgs vacuum expectation value (vev) is the only dimensionful parameter in the Standard Model and it is already known to vary during the electroweak phase transition, we consider the possibility that the vev is slightly different during BBN compared to its present value. A modification of the vev changes not only particle masses but also affects, through mass thresholds, the QCD confinement scale. We use the recently developed prymordial program to study this variation and its impact on the ${}^4\mathrm{He}$ and deuterium abundances. We find that bounds on $|\delta v/v|$ are approximately 0.01, and that the EMPRESS result can be explained within $2\sigma$ if $0.008<\delta v/v<0.02$, but at the cost of worsening the current $2\sigma$ discrepancy in the deuterium abundance to over $3\sigma$.

Scaling arguments are used to constrain the angular spectrum of distortions on boundaries of macroscopic causal diamonds, produced by Planck scale vacuum fluctuations of causally coherent quantum gravity. The small-angle spectrum of displacement is derived from a form of scale invariance: The variance and fluctuation rate of distortions normal to the surface of a causal diamond of radius $R$ at transverse physical separation $c\tau \ll R$ should depend only on $\tau$, with a normalization set by the Planck time $t_P$, and should not depend on $R$. For measurements on scale $R$, the principle leads to universal scaling for variance on angular scale $\mathrm{\Theta }$, $⟨\delta {\tau }^2{⟩}_{\mathrm{\Theta }}\simeq \tau t_p\sim \mathrm{\Theta }R{t}_P/c$ and angular power spectrum $C_{\ell }\sim (R{l}_P)/{\ell }^3$ at $\ell \gg 1$. This spectrum is consistent with a relational model of holographic noise based on causally coherent virtual null gravitational shocks, a general picture conjectured for all $\ell$. The high $\ell$ scaling is contrasted with that predicted in some other quantum models, which differ by one power of angular wave number $\ell$ and are shown to predict excessive blurring of images from distant sources.

Chromonatural inflation is a model where non-Abelian gauge fields are sustained by the coupling of the axion with the gauge field through the Chern-Simons term, while minimal warm inflation is a model where the axion produces a thermal bath of non-Abelian gauge particles through the Chern-Simons term. Since both axion inflation models are based on the same action, a natural question is if they are compatible or not. We study axion inflation with the Chern-Simons term and find that chromonatural inflation can accommodate radiation with a temperature much larger than the Hubble parameter during inflation, which is a characteristic feature of warm inflation. Thus, we conclude that chromonatural warm inflation exists, which must have phenomenologically interesting consequences.

We present forecasts for constraints on the Hu and Sawicki $f(R)$ modified gravity model using realistic mock data representative of future cluster and weak lensing surveys. We create mock thermal Sunyaev-Zel’dovich effect selected cluster samples for SPT-3G and CMB-S4 and the corresponding weak gravitational lensing data from next-generation weak-lensing (ngWL) surveys like Euclid and Rubin. We employ a state-of-the-art Bayesian likelihood approach that includes all observational effects and systematic uncertainties to obtain constraints on the $f(R)$ gravity parameter ${\log }_{10}|f_{R0}|$. In this analysis we vary the cosmological parameters $[{\mathrm{\Omega }}_{\mathrm{m}},{\mathrm{\Omega }}_{\nu }{h}^2,h,A_s,n_s,{\log }_{10}|f_{R0}|]$, which allows us to account for possible degeneracies between cosmological parameters and $f(R)$ modified gravity. The analysis accounts for $f(R)$ gravity via its effect on the halo mass function which is enhanced on cluster mass scales compared to the expectations within general relativity (GR). Assuming a fiducial GR model, the upcoming cluster dataset $\mathrm{SPT}\text{−}3\mathrm{G}\times \mathrm{ngWL}$ is expected to obtain an upper limit of ${\log }_{10}|f_{R0}|<-5.95$ at 95% credibility, which significantly improves upon the current best bounds. The $\mathrm{CMB}\text{−}\mathrm{S}4\times \mathrm{ngWL}$ dataset is expected to improve this even further to ${\log }_{10}|f_{R0}|<-6.23$. Furthermore, $f(R)$ gravity models with ${\log }_{10}|f_{R0}|\ge -6$, which have larger numbers of clusters, would be distinguishable from GR with both datasets. We also report degeneracies between ${\log }_{10}|f_{R0}|$ and ${\mathrm{\Omega }}_{\mathrm{m}}$ as well as ${\sigma }_8$ for ${\log }_{10}|f_{R0}|>-6$ and ${\log }_{10}|f_{R0}|>-5$ respectively. Our forecasts indicate that future cluster abundance studies of $f(R)$ gravity will enable substantially improved constraints that are competitive with other cosmological probes.

We discuss the challenges of motivating, constructing, and quantizing a canonically normalized inflationary perturbation in spatially curved universes. We show that this has historically proved challenging due to the interaction of nonadiabaticity with spatial curvature. We construct a novel curvature perturbation that is canonically normalized in the sense of its equation of motion and is unique up to a single scalar parameter. With this construction it becomes possible to set initial conditions invariant under canonical transformations, overcoming known ambiguities in the literature. This corrected quantization has potentially observational consequences via modifications to the primordial power spectrum at large angular scales, as well as theoretical implications for quantization procedures in curved cosmologies filled with a scalar field.

We investigate the viability of primordial black hole (PBH) formation in the standard model (SM) in a scenario that does not rely on specific inflationary features or any exotic physics such as phase transitions or nonminimal coupling to gravity. If the Brout-Englert-Higgs (BEH) field lies exactly at the transition between metastability and stability, its potential exhibits an inflexion point due to radiative corrections. The BEH can act like a stochastic curvaton field, leading to a non-Gaussian tail of large curvature fluctuations that later collapse into PBHs when they reenter inside the horizon. This scenario would require a precise value of the top-quark mass to ensure the Higgs stability, which is disfavored but still consistent with the most recent measurements. However, we also find that large curvature fluctuations are also generated on cosmological scales that are inconsistent with cosmic microwave background observations. We therefore conclude that the SM cannot have led to the formation of PBHs based on this mechanism. Nevertheless, a variation of the scenario based on the Palatini formulation of gravity may have provided the conditions to produce stellar-mass PBHs with an abundance comparable to dark matter, without producing too large curvature fluctuations on cosmological scales.

Fast flavor conversions (FFCs) of neutrinos, which can occur in core-collapse supernovae (CCSNe), are multiangle effects. They depend on the angular distribution of the neutrino’s electron lepton number (ELN). In this work, we present a comprehensive study of the FFCs by solving the multienergy and multiangle quantum kinetic equations with an extended set of collisional weak processes based on a static and spherically symmetric CCSN matter background profile. We investigate the emergence and evolution of FFCs in models featuring different ELN angular distributions, considering scenarios with two and three neutrino flavors. The spectrogram method is utilized to illustrate the small-scale spatial structure, and we show that this structure of neutrino flavor coherence and number densities in the nonlinear regime is qualitatively consistent with the dispersion relation analysis. On the coarse-grained level, we find that different asymptotic states can be achieved following the FFCs depending on the locations and shapes of the ELN distributions, despite sharing a common feature of the elimination of the ELN angular crossing. While equilibration among different neutrino flavors may be achieved immediately after the prompt FFCs, it is not a general outcome of the asymptotic state, as subsequent feedback effects from collisional neutrino-matter interactions come into play, particularly for cases where FFCs occur inside the neutrinosphere. The impacts of FFCs and the feedback effect on the net neutrino heating rates, the equilibrium electron fraction of CCSN matter, and the free-streaming neutrino energy spectra are quantitatively assessed. Other aspects including the impact of the vacuum term and the coexistence with other type of flavor instabilities are also discussed.

Asteroseismology has been shown to be, together with stellar modeling, an invaluable tool in constraining properties of novel physics. In this work, we study for the first time the influence of axionic production in the evolution of a late main-sequence star, comparing computational models with observational data in order to constrain the axion-photon $g_{a\gamma }$ coupling parameter. We first perform a high-precision calibration of a stellar model to our target star, in order to obtain a benchmark for our other diagnostics. We then apply a two-stage test, first using global quantities and then resorting to precision seismic ratios. We find that seismology allows us to place an independent upper bound of $g_{a\gamma }\le 0.98\times {10}^{-10}{\mathrm{GeV}}^{-1}$ at a 68% confidence level (CL), in the same order of magnitude as both the most recent constraints from the observation of globular clusters and previous bounds obtained through stellar modeling, but more stringent than most current direct axion detections. We also suggest a more conservative limit of $g_{a\gamma }\le 1.38\times {10}^{-10}{\mathrm{GeV}}^{-1}$ at a 95% CL. Moreover, this new diagnostic method can be applied to stellar data that will be obtained in future asteroseismic projects.