We study the non-modal stability of black hole spacetimes under linear perturbations. We show that large-amplitude growth can occur at finite time, despite asymptotic decay of linear perturbations. In the example presented, the physical mechanism is a transient form of superradiance, and is qualitatively similar to the transition to turbulence in Navier-Stokes shear flows. As part of the construction we provide a theorem for the positivity of QNM energies, and introduce a truncated-Hamiltonian approach to black hole pseudospectra which does not suffer from convergence issues.

Recently, two new quantum-corrected static spherically symmetric black hole models satisfying covariance have been proposed within the framework of effective quantum gravity. In this paper, we study how the quantum parameter $\zeta$ affects the optical properties of two quantum black hole models. We first analyze the photon sphere, critical impact parameter, and innermost stable circular orbit as $\zeta$ varies, and constrain $\zeta$ using Event Horizon Telescope data. Additionally, by employing the ray-tracing method to study photon trajectories near the two quantum black holes, we find that $\zeta$ can reduce the range of impact parameters corresponding to the photon ring and lensed ring. We then examine the optical appearance of these black holes with thin accretion disks, showing $\zeta$ significantly brightens the first model's image but has little effect on the second. Meanwhile, we demonstrate the contributions of the transfer functions to the observed intensity of direct and lensed ring in the observer's field of view, which has rarely been separately illustrated in previous studies. Finally, we study the optical appearance of both quantum black holes under a static spherical accretion model, with results consistent with the above. Therefore, we conclude that the second quantum black hole is almost indistinguishable from the Schwarzschild black hole, while the first quantum black hole can be distinguished from the Schwarzschild black hole through its optical appearance.

We investigate the divergence-free parametric form of the deceleration parameter within the simplest non-minimal matter-geometry coupling in $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor. Specifically, we consider the linear model $f(R,T) = R + 2\lambda T$, where $\lambda$ governs the interaction between matter and geometry. Using this parametric form, we derive the Hubble parameter as a function of redshift $z$ and incorporate it into the modified Friedmann equations. Constraining the model with OHD and Pantheon data, we obtain precise estimates for $H_0$, the present deceleration parameter $q_0$, and its evolutionary component $q_1$, confirming a smooth transition between cosmic deceleration and acceleration. Further, we analyze the evolution of the energy density $\rho$ and total EoS parameter $\omega$ for different $\lambda$ values, highlighting deviations from $\Lambda$CDM and the role of $\lambda$ in shaping cosmic dynamics. In addition, we examine energy conditions, finding that the NEC and DEC are satisfied throughout evolution, while the SEC is violated at late times, supporting the observed acceleration. Our findings demonstrate that this divergence-free parameterization within $f(R,T)$ gravity offers a viable framework for explaining late-time cosmic acceleration while maintaining key observational and theoretical constraints.

In this study, we explore the impact of the interacting parameter on dark matter in a model resulting from a parametrization of dark energy density. To ensure a model-independent approach, we treat \( r_d \) as a free parameter, avoiding assumptions about the physics of the early Universe or specific recombination models. This approach allows late-time cosmological observations to directly constrain \( r_d \) along with other parameters. Using recent measurements from the Dark Energy Spectroscopic Instrument (DESI) Year 1, cosmic chronometers (CC) and Pantheon\(^{+}\) supernova (SNe Ia) data, we uncover a significant effect of the interacting parameter on dark matter. Our analysis reveals that while non-interacting models attribute 68.2\% of the cosmic energy density to dark energy, interacting models increase this share to 73.4\%. To further probe these differences, we evaluate the evolution of the deceleration parameter for each model, contrasting them against the \(\Lambda\)CDM paradigm and observational data from CC and SNe Ia measurements. Finally, we apply various statistical metrics to rigorously assess the performance of these models.

We derive analytically some general features of the power-law sensitivity curve. They include an exact parametric equation, a formula for the peak sensitivity and a proof of convexity in log-log plot. A few conceptual points are also clarified.

In the present work, we theoretically investigate light deflection in the weak and strong field regimes for two regular spacetimes with corrections from loop quantum gravity. We treat analytically the expansions for both limits and use them as a basis for investigating gravitational lensing observables. We analyze and provide reasonable values for observables related to the second model that observational tools may be able to detect.

In this paper, we investigate the effects of Lorentz violation on correlations harvesting, specifically focusing on the harvested entanglement and harvested mutual information between two Unruh-DeWitt detectors interacting with a quantum field in the Lorentz-violating BTZ black hole spacetime. Our findings reveal that Lorentz symmetry breaking has contrasting impacts on entanglement harvesting and mutual information harvesting in BTZ backgrounds: it enhances mutual information harvesting while suppressing entanglement harvesting. This phenomenon suggests that the increase in total correlations in Lorentz-violating vector field backgrounds with gravitational coupling is predominantly driven by classical components, with quantum correlations contributing less to the overall mutual information. These results indicate that Lorentz violation, as a quantum property of spacetime, may impose intrinsic constraints on the quantum information capacity encoded in spacetime due to competition among quantum degrees of freedom for resources. Furthermore, Lorentz symmetry breaking expands the \textit{entanglement shadow} region, further demonstrating its disruptive effect on quantum correlations.

This paper evaluates the potential for constraining the quantum scale parameter $\xi$ of regular black hole within the asymptotically safe gravity framework using gravitational waves from extreme mass ratio inspirals (EMRI). Since $\xi$ cannot be precisely determined from first principles, observational constraints become crucial. We employ the Augmented Analytical Kludge (AAK) method to calculate gravitational waveforms in the equatorial plane and systematically analyze the influence of different $\xi$ values on phase evolution. Comparison with the Schwarzschild case demonstrates that the corrective effects of $\xi$ accumulate in the phase over observation time, thereby providing distinguishable observational signatures. Through waveform mismatch analysis, our results indicate that the LISA detector can effectively detect the presence of $\xi$ at the $\sim10^{-4}$ level for systems with a mass of $10^6M_\odot$. Further assessment using the Fisher information matrix (FIM) confirms a measurement precision of $\Delta\xi\approx3.225\times10^{-4}$, which significantly surpasses existing observational methods, providing quantitative observational evidence for asymptotically safe quantum gravity theory in the strong-field regime.

We perform full integration of the stationary axisymmetric Einstein-Maxwell-dilaton-axion (EMDA) theory with and without potential using a recently proposed generalization of Carter's approach to spacetimes beyond type D, allowing the Killing tensor. Crucial to our construction is a new parametrization of the dilaton and axion fields based on the analyticity argument. The general solution in the ungauged case is asymptotically locally flat and contains two more parameters compared to EMDA black holes previously obtained using Harrison transformations. In the gauged case, the general solution is asymptotically AdS and includes flat and hyperbolic topological solutions, as well as generalization of the Kerr-Sen-AdS metric with three additional parameters. Our approach can be applied to more general four-dimensional ungauged and gauged supergravities.

In this paper, we investigate how the gravitational field generated by a four-dimensional electrovacuum cosmological space-time influences the dynamics of fermionic fields governed by the Dirac equation, while also considering the effects of topology. We derive the radial wave equation corresponding to the relativistic Dirac equation and subsequently obtain analytical solutions for the energy levels and wave functions of the fermionic field within our chosen framework. Our analysis reveals that various parameters, including geometric topology, the cosmological constant, and quantum numbers, play significant roles in determining the eigenvalue solution of the quantum particles. Specifically, we demonstrate that the presence of the topological parameter disrupts the degeneracy of the energy spectrum.

In this study, we explore the influence of the quantum correction parameter $\xi$ on the motion of particles and the properties of quasiperiodic oscillations (QPOs) around a quantum-corrected black hole (QCBH). We first analyze the geodesics of a test particle and derive weak-field constraints on parameter $\xi$ from the perihelion precession of orbits, using observations from the Solar System and the S2 star's orbit around $\text{SgrA}^\star$ supermassive black hole in the center of our galaxy. We obtain $\xi \leq 0.01869$ and $\xi \leq 0.73528$ using the analysis of Solar System observations and the orbit of the S2 star around $\text{SgrA}^\star$, respectively. In the strong-field regime, we examine the dynamics of epicyclic motion around astrophysical black holes and, using observational data from four QPO sources and the Markov Chain Monte Carlo (MCMC) method, we determine the upper constraint $\xi \leq 2.086$. Our results provide new insights into the effects of quantum corrections on black hole spacetimes and highlight the potential of QPOs as a probe for testing quantum gravity in astrophysical environments.

Most distinguishing features of black holes and their mimickers are concentrated near the horizon. In contrast, astrophysical observations and theoretical considerations primarily constrain the far-field geometry. In this work we develop tools to effectively describe both, using the two-point Pad\'e approximation to construct interpolating metrics connecting the near and far-field. We extend our previous work by computing the quasinormal modes of gravitational perturbations for static, spherically symmetric metrics that deviate from Schwarzschild spacetime. Even at the lowest order, this approach compares well with existing methods in both accuracy and applicability. Additionally, we show that the lowest-order interpolating metric reliably predicts light ring locations. It closely matches exact results, even when unsuitable for quasinormal frequency calculations.

Gravitational perturbations of higher-dimensional black holes in the Einstein-Gauss-Bonnet theory, proposed by Boulware and Deser, have been extensively studied in numerous works, primarily focusing on the fundamental mode. These studies have shown that for sufficiently small black holes, comparing to the Gauss-Bonnet coupling parameter, a dynamical instability arises. In this work, for the first time, we conduct a comprehensive analysis of the behavior of overtones. We demonstrate that while the fundamental mode remains largely unchanged due to the limited stability region, the first few overtones deviate from their Tangherlini limits at an increasing rate. This deviation reflects the impact of the coupling parameter on the near-horizon structure of the black hole.

We show that in the Starobinsky inflation model stochastic gravitational waves are produced when the scalaron - which is the massive scalar mode of the metric - decays into gravitons during reheating. This decay is accompanied by decay of scalaron into matter as well through a similar coupling, proving an efficient reheating stage. The stochastic gravitational waves thus produced have characteristic strain $h_c\sim 10^{-35}-10^{-34}$ in the frequency range $10^{5}-10^{12}\, {\rm Hz}$ which makes them accessible to resonant cavity searches for graviton to photon conversions. Their detection could conclusively validate the Starobinsky inflation model.

The Palatini formulation has been successful in the development of several alternative theories of gravity. It is well understood that the Palatini and metric formulations are equivalent in minimally coupled scalar-tensor models, but nonminimal scalar-tensor models can lead to physically distinct theories depending on the underlying formulation. Once a model has been selected, the choice of formulation is a discrete one, and so promoting it to be continuous is expected to give rise to a wider class of actions. To this end, we propose the "quasi-Palatini" formulation, a method for interpolating between the metric and Palatini formulations for a given model that gives rise to a continuous family of models. We apply the quasi-Palatini formulation to Higgs inflation, induced gravity inflation, and Starobinsky inflation, and demonstrate how this leads to a deformation of the potential, studying its impact on observables. We also discuss how the interpolation between different actions can be extended to scalar-torsion and scalar-nonmetricity models.

We present a new rotating black hole solution to the Einstein equations as an extension of the Kerr spacetime. To derive this solution, we use the Newman-Janis algorithm as a mathematical tool that reduces a general rotating metric into a tractable form by applying simple physical requirements. Interestingly, the solution we found may not be uniquely characterized by asymptotic parameters such as mass, angular momentum, and charge, thereby challenging the no-hair theorem. We also analyze in detail how this additional characteristics (``hair") affects the thermodynamic properties of the black hole.

A regular black hole, unconstrained by the weak cosmic censorship conjecture, can exceed its critical spin limit and transition into a superspinar. In this paper, we investigate the observational appearance of a rotating regular black hole, specifically the Ghosh black hole and its superspinar counterpart, when surrounded by a thin accretion disk. The resulting images reveal distinct features: the black hole closely resembles its Kerr counterpart with slight deviations, while the superspinar configuration exhibits an inner ring-like structure. Furthermore, we explore the image transition of the Ghosh black hole that has been recently destroyed by the capture of a test particle. Our findings suggest that the transition timescale becomes relevant for supermassive black holes with masses approximately twice that of M87*, making these effects potentially observable with future high-resolution instruments.

The iconic, deep-MOND-limit (DML) relation between acceleration and mass, $a\sim (M\mathcal{A}_0)^{1/2}/r$, implies that, in MOND, accelerations cannot be linear in the mass distribution ($\mathcal{A}_0\equiv Ga_0$ is the DML constant, and $a_0$ the MOND acceleration). This leads to important idiosyncracies of MOND, such as a breakdown of the strong equivalence principle, and the resulting ``external-field effect''. I show that the DML axioms are, in themselves, consistent with a, possibly unique, nonrelativistic, action-based, linear formulation of the DML. This model suffers from important drawbacks, which may make it unacceptable as a basis for a full-fledged MOND theory. The model is unique among MOND theories propounded to date not only in being linear -- hence not exhibiting an external-field effect, for example -- but in constituting a modification of both Newtonian inertia and Newtonian gravity. This linear and time-local model inspires and begets several, one-parameter families of models. One family employs nonlinear, time-nonlocal kinetic terms, but still linear gravitational-field equations. Other families generalize the DMLs of AQUAL and QUMOND, modifying gravity as well as inertia. All families employ fractional time derivatives and possibly fractional Laplacians. At present, I cannot base some acceptable MOND theory on these models -- for example, I cannot offer a sensible umbrella theory that interpolates between these DML models and Newtonian dynamics. They are, however, quite useful in elucidating various matter-of-principle aspects of MOND; e.g., they help to understand which predictions follow from only the basic tenets of MOND -- so-called primary predictions -- and which are secondary, i.e., theory dependent. The models may also show the way to a wider class of MOND theories. (Abridged.)

We investigate the evolution of anisotropies in Einstein-Gauss-Bonnet theory with a scalar field coupled to the Gauss-Bonnet term. Specifically, we examine the simplest scenario in which the scalar field lacks a kinetic term, and its kinetic contribution arises from an integration by parts of the Gauss-Bonnet scalar. We consider four- and five-dimensional anisotropic spacetimes, focusing on Bianchi I and extended Bianchi I geometries. Our study reveals that the asymptotic solutions correspond to locally symmetric spacetimes where at least two scale factors exhibit analogous behavior or, alternatively, to isotropic configurations where all scale factors evolve identically. Additionally, we discuss the effects of a cosmological constant, finding that the presence of the cosmological constant does not lead to an isotropic universe.

The current LAGEOS-LARES 2 experiment aims to accurately measure the general relativistic Lense-Thirring effect in the gravitomagnetic field of the spinning Earth generated by the latter's angular momentum $\boldsymbol{J}$. The key quantity to a priori analytically assess the overall systematic uncertainty is the ratio $\mathcal{R}^{J_2}$ of the sum of the classical precessions of the satellites' nodes $\Omega$ induced by the Earth's oblateness $J_2$ to the sum of their post-Newtonian counterparts. $In$ $principle$, if the sum of the inclinations $I$ of both satellites were $exactly$ $180^\circ$, the semimajor axes $a$ and the eccentricities $e$ being $identical$, $\mathcal{R}^{J_2}$ would $exactly$ vanish. Actually, it is $not$ so by a large amount because of the departures of the $real$ satellites' orbital configurations from their $ideal$ ones. Thus, $J_2$ impacts not only directly through its own uncertainty, but also $indirectly$ through the errors in all the other physical and orbital parameters entering $\mathcal{R}^{J_2}$. The consequences of this fact are examined in greater details than done so far in the literature. The Van Patten and Everitt's proposal in 1976 of looking at the sum of the node precessions of two counter-orbiting spacecraft in (low-altitude) circular polar orbits is revamped rebranding it POLAr RElativity Satellites (POLARES). (Abridged)

The ringdown of perturbed black holes has been studied since the 1970s, but until recently, studies have focused on linear perturbations. There is now burgeoning interest in nonlinear perturbative effects during ringdown. Here, using a hyperboloidal framework, we provide a complete treatment of linear and quadratic quasinormal modes (QNMs and QQNMs) in second-order perturbation theory, in Schwarzschild spacetime. We include novel methods for extracting QNMs and QQNMs amplitudes using a Laplace transform treatment, allowing for the inclusion of arbitrary initial data. We produce both time- and frequency-domain codes. From these codes, we present new results further exploring the unforeseen dependence of QQNMs amplitudes on the parity of the progenitor system, as demonstrated in our letter [Phys. Rev. Lett. 134, 061401 (2025)]. Our numerical results are restricted to perturbations of a Schwarzschild black hole, but our methods extend straightforwardly to the astrophysically realistic case of a Kerr black hole.

We study Proca theory with non-minimal coupling to gravity through the Ricci tensor and Ricci scalar interactions. We show that in the homogeneous and isotropic Universe together with cosmological constant, the temporal component of the vector field acquires a background value. As a result, we show that the theory propagates an additional degree of freedom, with respect to the generalized Proca theories, whose kinetic term suggests the presence of several strong coupling regimes that depend on the value of the background solution, the combination and vanishing of coupling constants, together with a scale-dependent one. We show in addition, that the speed of propagation for this mode vanishes, indicating the presence of another type of strong coupling. To further investigate this, we extend our analysis to the Bianchi Type I Universe, with the most general solution for the vector field. We show that the extra degree of freedom remains in the theory. Among the modes, we further show that the mode with vanishing speed of propagation is still present, pointing to the strong coupling. In addition, we discover a mode with scale-dependent strong coupling (vanishing kinetic term), one mode that propagates only in one single direction and two unstable modes.

In the phase space perspective, scalar field slow roll inflation is described by a heteroclinic orbit from a saddle type fixed point to a final attractive point. In many models the saddle point resides in the scalar field asymptotics, and thus for a comprehensive view of the dynamics a global phase portrait is necessary. For this task, in the literature one mostly encounters dynamical variables that either render the initial or the final state singular, thus obscuring the full picture. In this work we construct a hybrid set of variables which allow the depiction of both the initial and final states distinctly in nonsingular manner. To illustrate the method, we apply these variables to portray various interesting types of scalar field inflationary models like metric Higgs inflation, metric Starobinsky inflation, pole inflation, and a nonminimal Palatini model.

We investigate the dynamical collapse of Bronnikov-Ellis (BE) wormhole using the double-null formalism, where its throat is characterized by the coincidence of two curves $r_{,u} = 0$ and $r_{,v} = 0$. The emission of two ingoing pulses: normal scalar and phantom fields in the wormhole spacetime reveals two distinct instability scenarios: a normal scalar field triggers gravitational collapse into a black hole where the singularity $r=0$ hidden by the event horizon ($r_{,u}=0$ and $r_{,v}=0$); while a phantom field drives inflationary expansion of wormhole, decoupling two asymptotic regions with the cosmological horizon ($r_{,u}=0$ and $r_{,v}=0$). The process of two scenarios can be accelerated by increasing the amplitude of pulses but can be delayed by increasing the wormhole's mass. Additionally, the collisions of two identical pulses from ingoing and outgoing null directions in the massless BE wormhole fail to cure the instabilities because the two scenarios can still occur, but the formation of a black hole can be delayed for the collision of normal and phantom fields. Interestingly, the strategic tuning of emission timing for outgoing phantom field to collide with ingoing normal scalar field can temporarily stabilize the wormhole throat by restoring the coincidence of $r_{,u}$ and $r_{,v}$ again after their separation. This offers us valuable insights into extending the lifetime of a traversable wormhole.

Cosmological correlators are fundamental observables in an expanding universe and are highly non-trivial functions even at tree-level. In this work, we uncover novel structures in the space of such tree-level correlators that enable us to develop a new recursive algorithm for their explicit computation. We begin by formulating cosmological correlators as solutions to GKZ systems and develop a general strategy to construct additional differential operators, called reduction operators, when a GKZ system is reducible. Applying this framework, we determine all relevant reduction operators, and show that they can be used to build up the space of functions needed to represent the correlators. Beyond relating different integrals, these operators also yield a large number of algebraic relations, including cut and contraction relations between diagrams. This implies a significant reduction in the number of functions needed to represent each tree-level cosmological correlator. We present first steps to quantify the complexity of our reduction algorithm by using the Pfaffian framework. While we focus on tree-level cosmological correlators, our approach provides a blueprint for other perturbative settings.

We present a quantum response approach to momentum-space gravity in dissipative multiband systems, which dresses both the quantum geometry--through an interband Weyl transformation--and the equations of motion. In addition to clarifying the roles of the contorsion and symplectic terms, we introduce the three-state quantum geometric tensor and discuss the significance of the emergent terms from a gravitational point of view. We also identify a dual quantum geometric drag force in momentum space that provides an entropic source term for the multiband matrix of Einstein field equations.

We explore various field theory aspects of integrable $ \eta $-deformed geometry in type IIB supergravity by employing several holographic probes. These include the computation of holographic timelike entanglement entropy and estimation of various other field theory observables for example, the flow central charge and the quantum complexity. We also discuss the associated brane set up and compute Page charges. We further use them to calculate the coupling constant in the dual QFTs considering both small and large deformation limits.

We present for the first time an analysis of high-frequency gravitational wave (GW) emission from proto-neutron stars (PNS) in core collapse supernovae (CCSNe) that combines spatial decomposition and modal decomposition to both source and characterize the emission. Our analysis is based on three-dimensional CCSN simulations initiated from two progenitors with differing mass and metallicity. We spatially decompose GW strains into five regions and show they are initially largest in the PNS surface layers from accretion and later largest from the Ledoux convective and convective overshoot regions within the PNS. We compute the fractional GW luminosity and observe that the majority of the luminosity moves from the same outer layers to deep within the PNS at comparable times. Using a self-consistent perturbative analysis, we investigate the evolution of the oscillation modes of the PNS. We find that the frequency of the evolving high-frequency component of the GW signal is well matched to the ${}^2g_2$-mode, the ${}^2g_1$-mode, and the ${}^2f$-mode over time. We show that the ${}^2g$-modes emit most of their power in GWs initially from the PNS surface region, but within a few 100 ms after bounce, it is the convective overshoot region of the PNS that emits the most GW power for the ${}^2g_1$-mode. Eventually, the ${}^2f$-mode is the dominant mode producing GWs, and they are emitted primarily from the convective overshoot region. Thus, with three interconnected analyses, we show that, while the GW emission is global, stemming from multiple regions in and around the PNS, we are able to source the dominant contributions to it. We find that high-frequency GW emission from the PNS in CCSNe is more complex than assessed by other methods, and dependent, first emitted mainly by ${}^2g$-modes driven by accretion onto the PNS and later emitted by the ${}^2f$-mode driven by sustained Ledoux convection.

A quantum clock cannot be modeled as a point mass moving along a single geodesic if it is in a state with nonzero position fluctuations. Instead, it is an extended object subject to tidal forces and a superposition of time dilations at different altitudes. Here, a geometrical formulation of quantum mechanics is used to show that additional quantum properties representing correlations between different directions imply a non-Riemannian geometrical structure experienced by a quantum clock. A specific version of Finsler geometry parameterized by entropy and purity of the state provides a novel setting for a combination of quantum and gravitational effects. A crucial ingredient is given by a new parameterization of quantum-information properties related to second-order moments of a state and may also be useful in other applications.

The photon sphere defines the unstable circular orbit of photons in a black hole spacetime. Photons emitted by a source located inside the photon sphere can be gravitationally lensed by the black hole and have time delays when reaching the observer. These delays may lead to light echoes produced in the light curve if an accretion event in the vicinity of the horizon can be observed. In this work, we present fully analytical formulas with high accuracy to describe the change of the azimuthal angle and the travel time of those photons. By employing the analytical approaches, we find that the time delay between photons emitted from the interior of the photon sphere has a typical time scale of $2(\pi - \phi_\mathrm{S}) u_\mathrm{m}$ with $\phi_\mathrm{S}$ and $u_\mathrm{m}$ being respectively the azimuthal angle of the source and the impact parameter evaluated at the photon sphere, which can provide some clues on the future search for gravitational lensing signatures in the accretion inflow event.

This note examines the BV formulation of $N=1$, $D=4$ supergravity in the first-order Palatini--Cartan framework. Challenges in achieving an off-shell formulation are addressed by introducing corrections to the rank 2 BV action, offering in addition a solid foundation for the study of the theory on manifolds with boundary.

We quote a definitive simple proof that neither classical stochastic dynamics nor quantum dynamics can be nonlinear if we stick to their standard statistical interpretations. A recently proposed optomechanical test of gravity's classicality versus quantumness is based on the nonlinear Schr\"odinger-Newton equation (SNE) which is the nonrelativistic limit of standard semiclassical gravity. While in typical cosmological applications of semiclassical gravity the predicted violation of causality is ignored, it cannot be disregarded in applications of the SNE in high sensitive laboratory tests hoped for the coming years. We reveal that, in a recently designed experiment, quantum optical monitoring of massive probes predicts fake action-at-a-distance (acausality) on a single probe already. The proposed experiment might first include the direct test of this acausality.

We explore the implications of finite-temperature quantum field theory effects on cosmological parameters within the framework of the $\Lambda$CDM model and its modification. By incorporating temperature-dependent corrections to the cosmological constant, we extend the standard cosmological model to include additional density parameters, $\Omega_{\Lambda_2}$ and $\Omega_{\Lambda_3}$, which arise from finite-T quantum gravitational effects. Using the Cosmic Linear Anisotropy Solving System, we analyze the impact of these corrections on the cosmic microwave background power spectrum and compare the results with the Planck 2018 data. Through brute-force parameter scans and advanced machine learning techniques, including quartic regression, we demonstrate that the inclusion of $\Omega_{\Lambda_2}$ and $\Omega_{\Lambda_3}$ improves the model's predictive accuracy, achieving high $R^2$ values and low mean squared error. The present work paves the way for future research into higher-order corrections and enhanced computational methods for cosmological parameter estimation.

In this study, we first heuristically constitute the charges for the chiral transformation associated with the large U(1) gauge symmetry. We name those as the large chiral charges, and the chiral transformation those generate as the large chiral transformations. Then, showing that those can be obtained based on Noether's theorem, we once obtain the anomaly equation associated with those large chiral transformations. Then, for the one-loop diagrams of the fermionic field coupling to the multiple classical gauge fields (those constitute the effective action of the model in this study with regard to the gauge field), we perform an axailization. Then, defining the BRS transformations for the large U(1) gauge symmetry (we name those as the large BRS transformation), we perform those large BRS transformations to those axialized one-loop diagrams. Then, evaluating those, we show that the anomaly equations mentioned above can be derived. It is also shown that those anomaly equations can be derived in Fujikawa method. The result in this study would be important as a development of the large U(1) gauge symmetry.