Search Results (54)

We develop a symmetry-based variational theory that shows the coarse-grained balance of work inflow to heat outflow in a driven, dissipative system relaxed to the golden ratio. Two order-2 Möbius transformations—a self-dual flip and a self-similar shift—generate a discrete non-abelian subgroup of $\mathrm{PGL}(2,\mathbb{Q}\left(\sqrt{5}\right))$. Requiring any smooth, strictly convex Lyapunov functional to be invariant under both maps enforces a single non-equilibrium fixed point: the golden mean. We confirm this result by (i) a gradient-flow partial-differential equation, (ii) a birth–death Markov chain whose continuum limit is Fokker–Planck, (iii) a Martin–Siggia–Rose field theory, and (iv) exact Ward identities that protect the fixed point against noise. Microscopic kinetics merely set the approach rate; three parameter-free invariants emerge: a $62\%:38\%$ split between entropy production and useful power, an RG-invariant diffusion coefficient linking relaxation time and correlation length ${\mathcal{D}}_{\alpha }={\xi }^z/\tau$, and a $\vartheta ={45}^{\circ }$ eigen-angle that maps to the golden logarithmic spiral. The same dual symmetry underlies scaling laws in rotating turbulence, plant phyllotaxis, cortical avalanches, quantum critical metals, and even de-Sitter cosmology, providing a falsifiable, unifying principle for pattern formation far from equilibrium. Full article

It has been shown that at the present stage of the evolution of the universe, cosmological acceleration is an inevitable kinematical consequence of quantum theory in semiclassical approximation. Quantum theory does not involve such classical concepts as Minkowski or de Sitter spaces. In classical theory, when choosing Minkowski space, a vacuum catastrophe occurs, while when choosing de Sitter space, the value of the cosmological constant can be arbitrary. On the contrary, in quantum theory, there is no uncertainties in view of the following: (1) the de Sitter algebra is the most general ten-dimensional Lie algebra; (2) the Poincare algebra is a special degenerate case of the de Sitter algebra in the limit $R\to \infty$ where R is the contraction parameter for the transition from the de Sitter to the Poincare algebra and R has nothing to do with the radius of de Sitter space; (3) R is fundamental to the same extent as c and ℏ: c is the contraction parameter for the transition from the Poincare to the Galilean algebra and ℏ is the contraction parameter for the transition from quantum to classical theory; (4) as a consequence, the question (why the quantities (c, ℏ, R) have the values which they actually have) does not arise. The solution to the problem of cosmological acceleration follows on from the results of irreducible representations of the de Sitter algebra. This solution is free of uncertainties and does not involve dark energy, quintessence, and other exotic mechanisms, the physical meaning of which is a mystery. Full article

As shown by Dyson in his famous paper “Missed Opportunities”, it follows, even from purely mathematical considerations, that quantum Poincare symmetry is a special degenerate case of quantum de Sitter symmetries. Thus, the usual explanation of why, in particle physics, Poincare symmetry works with a very high accuracy is as follows. A theory in de Sitter space becomes a theory in Minkowski space when the radius of de Sitter space is very high. However, the answer to this question must be given only in terms of quantum concepts, while de Sitter and Minkowski spaces are purely classical concepts. Quantum Poincare symmetry is a good approximate symmetry if the eigenvalues of the representation operators $M_{4\mu }$ of the anti-de Sitter algebra are much greater than the eigenvalues of the operators $M_{\mu \nu }$ ($\mu ,\nu =0,1,2,3$). We explicitly show that this is the case in the Flato–Fronsdal approach, where elementary particles in standard theory are bound states of two Dirac singletons. Full article

This work explores the geometry of extremal Kerr-Newman black holes by analyzing their mass/energy relationships and the conditions ensuring black hole existence. Using differential geometry in $E^3$, we examine the topology of the event horizon surface and identify two distinct families of extremal black holes, each defined by unique proportionalities between their core parameters: mass (m), charge (Q), angular momentum (L), and the irreducible mass ($m_{ir}$). In the first family, these parameters are proportionally related to the irreducible mass by irrational numbers, with a characteristic flat Gaussian curvature at the poles. In the second family, we uncover a more intriguing structure where m, Q, and L are connected to $m_{ir}$ through coefficients involving the golden ratio $-{\varphi }_{-}$. Within this family lies a unique black hole whose physical parameters converge on the golden ratio, including the irreducible mass and polar Gauss curvature. This black hole represents the highest symmetry achievable within the constraints of the Kerr-Newman metric. This remarkable symmetry invites further speculation about its implications, such as the potential determination of the dark energy density parameter ${\Omega }_{\Lambda }$ for Kerr-Newman-de Sitter black holes. Additionally, we compute the maximum energy that can be extracted through reversible transformations. We have determined that the second, golden-ratio-linked family allows for a greater energy yield than the first. Full article

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space–times. Our main results here are as follows: (i) We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, such as the spectral scalar and tensor indices, $n_S$ and $n_T$, and the tensor-to-scalar ratio r. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) $Mp\left(n\right)$ representation for quantum de Sitter space–time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the $Mp\left(n\right)$ group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) Mean value generators of $Mp\left(2\right)$ are related to the adiabatic invariant and topological charge of the space–time, (matrix element of the transition $-\infty <t<\infty$). (v) The basic even and odd n-sectors of the Hilbert space are intrinsic to the quantum space–time and its discrete levels (in particular, continuum for $n\to \infty$), they do not require any extrinsic generation process such as the standard Schrodinger cat states, and are entangled. (vi) The gravity or cosmological domains on one side and another of the Planck scale are entangled. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity region and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space–time are entangled. (vii) The general classical-quantum gravity duality is associated with the Metaplectic $Mp\left(n\right)$ group symmetry which provides the complete full covering of the phase space and of the quantum space–time mapped from it. Full article

Quantum field theory (QFT) in Rindler spacetime is a gateway to understanding unitarity and information loss paradoxes in curved spacetime. Rindler coordinates map Minkowski spacetime onto regions with horizons, effectively dividing accelerated observers into causally disconnected sectors. Employing standard quantum field theory techniques and Bogoliubov transformations between Minkowski and Rindler coordinates yields entanglement between states across these causally separated regions of spacetime. This results in a breakdown of unitarity, implying that information regarding the entangled partner may be irretrievably lost beyond the Rindler horizon. As a consequence, one has a situation of pure states evolving into mixed states. In this paper, we introduce a novel framework for comprehending this phenomenon using a recently proposed formulation of direct-sum quantum field theory (DQFT), which is grounded in superselection rules formulated by the parity and time reversal ($\mathcal{P}\mathcal{T}$) symmetry of Minkowski spacetime. In the context of DQFT applied to Rindler spacetime, we demonstrate that each Rindler observer can, in principle, access pure states within the horizon, thereby restoring unitarity. However, our analysis also reveals the emergence of a thermal spectrum of Unruh radiation. This prompts a reevaluation of entanglement in Rindler spacetime, where we propose a novel perspective on how Rindler observers may reconstruct complementary information beyond the horizon. Furthermore, we revisit the implications of the Reeh-Schlieder theorem within the framework of DQFT. Lastly, we underscore how our findings contribute to ongoing efforts aimed at elucidating the role of unitarity in quantum field theory within the context of de Sitter and black hole spacetimes. Full article

We discuss the consequences of the unique symmetry of de Sitter spacetime. This symmetry leads to the specific thermodynamic properties of the de Sitter vacuum, which produces a thermal bath for matter. de Sitter spacetime is invariant under the modified translations, $\mathbf{r}\to \mathbf{r}-e^{Ht}\mathbf{a}$, where H is the Hubble parameter. For $H\to 0$, this symmetry corresponds to the conventional invariance of Minkowski spacetime under translations $\mathbf{r}\to \mathbf{r}-\mathbf{a}$. Due to this symmetry, all the comoving observers at any point of the de Sitter space perceive the de Sitter environment as the thermal bath with temperature $T=H/\pi$, which is twice as large as the Gibbons–Hawking temperature of the cosmological horizon. This temperature does not violate de Sitter symmetry and, thus, does not require the preferred reference frame, as distinct from the thermal state of matter, which violates de Sitter symmetry. This leads to the heat exchange between gravity and matter and to the instability of the de Sitter state towards the creation of matter, its further heating, and finally the decay of the de Sitter state. The temperature $T=H/\pi$ determines different processes in the de Sitter environment that are not possible in the Minkowski vacuum, such as the process of ionization of an atom in the de Sitter environment. This temperature also determines the local entropy of the de Sitter vacuum state, and this allows us to calculate the total entropy of the volume inside the cosmological horizon. The result reproduces the Gibbons–Hawking area law, which is attributed to the cosmological horizon, $S_{\mathrm{hor}}=4\pi KA$, where $K=1/\left(16\pi G\right)$. This supports the holographic properties of the cosmological event horizon. We extend the consideration of the local thermodynamics of the de Sitter state using the $f\left(\mathcal{R}\right)$ gravity. In this thermodynamics, the Ricci scalar curvature $\mathcal{R}$ and the effective gravitational coupling K are thermodynamically conjugate variables. The holographic connection between the bulk entropy of the Hubble volume and the surface entropy of the cosmological horizon remains the same but with the gravitational coupling $K=df/d\mathcal{R}$. Such a connection takes place only in the $3+1$ spacetime, where there is a special symmetry due to which the variables K and $\mathcal{R}$ have the same dimensionality. We also consider the lessons from de Sitter symmetry for the thermodynamics of black and white holes. Full article

We consider F-term hybrid inflation (FHI) and SUSY breaking in the context of a $B-L$ extension of the MSSM that largely respects a global $U\left(1\right)$R symmetry. The hidden sector Kaehler manifold enjoys an enhanced $SU(1,1)/U\left(1\right)$ symmetry, with the scalar curvature determined by the achievement of a SUSY-breaking de Sitter vacuum without undesirable tuning. FHI turns out to be consistent with the data, provided that the magnitude of the emergent soft tadpole term is confined to the range $(1.2$–$100)$ TeV, and it is accompanied by the production of $B-L$ cosmic strings. If these are metastable, they are consistent with the present observations from PTA experiments on the stochastic background of gravitational waves with dimensionless tension $G{\mu }_{\mathrm{cs}}\simeq (1-9.2)·{10}^{-8}$. The $\mu$ parameter of the MSSM arises by appropriately adapting the Giudice–Masiero mechanism and facilitates the out-of-equilibrium decay of the R saxion at a reheat temperature lower than about 71 GeV. Due to the prolonged matter-dominated era, the gravitational wave signal is suppressed at high frequencies. The SUSY mass scale turns out to lie in the PeV region. Full article

We analyze the transformation of a very broad class of metrics that can be expressed in terms of static coordinates. Starting from a general ansatz, we obtain a relation for the parameters in which one can impose further symmetries or restrictions. One of the simplest restrictions leads to FLRW cases, while transforming from the initial static to other static-type coordinates can lead to near horizon coordinates, Wheeler–Regge, and isotropic coordinates, among others. As less restrictive cases, we show an indirect route for obtaining Kruskal–Szekeres within this approach, as well as Lemaître coordinates. We use Schwarzschild spacetime as a prototype for testing the procedure in individual cases. However, application to other spacetimes, such as de-Sitter, Reissner–Nordström, and Schwarzschild de Sitter, can be readily generalized. Full article

We solve the particle-antiparticle and cosmological constant problems proceeding from quantum theory, which postulates that: various states of the system under consideration are elements of a Hilbert space $\mathcal{H}$ with a positive definite metric; each physical quantity is defined by a self-adjoint operator in $\mathcal{H}$; symmetry at the quantum level is defined by a representation of a real Lie algebra A in $\mathcal{H}$ such that the representation operator of any basis element of A is self-adjoint. These conditions guarantee the probabilistic interpretation of quantum theory. We explain that in the approaches to solving these problems that are described in the literature, not all of these conditions have been met. We argue that fundamental objects in particle theory are not elementary particles and antiparticles but objects described by irreducible representations (IRs) of the de Sitter (dS) algebra. One might ask why, then, experimental data give the impression that particles and antiparticles are fundamental and there are conserved additive quantum numbers (electric charge, baryon quantum number and others). The reason is that, at the present stage of the universe, the contraction parameter R from the dS to the Poincare algebra is very large and, in the formal limit $R\to \infty$, one IR of the dS algebra splits into two IRs of the Poincare algebra corresponding to a particle and its antiparticle with the same masses. The problem of why the quantities $(c,\hslash ,R)$ are as are does not arise because they are contraction parameters for transitions from more general Lie algebras to less general ones. Then the baryon asymmetry of the universe problem does not arise. At the present stage of the universe, the phenomenon of cosmological acceleration (PCA) is described without uncertainties as an inevitable kinematical consequence of quantum theory in semiclassical approximation. In particular, it is not necessary to involve dark energy the physical meaning of which is a mystery. In our approach, background space and its geometry are not used and R has nothing to do with the radius of dS space. In semiclassical approximation, the results for the PCA are the same as in General Relativity if $\mathsf{\Lambda }=3/R^2$, i.e., $\mathsf{\Lambda }>0$ and there is no freedom for choosing the value of $\mathsf{\Lambda }$. Full article

We show that Einstein’s conformal gravity can explain, simply, and on the geometric ground, galactic rotation curves, without the need to introduce any modification in both the gravitational as well as in the matter sector of the theory. The geometry of each galaxy is described by a metric obtained, making a singular rescaling of Schwarzschild’s spacetime. The new exact solution, asymptotically anti-de Sitter, manifests an unattainable singularity at infinity that cannot be reached in finite proper time; namely, the spacetime is geodetically complete. It deserves to be noticed that, in this paper, we have a different opinion from the usual one. Indeed, instead of making the metric singularity-free, we make it apparently but harmlessly even more singular than Schwarzschild’s. Finally, it is crucial to point out that Weyl’s conformal symmetry is spontaneously broken into the new singular vacuum rather than the asymptotically flat Schwarzschild’s one. The metric is unique according to the null energy condition, the zero acceleration for photons in the Newtonian regime, and the homogeneity of the Universe at large scales. Once the matter is conformally coupled to gravity, the orbital velocity for a probe star in the galaxy turns out to be asymptotically constant consistent with the observations and the Tully–Fisher relation. Therefore, we compare our model with a sample of 175 galaxies and show that our velocity profile very well interpolates the galactic rotation curves after a proper choice of the only free parameter in the metric. The mass-to-luminosity ratios of galaxies turn out to be close to 1, consistent with the absence of dark matter. Full article

We deduce a non-linear commutator higher-spin (HS) symmetry algebra which encodes unitary irreducible representations of the AdS group—subject to a Young tableaux $Y(s_1,\dots ,s_k)$ with $k\ge 2$ rows—in a d-dimensional anti-de Sitter space. Auxiliary representations for a deformed non-linear HS symmetry algebra in terms of a generalized Verma module, as applied to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints, are found explicitly in the case of a $k=2$ Young tableaux. An oscillator realization over the Heisenberg algebra for the Verma module is constructed. The results generalize the method of constructing auxiliary representations for the symplectic $sp\left(2k\right)$ algebra used for mixed-symmetry HS fields in flat spaces [Buchbinder, I.L.; et al. Nucl. Phys. B 2012, 862, 270–326]. Polynomial deformations of the $su(1,1)$ algebra related to the Bethe ansatz are studied as a byproduct. A nilpotent BRST operator for a non-linear HS symmetry algebra of the converted constraints for $Y(s_1,s_2)$ is found, with non-vanishing terms (resolving the Jacobi identities) of the third order in powers of ghost coordinates. A gauge-invariant unconstrained reducible Lagrangian formulation for a free bosonic HS field of generalized spin $(s_1,s_2)$ is deduced. Following the results of [Buchbinder, I.L.; et al. Phys. Lett. B 2021, 820, 136470.; Buchbinder, I.L.; et al. arXiv 2022, arXiv:2212.07097], we develop a BRST approach to constructing general off-shell local cubic interaction vertices for irreducible massive higher-spin fields (being candidates for massive particles in the Dark Matter problem). A new reducible gauge-invariant Lagrangian formulation for an antisymmetric massive tensor field of spin $(1,1)$ is obtained. Full article

The current study examines the realisation of cosmic bounce in two situations involving two distinct scale factor selections, one of which is a scale factor already developed for bouncing and the other of which is a scale factor created by truncating a series expansion of a de Sitter scale factor. Generalized Chaplygin gas (GCG) is assumed to be the background fluid in both situations. When the scale factor is set to the first kind, the pre-bounce scenario’s GCG energy density decreases due to contraction, reaches its lowest point at $t=0$ during the bounce, and then rises as a result of expansion following the bounce. However, it is noted that the truncation has an impact on the density evolution from pre-bounce in the other scale factor scenario. The influence of bulk viscosity is shown in all circumstances, in addition to the influence of non-viscosity, and the test for stability makes use of the squared speed of sound. At the turn-around places, the null energy criterion is also violated. The final stage of the study includes a cosmographic analysis and a demonstration of the Hubble flow dynamics. In conclusion, we find that inflationary cosmology can also be realized with GCG as the background fluid for two-scale factor options. When the equivalent cosmic parameter is examined for pre-bounce and post-bounce scenarios, a symmetry is frequently seen. The symmetry occurs near the point of bouncing or turning. Full article

We uncover the general mechanism and the nature of today’s dark energy (DE). This is only based on well-known quantum physics and cosmology. We show that the observed DE today originates from the cosmological quantum vacuum of light particles, which provides a continuous energy distribution able to reproduce the data. Bosons give positive contributions to the DE, while fermions yield negative contributions. As usual in field theory, ultraviolet divergences are subtracted from the physical quantities. The subtractions respect the symmetries of the theory, and we normalize the physical quantities to be zero for the Minkowski vacuum. The resulting finite contributions to the energy density and the pressure from the quantum vacuum grow as $loga\left(t\right)$, where $a\left(t\right)$ is the scale factor, while the particle contributions dilute as $1/a^3\left(t\right)$, as it must be for massive particles. We find the explicit dark energy equation of state of today to be $P=w\left(z\right)\mathcal{H}$: it turns to be slightly $w\left(z\right)<-1$ with $w\left(z\right)$ asymptotically reaching the value $-1$ from below. A scalar particle can produce the observed dark energy through its quantum cosmological vacuum provided that (i) its mass is of the order of ${10}^{-3}$ eV = 1 meV, (ii) it is very weakly coupled, and (iii) it is stable on the time scale of the age of the universe. The axion vacuum thus appears as a natural candidate. The neutrino vacuum (especially the lightest mass eigenstate) can give negative contributions to the dark energy. We find that $w(z=0)$ is slightly below $-1$ by an amount ranging from $(-1.5\times {10}^{-3})$ to $(-8\times {10}^{-3})$ and we predict the axion mass to be in the range between 4 and 5 $\mathrm{meV}$. We find that the universe will expand in the future faster than the de Sitter universe as an exponential in the square of the cosmic time. Dark energy today arises from the quantum vacuum of light particles in FRW cosmological space-time in an analogous way to the Casimir vacuum effect of quantum fields in Minkowski space-time with non-trivial boundary conditions. Full article

We investigate the shadows cast by a sort of new regular black hole which are characterized by an asymptotic Minkowski core and sub-Planckian curvature. First, we extend the metric with spherical symmetry to the one of rotating Kerr-like black holes and derive the null geodesics with a circular orbit near the horizon of the black hole. Then, we plot the shadows of black holes with different values for the deviation parameter. It is found that the size of the shadow shrinks with the increase in the deviation parameter, while the shape of the shadow becomes more deformed. In particular, by comparing with the shadow a Bardeen black hole and Hayward black hole with the same parameter values, we find that, in general, the shadows of black holes with Minkowski cores have larger deformations than those with de Sitter cores, which potentially provides a strategy to distinguish these two sorts of regular black holes with different cores by astronomical observation in the future. Full article