Search Results (59)

In this work, a closed isotropic universe with scalar and spinor fields is considered within the framework of the extended phase space approach. Unlike conventional canonical quantization that yields the Wheeler–DeWitt equation, our method allows us to derive the Schrödinger equation for the wave function of the Universe directly from the path integral constructed with the Faddeev–Popov effective action, including gauge-fixing and ghost terms. We employ a mixed representation in the path integral: a coordinate representation for gravitational variables (lapse function and scale factor) and ghost fields, together with a holomorphic representation for matter fields. Assuming a conformally coupled scalar field as a first step, we obtain exact solutions to the Schrödinger equation under specific gauge conditions. To address the problem of vacuum divergences, we introduce supersymmetric multiplets of scalar and spinor fields, which systematically cancel the divergences and yield a finite vacuum energy in the closed universe. The resulting finite vacuum energy is interpreted as a topological Casimir effect. Full article

We study the quantum dynamics in Krylov space of a spatially flat, homogeneous, and isotropic universe sourced with a massless scalar field within Wheeler–DeWitt (WDW) quantum cosmology and loop quantum cosmology (LQC) frameworks. The availability of a physical Hilbert space and physical Hamiltonian and the presence of an internal clock enable us to construct the Krylov basis analytically by applying the Lanczos algorithm. We then evaluate both the Krylov state and operator complexity for WDW quantum cosmology and LQC on this basis. In regimes where the wave function of the universe is sharply peaked, our results indicate that the Krylov complexity grows quadratically with the scalar field clock for the state and operator complexities in both the WDW quantum cosmology and LQC. We further show that the operator complexity is exactly twice the state complexity in these regimes. We discuss the interpretation of the global behavior of these systems by calculating the Krylov entropy for both quantum cosmological frameworks. We observe that in LQC, the Krylov complexity and entropy remain finite at the bounce, whereas in the WDW quantum cosmology, they diverge at the big bang/crunch singularity. Our work provides the first example of computing Krylov complexity for a system with a totally constrained Hamiltonian and no external time, a framework to calculate a purely quantum-mechanical entropy in quantum cosmology, and, to our knowledge, the first direct bridge between Krylov complexity and canonical quantum cosmology, as a first step toward understanding how polymerized quantum geometry modifies complexity and entropy. Full article

We propose a foundational framework in which internal temporal ordering, the low-entropy boundary of the observable branch, the compatibility of a local thermodynamic arrow with a global partition lifecycle, and a qualitative late-time dark-energy sign relation are organized as projections of a single internal-access architecture. The observable universe is treated as an internally accessible partition of a larger pure atemporal quantum state satisfying the Wheeler–DeWitt constraint. The ordering parameter is not identified with partition entropy itself; it is interpreted as an algebraic readout-depth parameter associated with a nested tower of admissible factor-like subalgebras, each inclusion adding one unit of autonomous distinguishability to the accessible sector. The reduced entropy S(rho_S) is then the Page-like scalar profile evaluated along this depth. This separates the internal ordering structure from the entropy being measured while retaining Page complementarity between accessible and inaccessible capacities. A minimal cosmological bridge is introduced: in the semiclassical Friedmann–Lemaitre–Robertson–Walker regime, if the effective Hubble rate is monotonic in partition entropy and readout depth is monotonically oriented with observer time, standard kinematics imply a sign correspondence between entropy change and the effective dark-energy equation of state. The metric map remains open. Full article

This work formulates semiclassical gravity within a causal-diamond framework where a finite-resolution boundary provides the edge structure for a local Wheeler–DeWitt description. Because the diffeomorphism-invariant Hilbert space does not factorize, each diamond is equipped with a boundary-completed algebra ${\mathfrak{A}}_O$, ensuring the operational state ${\rho }_O$ and the semiclassical reference family ${\sigma }_O[\Lambda ]$ share identical operator content. Dynamics are posed as local statistical inference: the relative-entropy functional $S_{\mathrm{rel}}({\rho }_O\parallel {\sigma }_O[\Lambda ])$ quantifies the mismatch between data and reference. This yields the minimal operational axioms defining subsystems, intrinsic clocks, and regulated observables in a finite-resolution, background-independent setting. The topology-locked boundary capacity budget fixes an effective channel multiplicity $N\approx 1.23\times {10}^{11}$. Calibrating its coherent fraction to Newton’s constant determines a matching scale $M_s\approx 3.02\times {10}^{13}\mathrm{GeV}$. In the modular/KMS regime, the relative-entropy Hessian (Kubo–Mori metric) block-diagonalizes into orthogonal tensor, vector, and scalar response sectors. A heat-kernel expansion on the fixed $S^3\times S^1$ history manifold maps this near-equilibrium response to a matching-scale effective field theory, yielding the Einstein–Hilbert tensor structure, Yang–Mills susceptibilities, and leading mass deformations. Vector and scalar responses remain intensive, while the tensor response scales extensively with coherent channel multiplicity. The fixed modular protocol and quantized boundary currents imply ${\alpha }^{-1}\left(M_s\right)=4\pi k$ at integer levels k, while the reduced $R^2$ plateau sector yields linked cosmological targets: $n_s\simeq 0.965$, $r\simeq 0.0038$, and $A_s\simeq 2.1\times {10}^{-9}$. Translations between causal diamonds act as completely positive trace-preserving (CPTP) updates. The resulting open-modular Walsh filtration selects the three-dimensional degree-one sector as the algebraic basis for family structure. Treating continuum fields as the structured response of a finite boundary, the framework yields correlated, falsifiable relations for gravitational stiffness, gauge response, plateau cosmology, and threefold matter-sector organization from one minimal operational architecture. Full article

In this paper, we reconsider two long-standing yet unsolved problems: the origin of the universe and the arrow of time. We show that only a closed universe is free from singularities and that the arrow of time is symmetric with respect to the universe’s maximum scale. The Wheeler–DeWitt equation is explicitly solved to obtain local dynamical times. It is shown that the thermodynamic arrow of time coincides with both the dynamical time and the cosmological (expanding universe) time. This correspondence is explicitly demonstrated in two-dimensional spacetime. Full article

The present work discusses the birth of the Universe via quantum tunneling through a potential barrier, based on quantum cosmology, taking a running cosmological constant into account. We consider the Friedmann–Lemaître–Robertson–Walker (FLRW) metric with positively curved spatial sections ($k=1$) and the matter’s content is a dust perfect fluid. The model was quantized by the Dirac formalism, leading to a Wheeler–DeWitt equation. We solve that equation both numerically and using a WKB approximation. We study the behavior of tunneling probabilities $T{P}_{WKB}$ and $T{P}_{int}$ by varying the energy E of the dust perfect fluid, the phenomenological parameter $\nu$, the present value of the Hubble function $H_0$, and the constant energy density ${\rho }_{\Lambda }^0$, with the last three parameters all being associated with the running cosmological constant. We observe that both tunneling probabilities, $T{P}_{WKB}$ and $T{P}_{int}$, decrease as one increases $\nu$. We also note that $T{P}_{WKB}$ and $T{P}_{int}$ grow as E increases, indicating that the Universe is more likely to be born with higher dust energy E values. The same is observed for the parameter ${\rho }_{\Lambda }^0$, that is, $T{P}_{WKB}$ and $T{P}_{int}$ are larger for higher values of ${\rho }_{\Lambda }^0$. Finally, the tunneling probabilities decrease as one increases the value of $H_0$. Therefore, the best conditions for the Universe to be born, in the present model, would be to have the highest possible values for E and $\Lambda$ and the lowest possible values for $\nu$ and $H_0$. Full article

We investigate pseudo-complex General Relativity (pcGR)—a coordinate-extended formulation of General Relativity (GR)—within the framework of Hořava-Lifshitz gravity, a regularized theory featuring anisotropic scaling. The pcGR framework bridges GR with modified gravitational theories through the introduction of a minimal length scale. Focusing on Schwarzschild black holes, we derive the Wheeler-deWitt equation, obtaining a quantized description of pcGR. Using perturbative methods and semi-classical approximations, we analyze the solutions of the equations and their physical implications. A key finding is the avoidance of the central singularity due to nonlinear interaction terms in the Hořava-Lifshitz action. Notably, extrinsic curvature (kinetic energy) contributions prove essential for singularity resolution, even in standard GR. Furthermore, the theory offers new perspectives on dark energy, proposing an alternative mechanism for its accumulation. Full article

In this work, we apply fractional calculus to study quantum cosmology. Specifically, our Wheeler-DeWitt (WDW) equation includes a Friedman-Robertson-Walker (FRW) geometry, a radiation fluid, a positive cosmological constant ($\mathsf{\Lambda }$), and an ad-hoc potential. We employ the Riesz fractional derivative, which introduces a parameter $\alpha$, where $1<\alpha \le 2$, in the WDW equation. We investigate numerically the tunneling probability for the Universe to emerge using a suitable WKB approximation. Our findings are as follows. When we decrease the value of $\alpha$, the tunneling probability also decreases, suggesting that if fractional features could be considered to ascertain among different early universe scenarios, then the value $\alpha =2$ (meaning strict locality and standard cosmology) would be the most likely. Finally, our results also allow for an interesting discussion between selecting values for $\mathsf{\Lambda }$ (in a non-fractional conventional set-up) versus balancing, e.g., both $\mathsf{\Lambda }$ and $\alpha$ in the fractional framework. Full article

We recently proved that in our model of quantum gravity, the solutions to the quantized version of the full Einstein equations or to the Wheeler–DeWitt equation could be expressed as products of spatial and temporal eigenfunctions, or eigendistributions, of self-adjoint operators acting in corresponding separable Hilbert spaces. Moreover, near the big bang singularity, we derived sharp asymptotic estimates for the temporal eigenfunctions. In this paper, we show that, by using these estimates, there exists a complete sequence of unitarily equivalent eigenfunctions which can be extended past the singularity by even or odd mirroring as sufficiently smooth functions such that the extended functions are solutions of the appropriately extended equations valid in $\mathbb{R}$ in the classical sense. We also use this phenomenon to explain the missing antimatter. Full article

Within the framework of symmetric teleparallel $f\left(Q\right)$-gravity, using a connection defined in the non-coincidence gauge, we derive the Wheeler–DeWitt equation of quantum cosmology. The gravitational field equation in $f\left(Q\right)$-gravity permits a minisuperspace description, rendering the Wheeler–DeWitt equation a single inhomogeneous partial differential equation. We use the power-law $f\left(Q\right)=f_0{Q}^{\mu }$ model, and with the application of linear quantum observables, we calculate the wave function of the universe. Finally, we investigate the effects of the quantum correction terms in the semi-classical limit. Full article

Considering the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and the Einstein scalar field system as an underlying gravitational model to construct fractional cosmological models has interesting implications in both classical and quantum regimes. Regarding the former, we just review the most fundamental approach to establishing an extended cosmological model. We demonstrate that employing new methodologies allows us to obtain exact solutions. Despite the corresponding standard models, we cannot use any arbitrary scalar potentials; instead, it is determined from solving three independent fractional field equations. This article concludes with an overview of a fractional quantum/semi-classical model that provides an inflationary scenario. Full article

We find a novel phenomenon in the solution to the Wheeler–DeWitt equation by solving numerically the equation assuming $O\left(4\right)$-symmetry and imposing the Hartle–Hawking wave function as a boundary condition. In the slow-roll limit, as expected, the numerical solution gives the most dominant steepest-descent that describes the probability distribution for the initial condition of a universe. The probability is consistent with the Euclidean computations, and the overall shape of the wave function is compatible with analytical approximations, although there exist novel differences in the detailed probability computation. Our approach gives an alternative point of view for the no-boundary wave function from the wave function point of view. Possible interpretations and conceptual issues of this wave function are discussed. Full article

Quantum de Sitter geometry is discussed using elementary field operator algebras in Krein space quantization from an observer-independent point of view, i.e., ambient space formalism. In quantum geometry, the conformal sector of the metric becomes a dynamical degree of freedom, which can be written in terms of a massless minimally coupled scalar field. The elementary fields necessary for the construction of quantum geometry are introduced and classified. A complete Krein–Fock space structure for elementary fields is presented using field operator algebras. We conclude that since quantum de Sitter geometry can be constructed by elementary fields operators, the geometry quantum state is immersed in the Krein–Fock space and evolves in it. The total number of accessible quantum states in the universe is chosen as a parameter of quantum state evolution, which has a relationship with the universe’s entropy. Inspired by the Wheeler–DeWitt constraint equation in cosmology, the evolution equation of the geometry quantum state is formulated in terms of the Lagrangian density of interaction fields in ambient space formalism. Full article

Grassmann variables are used to formally transform a system with constraints into an unconstrained system. As a result, the Schrödinger equation arises instead of the Wheeler–DeWitt one. The Schrödinger equation describes a system’s evolution, but a definition of the scalar product is needed to calculate the mean values of the operators. We suggest an explicit formula for the scalar product related to the Klein–Gordon scalar product. The calculation of the mean values is compared with an etalon method in which a redundant degree of freedom is excluded. Nevertheless, we note that a complete correspondence with the etalon picture is not found. Apparently, the picture with Grassmann variables requires a further understanding of the underlying Hilbert space. Full article

In the particular configuration of the scalar field k-essence in the Wheeler–DeWitt quantum equation, for some age in the Bianchi type I anisotropic cosmological model, a fractional differential equation for the scalar field arises naturally. The order of the fractional differential equation is $\beta =\frac{2\alpha }{2\alpha -1}$. This fractional equation belongs to different intervals depending on the value of the barotropic parameter; when ${\omega }_X\in [0,1]$, the order belongs to the interval $1\le \beta \le 2$, and when ${\omega }_X\in [-1,0)$, the order belongs to the interval $0<\beta \le 1$. In the quantum scheme, we introduce the factor ordering problem in the variables $(\mathsf{\Omega },\varphi )$ and its corresponding momenta $({\mathsf{\Pi }}_{\mathsf{\Omega }},{\mathsf{\Pi }}_{\varphi })$, obtaining a linear fractional differential equation with variable coefficients in the scalar field equation, then the solution is found using a fractional power series expansion. The corresponding quantum solutions are also given. We found the classical solution in the usual gauge N obtained in the Hamiltonian formalism and without a gauge. In the last case, the general solution is presented in a transformed time $T\left(\tau \right)$; however, in the dust era we found a closed solution in the gauge time $\tau$. Full article