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1.
This paper focuses on the implications of a commutative formulation that integrates branch-cutting cosmology, the Wheeler–DeWitt equation, and Hořava–Lifshitz quantum gravity. Building on a mini-superspace structure, we explore the impact of an inflaton-type scalar field on the wave function of the Universe. Specifically analyzing the dynamical solutions of branch-cut gravity within a mini-superspace framework, we emphasize the scalar field's influence on the evolution of the evolution of the wave function of the Universe. Our research unveils a helix-like function that characterizes a topologically foliated spacetime structure. The starting point is the Hořava–Lifshitz action, which depends on the scalar curvature of the branched Universe and its derivatives, with running coupling constants denoted as g i $$ {g}_i $$ . The corresponding wave equations are derived and are resolved. The commutative quantum gravity approach preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner formalism. Additionally, we delve into a mini-superspace of variables, incorporating scalar-inflaton fields and exploring inflationary models, particularly chaotic and nonchaotic scenarios. We obtained solutions for the wave equations without recurring to numerical approximations.  相似文献   

2.
This article focuses on the implications of the recently developed commutative formulation based on branch-cutting cosmology, the Wheeler–DeWitt equation, and Hořava–Lifshitz quantum gravity. Assuming a mini-superspace of variables, we explore the impact of an inflaton-type scalar field ϕ ( t ) $$ \phi (t) $$ on the dynamical equations that describe the trajectories evolution of the scale factor of the Universe, characterized by the dimensionless helix-like function ln − 1 [ β ( t ) ] $$ {\ln}^{-1}\left[\beta (t)\right] $$ . This scale factor characterizes a Riemannian foliated spacetime that topologically overcomes the big bang and big crunch singularities. Taking the Hořava–Lifshitz action as our starting point, which depends on the scalar curvature of the branched Universe and its derivatives, with running coupling constants denoted as g i $$ {g}_i $$ , the commutative quantum gravity approach preserves the diffeomorphism property of General Relativity, maintaining compatibility with the Arnowitt–Deser–Misner formalism. We investigate both chaotic and nonchaotic inflationary scenarios, demonstrating the sensitivity of the branch-cut Universe's dynamics to initial conditions and parameterizations of primordial matter content. The results suggest a continuous connection of Riemann surfaces, overcoming primordial singularities and exhibiting diverse evolutionary behaviors, from big crunch to moderate acceleration.  相似文献   

3.
We obtain a class of transformations between Brans–Dicke (BD) scalar field conformal factor of the metric and the Klein–Gordon (KG) wave (its amplitude and phase), such that the BD action described by conformaly flat (CF) metrics is reduced to the KG action. We then present a modified theory as a causal Bohmian quantum gravity by using the quantum potential back reaction effects on the Minkowski background spacetime. We also derive Hamilton–Jacobi equations of the modified theory which is useful for obtaining its de Broglie pilot wave.  相似文献   

4.
Real-time evolution plays an important role to understand the dynamics of the early Universe. It would be of importance to be able to investigate such typical time dependent processes like particle production, reheating, creation and evolution of fluctuations, etc. In this paper we derive the one-loop renormalized coupled einstein field equations of a scalar field with λϕ4 interaction in a classical curved space-time of Friedmann-Robertson-Walker type. These equations can be used to calculate quantum corrections for the dynamics in the early Universe.  相似文献   

5.
This paper is devoted to investigate the modified f(R) theory of gravity, where R represents the Ricci scalar respectively. For our current work, we consider the Friedmann-Robertson-Walker (FRW) space-time for finding solutions of field equations. Furthermore, some numerical solutions are examined by taking the Klein-Gordon Equation and using distinct values of the equation of state (EoS) parameter. In this way, we have discussed the solutions for acceleration expansion of the Universe, sub-relativistic Universe, radiation Universe, ultra-relativistic Universe, dust Universe, and stiff fluid Universe respectively. Moreover, their behaviours are examined by using power-law and exponential law techniques. The bouncing scenario is also discussed by choosing some particular values of the model parameters and observed the energy conditions, which are satisfied for a successful bouncing model. It is also concluded that some solution in f(R) theory of gravity supports the concept of exotic matter and accelerated expansion of the Universe due to a large amount of negative pressure.  相似文献   

6.
本文利用Hartle和Hawking的方法,讨论了具有旋量场的量子宇宙学,得到了相应的Wheeler-De Witt方程。求出了具有旋量场的宇宙波函数。从波函数可以看出,当标度因子α很小时,旋量场的影响很强,具体的形式与初始条件有关,而当标度因子α很大时,旋量场的行为和标量场一样。  相似文献   

7.
The influence of short-wave turbulence on the expansion of a homogeneous and, on average, isotropic Universe was studied in Papers I–III. In the present paper we study the influence on the manner of expansion, for a complete spectrum of wavelengths, of scalar, tensor and vector perturbations. Ast»0, all waves become long (greater than the horizon); therefore, a knowledge of their influence on the averaged metric is required. It is shown that the long-wave modes of scalar and tensor perturbations which remain finite ast»0 deflect the metric for a homogeneous and, on average, isotropic Universe from the Friedmannian, giving it a form coinciding with the average quasi-isotropic solution of Lifshitz and Khalatnikov (1963). Ast»0 their contribution to the solution tends to zero. What remains to be determined is the contribution of those modes of scalar, tensor and vector perturbations which diverge ast»0. Att=0 the proposed solution for such modes becomes inapplicable. The behaviour of the metric of a homogeneous and, on average, isotropic Universe under the influence of all waves and all modes of perturbation is shown in Figure 1–3.  相似文献   

8.
In this paper we study the interacting dark energy model in the framework of Hořava-Lifshitz cosmology. Using an additional canonical scalar field, we formulate Hořava-Lifshitz cosmology with an effective interacting dark energy sector. We show that the interacting dark energy model in the framework of Hořava gravity exhibiting phantom behavior.  相似文献   

9.
In this paper, we formulate the gravitational wave equations in the hybrid metric-Palatini gravity and solve these equations to find the polarization states. This newly proposed theory is very successful in explaining the observed phenomenology based on the hybrid combination of Einstein Hilbert action and Palatini formalism of \(f(R)\) gravity. We compare the obtained results of gravitational polarized modes with the existing results in the original approaches of the hybrid combination. The difference in the results is due to the coupling of the Ricci scalar with the trace of the energy momentum tensor.  相似文献   

10.
Recently, a field theoretic model for a UV complete theory of gravity has been proposed by Hor̃ava. This theory is a non-relativistic renormalizable gravity theory which coincides with Einstein’s general relativity at large distances. Subsequently Lü et al. have formulated the modified Friedmann equations and have presented a solution in vacuum. In the present work, we rewrite the modified FRW equations in the form of usual FRW equations in Einstein gravity and consequences have been analyzed. Also the thermodynamics of the FRW universe has been studied.  相似文献   

11.
In the present investigation we are mainly concerned with a massive scalar field in an axially symmetric Bianchi type – I space-time. Einstein field equations are solved to obtain an exact cosmological model. We have used certain physically meaningful conditions for this purpose. Kinematical cosmological parameters are determined, and their dynamical aspects are discussed. It is observed that our model represents accelerated expansion of the Universe. It is observed that our model agrees with the scenario of accelerated expansion of the Universe confirmed by supernova 1a experimental data.  相似文献   

12.
Relativistic cosmological field equations are obtained for a Robertson-Walker space time interacting with viscous fluid and massive scalar field. The cosmological solutions to the field equations are obtained and the nature of the scalar field as well as the viscous fluid are studied. It is found that the solutions obtained are realistic only for a closed Universe. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

13.
Any attempt at unification of gravity with quantum physics inevitably leads to the Planck length, usually interpreted as defining the distance scale at which quantum corrections to general relativity are expected to become important. Here we arrive at a scalelength of the same magnitude from the cosmological requirement that gravitating vacuum or zero-point energy does not overdominate the dynamics of the Universe. Other cosmological considerations are again seen to imply such a constraining lower scalelength.  相似文献   

14.
We consider a cosmological model in which a scalar field is non-minimally coupled to scalar torsion and a vector field through two coupling functions in the framework of teleparallel gravity. The explicit forms of the coupling functions and the scalar field potential are explored, under the assumption that the Lagrangian admits the Noether symmetry in the Friedmann–Lemaître–Robertson–Walker (FLRW) space–time. The existence of such symmetry allows to solve the equations of motion and achieve exact solutions of the scale factor, scalar and vector fields. It is found that the vector field contributes significantly in the accelerating expansion of the universe in the early times, while the scalar field plays an essential role in the late times.  相似文献   

15.
Here we present an inhomogeneous cosmological model, in 2+1 gravity, which satisfy all the energy conditions, although it generates non deaccelerated universes. We work in a self-similar 2+1 gravity scenario, in order to simplify the equations system and to allow us to find analytical and simple solutions. Our propose is basically to improve our understanding on the role of inhomogeneities on the acceleration of the Universe.  相似文献   

16.
We consider an equation of motion for Glashow–Weinberg–Salam model and apply the semiclassical Hamilton–Jacobi process and WKB approximation in order to compute the tunneling probability of W-bosons in the background of electromagnetic field to analyze the quantum gravity effects of charged black hole(BH) in Einstein–Gauss–Bonnet gravity theory. After this, we examine the quantum gravity influences on the generalized Lagrangian field equation. We make clear that quantum gravity effects leave the remnants on the tunneling radiation becomes non-thermal. Moreover, we analyze the graphical behavior of quantum gravity influences on corrected Hawking temperature for spin-1 particles for charged BHs.  相似文献   

17.
The Hawking radiation is considered as a quantum tunneling process, which can be studied in the framework of the Hamilton–Jacobi method. In this study, we present the wave equation for a mass generating massive and charged scalar particle (boson). In sequel, we analyse the quantum tunneling of these bosons from a generic 4-dimensional spherically symmetric black hole. We apply the Hamilton–Jacobi formalism to derive the radial integral solution for the classically forbidden action which leads to the tunneling probability. To support our arguments, we take the dyonic Reissner–Nordström black hole as a test background. Comparing the tunneling probability obtained with the Boltzmann formula, we succeed in reading the standard Hawking temperature of the dyonic Reissner–Nordström black hole.  相似文献   

18.
Recently Hor̆ava has proposed a non-relativistic renormalisable gravity theory with higher spatial derivatives in four dimensions which reduces to Einstein’s gravity at large distances with a non-vanishing cosmological constant but with improved UV behaviour. In this paper, we have considered the Friedman-Lema?tre-Robertson-Walker cosmological model in Hor̆ava gravity and the emergent scenario for all values of the spatial curvature k (=0,±1) has been studied. As a result, there are constraints on the parameters involved.  相似文献   

19.
The f(R) theories of gravity have been interested in recent years. A considerable amount of work has been devoted to the study of modified field equations with the assumption of constant Ricci scalar which may be zero or nonzero. In this paper, the exact vacuum solutions of plane symmetric spacetime are analyzed in f(R) theory of gravity. The modified field equations are studied not only for R=constant but also for general case R≠constant. In particular, we show that the Novotný-Horský and anti-de Sitter spacetimes are the exact solutions of the field equations with the non-zero constant Ricci scalar. Finally, the family of solutions with R≠constant is obtained explicitly which includes the Novotný-Horský, Kottler-Whittaker, Taub and conformally flat spacetimes.  相似文献   

20.
Under the assumption of a power law between the expansion factor of the Universe and the scalar field of the second self-creation theory proposed by G. A. Barber, the cosmological equations are reduces to quadratures. Several exact solutions are obtained, among them linearly expanding and inflationary universes with a barotropic equation of state.  相似文献   

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