This paper uses the relation of the cosmic scale factor and scalar field to solve Wheeler-DeWitt equation, gives the tunnel effect of the cosmic scale factor a and quantum potential well of scalar field, and makes it fit with the physics of cosmic quantum birth. By solving Wheeler-DeWitt equation we achieve a general probability distribution of the cosmic birth, and give the analysis of cosmic quantum birth.
The radial Wheeler--De Witt equation on the asymptotically AdS spacetime proposed in [9] has as its semiclassical solution the wave function that asymptotically satisfies the conformal Ward identity, exemplifying the AdS/CFT correspondence. In this paper we show that this results holds also in the case of a complete quantum solution of the radial Wheeler--De Witt equation. It turns out that if the wavefunction is expanded in the parameter $ρ$ with $ρ\rightarrow0$ defines the asymptotic boundary of the spacetime, the quantum loop corrections to the semiclassical wave are of subleading order.
We study the energy representation of conformal quantum mechanics as the Whittaker vector without specifying classical Lagrangian. We show that a generating function of expectation values among two excited states of the dilatation operator in conformal quantum mechanics is a solution to the Wheeler-DeWitt equation and it corresponds to the AdS2 partition function evaluated as the minisuperspace wave function in Liouville field theory. We also show that the dilatation expectation values in conformal quantum mechanics lead to the asymptotic smoothed counting function of the Riemann zeros.
Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi Class A cosmologies. In particular, we consider General Relativity, minimally coupled scalar field gravity and Hybrid Gravity as paradigmatic examples of the approach. Several invariant solutions are determined and classified according to the form of the scalar field potential. The approach gives rise to a suitable method to select classical solutions and it is based on the first principle of the existence of symmetries.
Bouncing models are alternatives to inflationary cosmology that replace the initial Big-Bang singularity by a `bouncing' phase. A deeper understanding of the initial conditions of the universe, in these scenarios, requires knowledge of quantum aspects of bouncing models. In this work, we propose two classes of bouncing models that can be studied with great analytical ease and hence, provide test-bed for investigating more profound problems in quantum cosmology of bouncing universes. Our model's two key ingredients enable us to do straightforward analytical calculations: (i) a convenient parame…
Modified gravity theories have the potential of explaining the recent acceleration of the Universe without resorting to the mysterious concept of dark energy. In particular, it has been pointed out that matter-geometry coupling may be responsible for the recent cosmological dynamics of the Universe, and matter itself may play a more fundamental role in the description of the gravitational processes that usually assumed. We study the quantum cosmology of the $f(R,T)$ gravity theory, in which the effective Lagrangian of the gravitational field is given by an arbitrary function of the Ricci scala…
This work investigates the influence of a probe string on the complexity of braneworld according to the CA (Complexity equals action) conjecture within the Horndeski gravity. In the current study, it is considered that scalar fields that source Horndeski gravity has a spatial dependence. In addition, our system contains a particle moving on the boundary, which corresponds to the insertion of a fundamental string in the higher dimensional bulk. Such an effect is given by the Nambu-Goto term, which also incorporates the time-dependence and evolution in our system. Both warp factor, scalar field,…
The tunneling wave function of the universe is calculated exactly for a de Sitter minisuperspace model with a massless conformally coupled scalar field, both by solving the Wheeler-DeWitt equation and by evaluating the Lorentzian path integral. The same wave function is found in both approaches. The back-reaction of quantum field fluctuations on the scale factor amounts to a constant renormalization of the vacuum energy density. This is in contrast to the recent suggestion of Feldbrugge $et$ $al.$ that the back-reaction should diverge when the scale factor gets small, $a \to 0$. Similar result…
We study the time evolution of early universe which is developed by a cosmological constant $Λ_4$ and supersymmetric Yang-Mills (SYM) fields in the Friedmann-Robertson-Walker (FRW) space-time. The renormalized vacuum expectation value of energy-momentum tensor of the SYM theory is obtained in a holographic way. It includes a radiation of the SYM field, parametrized as $C$. The evolution is controlled by this radiation $C$ and the cosmological constant $Λ_4$. For positive $Λ_4$, an inflationary solution is obtained at late time. When $C$ is added, the quantum mechanical situation at early time …
In this review, we discuss effects of quantum gravity on black hole physics. After a brief review of the origin of the minimal observable length from various quantum gravity theories, we present the tunneling method. To incorporate quantum gravity effects, we modify the Klein-Gordon equation and Dirac equation by the modified fundamental commutation relations. Then we use the modified equations to discuss the tunneling radiation of scalar particles and fermions. The corrected Hawking temperatures are related to the quantum numbers of the emitted particles. Quantum gravity corrections slow down…
基于前一篇文章中演化非交换世界的思想，在演化模糊二球上构造了场论。运动方程类似于可以通过去掉Banks、Peskin和Susskind不久前导出的纯态到混合态演化方程的时间导数项而得到的方程。方程不包含明确的时间，因此遵循惠勒-德威特方程的精神。研究了场论的作用量、规范不变性、电荷和动量守恒等基本性质。标量场论的连续极限表明，相应的连续理论的背景几何由ds ^2 =-dt ^2 + t d Ω ^2给出，它使宇宙全息原理局部饱和。
One of the interesting open problems in the cosmological framework is applying quantum physics to the whole universe, consistently. Although different conceptual aspects of quantum cosmology are still very much alive, till now, all the attempts of obtaining a unique and well-defined version of quantum cosmology have been unfeasible. Motivated by what was mentioned above, in this paper, the quantum tunneling of thick brane is investigated by deriving the Wheeler-DeWitt equation and corresponding solutions. Besides, the cosmological analysis of the brane is studied based on two special cases of …
We study the null-boundaries of Wheeler-de Witt (WdW) patches in three dimensional Poincare-AdS, when the selected boundary timeslice is an arbitrary (non-constant) function, presenting some useful analytic statements about them. Special attention will be given to the piecewise smooth nature of the null-boundaries, due to the emergence of caustics and null-null joint curves. This is then applied, in the spirit of our previous paper arXiv:1806.08376, to the problem of how complexity of the CFT$_2$ groundstate changes under a small local conformal transformation according to the action (CA) prop…
We illustrate how it is possible to calculate the quantum gravitational effects on the spectra of primordial scalar/tensor perturbations starting from the canonical, Wheeler-De Witt, approach to quantum cosmology. The composite matter-gravity system is analysed through a Born-Oppenheimer approach in which gravitation is associated with the heavy degrees of freedom and matter (here represented by a scalar field) with the light ones. Once the independent degrees of freedom are identified the system is canonically quantised. The differential equation governing the dynamics of the primordial spect…
