Space-time curvature due to quantum vacuum fluctuations: An alternative to dark energy?

It is pointed out that quantum vacuum fluctuations may give rise to a curvature of space-time equivalent to the curvature currently attributed to dark energy. A simple calculation is made, involving plausible assumptions within the framework of quantized gravity, which suggests that the value of the dark energy density is roughly given by the product of Newton's constant times the quantity m⁶c⁴?−4, m being a typical mass of elementary particles. The estimate is compatible with observations.     

The length operator in Loop Quantum Gravity

The dual picture of quantum geometry provided by a spin network state is discussed. From this perspective, we introduce a new operator in Loop Quantum Gravity—the length operator. We describe its quantum geometrical meaning and derive some of its properties. In particular we show that the operator has a discrete spectrum and is diagonalized by appropriate superpositions of spin network states. A series of eigenstates and eigenvalues is presented and an explicit check of its semiclassical properties is discussed.     

Spin-0 and spin-1/2 particles in a constant scalar-curvature background

We study the Klein-Gordon and Dirac equations in the presence of a background metric ds²=−dt²+dx²+e^−2gx(dy²+dz²) in a semi-infinite lab (x>0). This metric has a constant scalar-curvature R=6g² and is produced by a perfect fluid with equation of state p=−ρ/3. The eigenfunctions of spin-0 and spin-1/2 particles are obtained exactly, and the quantized energy eigenvalues are compared. It is shown that both of these particles must have nonzero transverse momentum in this background. We show that there is a minimum energy E²_min=m²c⁴+g²c²?² for bosons (E_KG>E_min), while the fermions have no specific ground state (E_Dirac>mc²).     

Semiclassical regime of Regge calculus and spin foams

Recent attempts to recover the graviton propagator from spin foam models involve the use of a boundary quantum state peaked on a classical geometry. The question arises whether beyond the case of a single simplex this suffices for peaking the interior geometry in a semiclassical configuration. In this paper we explore this issue in the context of quantum Regge calculus with a general triangulation. Via a stationary phase approximation, we show that the boundary state succeeds in peaking the interior in the appropriate configuration, and that boundary correlations can be computed order by order in an asymptotic expansion. Further, we show that if we replace at each simplex the exponential of the Regge action by its cosine—as expected from the semiclassical limit of spin foam models—then the contribution from the sign-reversed terms is suppressed in the semiclassical regime and the results match those of conventional Regge calculus.     

Alternative quantization of the Hamiltonian in loop quantum cosmology

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities. In this Letter, we quantize the Lorentz term of the gravitational Hamiltonian constraint in the spatially flat FRW model by two approaches different from that of the Euclidean term. One of the approaches is very similar to the treatment of the Lorentz part of Hamiltonian in loop quantum gravity and hence inherits more features from the full theory. Two symmetric Hamiltonian constraint operators are constructed respectively in the improved scheme. Both of them are shown to have the correct classical limit by the semiclassical analysis. In the loop quantum cosmological model with a massless scalar field, the effective Hamiltonians and Friedmann equations are derived. It turns out that the classical big bang is again replaced by a quantum bounce in both cases. Moreover, there are still great possibilities for the expanding universe to recollapse due to the quantum gravity effect.     

Accelerating universe in two-dimensional noncommutative dilaton cosmology

We show that the phase transition from the decelerating universe to the accelerating universe, which is of relevance to the cosmological coincidence problem, is possible in the semiclassically quantized two-dimensional dilaton gravity by taking into account the noncommutative field variables during the finite time. Initially, the quantum-mechanically induced energy from the noncommutativity among the fields makes the early universe decelerate and subsequently the universe is accelerating because the dilaton driven cosmology becomes dominant later.     

Cosmological implications of Károlyházy uncertainty relation

Károlyházy uncertainty relation, which can be viewed also as a relation between UV and IR scales in the framework of an effective quantum field theory satisfying a black hole entropy bound, strongly favors the existence of dark energy with its observed value. Here we estimate the dynamics of dark energy predicted by the Károlyházy relation during the cosmological evolution of the universe.     

Quantum gravity, minimum length and Keplerian orbits

We conjecture that the modified commutation relations suggested in the context of quantum gravity (QG) persist also in the classical limit, if the momentum of the classical object is not too large, and calculate the corresponding perihelion precession rate for Keplerian orbits. The main result obtained in this Letter is not new. However the derivation is much simpler than the one proposed by Benczik et al. in [S. Benczik, L.N. Chang, D. Minic, N. Okamura, S. Rayyan, T. Takeuchi, Phys. Rev. D 66 (2002) 026003, arXiv:hep-th/0204049] where the corresponding precession rate was calculated for the first time. Our interpretation of the result is also quite different.     

Random versus holographic fluctuations of the background metric. I. (Cosmological) running of space–time dimension

A profound quantum-gravitational effect of space–time dimension running with respect to the size of space–time region has been discovered a few years ago through the numerical simulations of lattice quantum gravity in the framework of causal dynamical triangulation [hep-th/0505113] as well as in renormalization group approach to quantum gravity [hep-th/0508202]. Unfortunately, along these approaches the interpretation and the physical meaning of the effective change of dimension at shorter scales is not clear. The aim of this Letter is twofold. First, we find that box-counting dimension in face of finite resolution of space–time (generally implied by quantum gravity) shows a simple way how both the qualitative and the quantitative features of this effect can be understood. Second, considering two most interesting cases of random and holographic fluctuations of the background space, we find that it is random fluctuations that gives running dimension resulting in modification of Newton's inverse square law in a perfect agreement with the modification coming from one-loop gravitational radiative corrections.     

The entangled accelerating universe

Using the known result that the nucleation of baby universes in correlated pairs is equivalent to spacetime squeezing, we show in this Letter that there exists a T-duality symmetry between two-dimensional warp drives, which are physically expressible as localized de Sitter little universes, and two-dimensional Tolman–Hawking and Gidding–Strominger baby universes respectively correlated in pairs, so that the creation of warp drives is also equivalent to spacetime squeezing. Perhaps more importantly, it has been also seen that the nucleation of warp drives entails a violation of the Bell's inequalities, and hence the phenomena of quantum entanglement, complementarity and wave function collapse. These results are generalized to the case of any dynamically accelerating universe filled with dark or phantom energy whose creation is also physically equivalent to spacetime squeezing and to the violation of the Bell's inequalities, so that the universe we are living in should be governed by essential sharp quantum theory laws and must be a quantum entangled system.     

Lorentz violation at high energy: Concepts, phenomena, and astrophysical constraints

We consider here the possibility of quantum gravity induced violation of Lorentz symmetry (LV). Even if suppressed by the inverse Planck mass such LV can be tested by current experiments and astrophysical observations. We review the effective field theory approach to describing LV, the issue of naturalness, and many phenomena characteristic of LV. We discuss some of the current observational bounds on LV, focusing mostly on those from high energy astrophysics in the QED sector at order E/M_Planck. In this context, we present a number of new results which include the explicit computation of rates of the most relevant LV processes, the derivation of a new photon decay constraint, and modification of previous constraints taking proper account of the helicity dependence of the LV parameters implied by effective field theory.     

Space–time dimensionality from brane collisions

Collisions and subsequent decays of higher dimensional branes leave behind three-dimensional branes and anti-branes, one of which could play the rôle of our universe. This process also leads to the production of one-dimensional branes and anti-branes, however their number is expected to be suppressed. Brane collisions may also lead to the formation of bound states of branes. Their existence does not alter this result, it just allows for the existence of one-dimensional branes captured within the three-dimensional ones.     

Non-minimally coupled canonical,phantom and quintom models of holographic dark energy

We investigate canonical, phantom and quintom models, with the various fields being non-minimally coupled to gravity, in the framework of holographic dark energy. We classify them and we discuss their cosmological implications. In particular, we examine the present value of the dark energy equation-of-state parameter and the crossing through the phantom divide, and we extract the conditions for a future cosmological singularity. The combined scenarios are in agreement with observations and reveal interesting cosmological behaviors.     

The emergence of background geometry from quantum fluctuations

We show how the quantization of two-dimensional gravity leads to an (Euclidean) quantum space–time where the average geometry is that of constant negative curvature and where the Hartle–Hawking boundary condition arises naturally.     

Topological origin of inertia

The purpose of the present article, following “Mach’s principle” (the main elements of which have contributed to the foundations of general relativity) is to propose a new (non-local) interpretation of the inertial interaction. We then suggest that the inertial interaction can be correctly described by the topological field theory proposed by Witten in 1988. In such a context, the instantaneous propagation and the infinite range of the inertial interaction might be explained in terms of the topological amplitude connected with the singular zero size gravitational instanton corresponding to the Initial Singularity of space-time.     

Quantization of triangular Lie bialgebras

We derive a universal twisting element for an arbitrary triangularγ-matrix using a simple analogue of the Fedosov quantization method. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002. The work of SLL is partially supported by RFBR grant 00-02-17-956 and the grant INTAS 00-262. The work of AASh is supported by RFBR grant 02-02-06879 and Russian Ministry of Education under the grant E-00-33-184. The work of VAD is partially supported by the grant INTAS 00-561 and by the Grant for Support of Scientific Schools 00-15-96557. The work of API is partially supported by the RFBR grant 00-01-00299.     

光与信息

光不仅是维持生命活动的主要能量来源,也是一种有效的信息载体。阐述了光作为载体与信息之间的密切联系,讨论了海森堡不确定性原理对信息的解释,即每一比特信息都对应着一个光量子,受限于所在的信息元,并且与熵的消耗相关。分别给出了满足不确定性原理条件以及超出该限制时的例子,从而证明了时间和频率的分辨率不能被同时观测,但成像仍然可以在确定性条件的限制下获得。