The structure of perturbative quantum gravity on a de Sitter background

Classical gravitation on de Sitter space suffers from a linearization instability. One consequence is that the causal response to a spatially localized distribution of positive energy cannot be globally regular. We use this fact to show that no causal Green's function can give the correct linearized response to certain bilocalized distributions, even though these distributions obey the constraints of linearization stability. We avoid the problem by working on the open submanifold spanned by conformal coordinates. The retarded Green's function is first computed in a simple gauge, then the rest of the propagator is inferred by analyticity — up to the usual ambiguity about real, analytic and homogeneous terms. We show that the latter can be chosen so as to give a propagator which does not grow in any direction. The ghost propagator is also given and the interaction vertices are worked out.     

Remarks on quantum field theory on de Sitter and anti-de Sitter space-times

This is a short review of work done in common with Jacques Bros, Michel Gaudin, Ugo Moschella, and Vincent Pasquier. Among results are explicit K?llén?CLehmann representations for products of two free-field two-point functions in the de Sitter and the anti-de Sitter spaces and applications to particle decay.     

Conformal linear gravity in de Sitter space II

From the group theoretical point of view, it is proved that the theory of linear conformal gravity should be written in terms of a tensor field of rank-3 and mixed symmetry (Binegar et al. in Phys. Rev. D 27:2249, 1983). We obtained such a field equation in de Sitter space (Takook et al. in J. Math. Phys. 51:032503, 2010). In this paper, a proper solution to this equation is obtained as a product of a generalized polarization tensor and a massless scalar field and then the conformally invariant two-point function is calculated. This two-point function is de Sitter invariant and free of any pathological large-distance behavior.     

Positive-energy irreps of the quantum anti de Sitter algebra

We obtain positive-energy irreducible representations of theq-deformed anti de Sitter algebraU _q (so(3, 2)) by deformation of the classical ones. When the deformation parameterq isN-th root of unity, all these irreducible representations become unitary and finite-dimensional. Generically, their dimensions are smaller than those of the corresponding finite-dimensional non-unitary representations ofso(3, 2). We discuss in detail the singleton representations, i.e. the Di and Rac. WhenN is odd, the Di has dimension 1/2(N ²–1) and the Rac has dimension 1/2(N ²+1), while ifN is even, both the Di and Rac have dimension 1/2N ². These dimensions are classical only forN=3 when the Di and Rac are deformations of the two fundamental non-unitary representations ofso(3, 2).Presented at the 4th Colloquium Quantum groups and integrable systems, Prague, 22–24 June 1995.On leave from Bulgarian Acad. Sci., Institute of Nuclear Research and Nuclear Energy, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria.On leave from Pennsylvania State University (Fulbright scholar).     

Higher dimensional Vaidya metric in Einstein and de Sitter background

Spherically symmetric non-static higher dimensional metrics are considered in connection with Einstein’s field equations. Two exact solutions are derived. One of them corresponds to a mixture of perfect fluid and pure radiation field and represents higher dimensional Vaidya metric in the cosmological background of Einstein static universe. The other corresponds to a pure radiation field and represents higher dimensional Vaidya metric in the background de Sitter universe. For both of these solutions, the cosmological constant is taken to be non-zero. Many known solutions are derived as particular cases.     

Fluctuation with dust of de Sitter ground state of scalar-tensor gravity

An exact de Sitter solution of scalar-tensor gravity is found in our recent work, in which the non-minimal coupling scalar is rolling along a non-constant potential. Based on this solution, a dust-filled FRW universe is explored in frame of scalar-tensor gravity in this article. The effective dark energy induced by the sole non-minimal scalar can be quintessence-like, phantom-like, and more significantly, can cross the phantom divide. The rich and varied properties of scalar-tensor gravity even with only one scalar is shown.     

One loop vacuum polarization in a locally de Sitter background

We compute the one loop vacuum polarization from massless, minimally coupled scalar QED in a locally de Sitter background. Gauge invariance is maintained through the use of dimensional regularization, whereas conformal invariance is explicitly broken by the scalar kinetic term as well as through the conformal anomaly. A fully renormalized result is obtained. The one loop corrections to the linearized, effective field equations do not vanish when evaluated on-shell. In fact the on-shell one loop correction depends quadratically on the inflationary scale factor, similar to a photon mass. The contribution from the conformal anomaly is insignificant by comparison.     

The background scale Ward identity in quantum gravity

We show that with suitable choices of parametrization, gauge fixing and cutoff, the anomalous variation of the effective action under global rescalings of the background metric is identical to the derivative with respect to the cutoff, i.e. to the beta functional, as defined by the exact RG equation. The Ward identity and the RG equation can be combined, resulting in a modified flow equation that is manifestly invariant under global background rescalings.     

Reissner-Nordstroem de Sitter黑洞的量子隧穿效应

运用Parikh的量子隧穿模型，研究了Reissner—Nordstrom de Sitter黑洞的量子隧穿效应。结果表明，在能量守恒的条件下，黑洞外视界和宇宙视界处的粒子出射率与Bekenstein—Hawking熵有关，辐射谱不再是严格的纯热谱。     

de Sitter invariant gravity coupled with matter and its cosmological consequences

A new mathematical framework for de Sitter invariant gravity is described. Gauge symmetry follows the pattern of symmetry breaking; O(4, 2) → O(4, 1) → O(3, 1). Intimate relationships between spacetime and matter are exhibited via the interaction of gravity with scalar and spinor fields. The relevance of these results to GUT cosmology is discussed. It is shown that the cosmological constant is zero after the phase transition.     

Gauge-invariant metric fluctuations from NKK theory of gravity: de Sitter expansion

In this Letter we study gauge-invariant metric fluctuations from a noncompact Kaluza–Klein (NKK) theory of gravity in de Sitter expansion. We recover the well-known result δρ/ρ?2Φ$\delta \rho /\rho ?2\Phi$, obtained from the standard 4D semiclassical approach to inflation. The spectrum for these fluctuations should be dependent of the fifth (spatial-like) coordinate.     

Probing Planckian physics in de Sitter space with quantum correlations

We study the quantum correlation and quantum communication channel of both free scalar and fermionic fields in de Sitter space, while the Planckian modification presented by the choice of a particular α$\alpha$-vacuum has been considered. We show the occurrence of degradation of quantum entanglement between field modes for an inertial observer in curved space, due to the radiation associated with its cosmological horizon. Comparing with standard Bunch–Davies choice, the possible Planckian physics causes some extra decrement on the quantum correlation, which may provide the means to detect quantum gravitational effects via quantum information methodology in future. Beyond single-mode approximation, we construct proper Unruh modes admitting general α$\alpha$-vacua, and find a convergent feature of both bosonic and fermionic entanglements. In particular, we show that the convergent points of fermionic entanglement negativity are dependent on the choice of α$\alpha$. Moreover, an one-to-one correspondence between convergent points H_c$H_c$ of negativity and zeros of quantum capacity of quantum channels in de Sitter space has been proved.     

用圈量子引力解除Schwarichild-de Sitter黑洞的时空奇点

通过引入圈量子引力中holonomy基本变量的类比变量和采用相应的量子化方法,对Schwarichild-de Sitter黑洞中心附近的引力场进行量子化.分析和计算了黑洞中心附近的1r和曲率标量的谱分布,得到了它们均存在有限上界的结果.通过求解经典时空奇点r=0附近的量子哈密顿约束方程,给出了黑洞波函数在黑洞中心附近的时间演化行为,得到了该波函数可以通过经典奇点进行量子演化的结果.     

Dynamics and quantum entanglement of two-level atoms in de Sitter spacetime

In the framework of open quantum systems, we study the internal dynamics of both freely falling and static two-level atoms interacting with quantized conformally coupled massless scalar field in de Sitter spacetime. We find that the atomic transition rates depend on both the nature of de Sitter spacetime and the motion of atoms, interestingly the steady states for both cases are always driven to being purely thermal, regardless of the atomic initial states. This thermalization phenomenon is structurally similar to what happens to an elementary quantum system immersed in a thermal field, and thus reveals the thermal nature of de Sitter spacetime. Besides, we find that the thermal baths will drive the entanglement shared by the freely falling atom (the static atom) and its auxiliary partner, a same two-level atom which is isolated from external fields, to being sudden death, and the proper time for the entanglement to be extinguished is computed. We also analyze that such thermalization and disentanglement phenomena, in principle, could be understood from the perspective of table-top simulation experiment.