Field In De Sitter Spacetime Research Articles

Vacuum densities for a charged scalar field in de Sitter space-time with compact dimensions

The vacuum expectation value of the energy-momentum tensor is investigated for a charged scalar field in dS space-time with toroidally compact spatial dimensions in the presence of a classical constant gauge field. Due to the nontrivial topology, the latter gives rise to an Aharonov-Bohm-like effect on the vacuum characteristics. The vacuum energy density and stresses are even periodic functions of the magnetic flux enclosed by the compact dimensions. For small values of the comoving lengths of the compact dimensions as compared with the dS curvature radius, the effects of gravity on the topological contributions are small, and the expectation values are expressed in terms of the corresponding quantities in the Minkowski bulk by the standard conformal relation. For large values of the comoving lengths, depending on the field mass, two regimes are realized with monotonic and oscillatory damping of the expectation values. We show that the sign of the the vacuum energy density can be controlled by tuning the magnetic flux enclosed by the compact dimensions.

Long-time asymptotics of a Bohmian scalar quantum field in de Sitter space-time

We consider a model quantum field theory with a scalar quantum field in de Sitter space-time in a Bohmian version with a field ontology, i.e., an actual field configuration $\varphi({\bf x},t)$ guided by a wave function on the space of field configurations. We analyze the asymptotics at late times ($t\to\infty$) and provide reason to believe that for more or less any wave function and initial field configuration, every Fourier coefficient $\varphi_{\bf k}(t)$ of the field is asymptotically of the form $c_{\bf k}\sqrt{1+{\bf k}^2 \exp(-2Ht)/H^2}$, where the limiting coefficients $c_{\bf k}=\varphi_{\bf k}(\infty)$ are independent of $t$ and $H$ is the Hubble constant quantifying the expansion rate of de Sitter space-time. In particular, every field mode $\varphi_{\bf k}$ possesses a limit as $t\to\infty$ and thus "freezes." This result is relevant to the question whether Boltzmann brains form in the late universe according to this theory, and supports that they do not.

Holographic representation of higher spin gauge fields

Extending the results of \cite{Heem}, \cite{KLRS} on the holographic representation of local gauge field operators in anti de Sitter space, here we construct the bulk operators for higher spin gauge fields in the leading order of $\frac{1}{N}$ expansion. Working in holographic gauge for higher spin gauge fields, we show that gauge field operators with integer spin $s>1$ can be represented by an integration over a ball region, which is the interior region of the spacelike bulk lightcone on the boundary. The construction is shown to be AdS-covariant up to gauge transformations, and the two-point function between higher spin gauge fields and boundary higher spin current exhibit singularities on both bulk and boundary lightcones. We also comment on possible extension to the level of three-point functions and carry out a causal construction for higher spin fields in de Sitter spacetime.

Large-Scale Effect of Krein Quantization Method on the Matter Density Perturbations

According to the theoretical results obtained in usual quantum cosmology in which the field operator is constructed on the Hilbert space, the power spectrum of the scalar field fluctuations is scale invariant in the inflationary epoch. On the other hand, the observational data predict some deviation from scale-invariance in the power spectrum. It has been shown previously that by using Krein quantization method for constructing field operator, the power spectrum is obtained scale dependent (Mohsenzadeh et al. IJTP 48, 755, 2009). The main goal in this work is to investigate the effect of Krein quantization method on the matter density perturbation at present. The results show if one uses covariant two point function for mass-less minimally coupled scalar field in de Sitter space-time which is calculated via Krein quantization method, the power spectrum of primordial gravitational potential set up during inflation and the power spectrum of matter density perturbation at present deviate from scale-invariant result.

Relation between Lyapunov exponents and decoherence for real scalar fields in de Sitter spacetime

We investigate the relationship between orbital instability and decoherence in de Sitter (dS) spacetime. We consider a simple quadratic toy model proposed by Brandenberger, Laflamme and Miji\ifmmode \acute{c}\else \'{c}\fi{} of two interacting scalar fields in a dS background. It admits a modewise separation, with each mode consisting of a pair of nonautonomous coupled harmonic oscillators. We show that the (classical) maximal Lyapunov exponent of every mode equals the asymptotic rate of (quantum) von Neumann entropy production of each oscillator, assuming an initial vacuum. We find that for moderately long times after horizon crossing, orbital instability, entropy and single-mode squeezing are larger for increasing coupling strength. If the entropy of an oscillator increases more rapidly than squeezing, for example in the strong-coupling regime for not too high frequencies, the noise of every quadrature of the asymptotic state will be larger than the vacuum noise. The results suggest the possibility that simple, nonlinear interacting physical processes with unstable or chaotic classical counterparts may provide an important contribution to the effectiveness of the classicalization of cosmological scalar fields during a dS stage of spacetime expansion.

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.

Entanglement Structure in Expanding Universes

We investigate entanglement of a quantum field in de Sitter spacetime using a particle detector model. By considering the entanglement between two comoving detectors interacting with a scalar field, it is possible to detect the entanglement of the scalar field by swapping it to detectors. For the massless minimal scalar field, we find that the entanglement between the detectors cannot be detected when their physical separation exceeds the Hubble horizon scale. This behavior supports the appearance of the classical nature of quantum fluctuations generated during the inflationary era.

Massless scalar field in de Sitter spacetime: unitary quantum time evolution

We prove that, under the standard conformal scaling, a free scalar field in de Sitter spacetime admits an O(4)-invariant Fock quantization such that time evolution is unitarily implemented. Since this applies in particular to the massless case, this result disproves previous claims in the literature. We discuss the relationship between this quantization with unitary dynamics and the family of O(4)-invariant Hadamard states given by Allen and Folacci, as well as with the Bunch–Davies vacuum.

Correlators, Feynman Diagrams, and Quantum No-hair in deSitter Spacetime

We provide a parametric representation for position-space Feynman integrals of a massive, self-interacting scalar field in deSitter spacetime, for an arbitrary graph. The expression is given as a multiple contour integral over a kernel whose structure is determined by the set of all trees (or forests) within the graph, and it belongs to a class of generalized hypergeometric functions. We argue from this representation that connected deSitter n-point vacuum correlation functions have exponential decay for large proper time-separation, and also decay for large spatial separation, to arbitrary orders in perturbation theory. Our results may be viewed as an analog of the so-called cosmic-no-hair theorem in the context of a quantized test scalar field. This work has significant overlap with a paper by Marolf and Morrison, which is being released simultaneously.

Do scale-invariant fluctuations imply the breaking of de Sitter invariance?

The quantization of the massless minimally coupled (mmc) scalar field in de Sitter spacetime is known to be a non-trivial problem due to the appearance of strong infrared (IR) effects. In particular, the scale-invariance of the CMB power-spectrum – certainly one of the most successful predictions of modern cosmology – is widely believed to be inconsistent with a de Sitter invariant mmc two-point function. Using a Cesaro-summability technique to properly define an otherwise divergent Fourier transform, we show in this Letter that de Sitter symmetry breaking is not a necessary consequence of the scale-invariant fluctuation spectrum. We also generalize our result to the tachyonic scalar fields, i.e. the discrete series of representations of the de Sitter group, that suffer from similar strong IR effects.

Spontaneous symmetry breaking in inflationary cosmology: On the fate of Goldstone bosons

We argue that in an inflationary cosmology a consequence of the lack of time translational invariance is that spontaneous breaking of a continuous symmetry and Goldstone's theorem do not imply the existence of massless Goldstone modes. We study spontaneous symmetry breaking in an $O(2)$ model, and implications for $O(N)$ in de Sitter space-time. The Goldstone mode acquires a radiatively generated mass as a consequence of infrared divergences, and the continuous symmetry is spontaneously broken for any finite $N$; however there is a first order phase transition as a function of the Hawking temperature ${T}_{H}=H/2\ensuremath{\pi}$. For $O(2)$ the symmetry is spontaneously broken for ${T}_{H}<{T}_{c}={\ensuremath{\lambda}}^{1/4}v/2.419$ where $\ensuremath{\lambda}$ is the quartic coupling and $v$ is the tree-level vacuum expectation value and the Goldstone mode acquires a radiatively generated mass ${\mathcal{M}}_{\ensuremath{\pi}}^{2}\ensuremath{\propto}{\ensuremath{\lambda}}^{1/4}H$. The first order nature of the transition is a consequence of the strong infrared behavior of minimally coupled scalar fields in de Sitter space-time; the jump in the order parameter at ${T}_{H}={T}_{c}$ is ${\ensuremath{\sigma}}_{0c}\ensuremath{\simeq}0.61H/{\ensuremath{\lambda}}^{1/4}$. In the strict $N\ensuremath{\rightarrow}\ensuremath{\infty}$ the symmetry cannot be spontaneously broken. Furthermore, the lack of kinematic thresholds imply that the Goldstone modes decay into Goldstone and Higgs modes by emission and absorption of superhorizon quanta.

QUANTUM EFFECTS IN HIGHER-DIMENSIONAL COSMOLOGICAL MODELS

Vacuum energy density and stresses are investigated for a scalar field in de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions and in anti-de Sitter spacetime with two parallel branes. On the branes the field obeys the Robin boundary conditions. The behavior of the vacuum expectation values is discussed in various asymptotic regions of the parameters. Applications are given to Randall-Sundrum type braneworlds.

Conformal graviton two-point function in de Sitter space

The conformally invariant linearized de Sitter gravitational wave equation has recently received a lot of attention. In this article, using the ambient space notations, we solve this field equation in five various cases. In each case, it has been shown that the solution can be written as the product of a generalized symmetric polarization tensor of rank 2 and a massless minimally or conformally coupled scalar field in de Sitter space-time. The conformally covariant graviton two-point functions have been calculated in terms of the massless minimally or conformally coupled scalar two-point functions, using ambient space notations. In the case of massless minimally coupled scalar field, the Krien space quantization has been used to avoid the violation of de Sitter invariance. The two-point functions are expressed in terms of de Sitter intrinsic coordinates from their ambient space counterparts, which are free of any theoretical problem.

The Worldline Quantum Mechanics Model at Finite Temperature, Which Is Dual to the Static Patch Observer in de Sitter Space

A simple conformal quantum mechanics model of a d-component variable is proposed, which exactly reproduces the retarded Green functions and conformal weights of conformally coupled scalar fields in de Sitter spacetime seen by a static patch observer. It is found that the action integral of this model is automatically expressed by a complex integral over the time variable t along a closed contour in a way which is typical to the Schwinger-Keldysh formalism of a thermofield theory. Hence this model is at finite temperature. The case of conformally coupled scalar fields in 3d Schwarzschild de Sitter space is also considered and then a large-N matrix model is obtained.

Infrared Behavior and Gauge Artifacts in de Sitter Spacetime: The Photon Field

We study the infrared (long-distance) behavior of the free photon field in de Sitter spacetime. Using a two-parameter family of gauge-fixing terms, we show that the infrared (IR) behavior of the two-point function is highly gauge-dependent and ranges from vanishing to growing. This situation is in disagreement with its counterpart in flat spacetime, where the two-point function vanishes in the IR region for any choice of the gauge-fixing parameters. A criterion to isolate the physical part of the two-point function is given and is shown to lead to a well-behaved two-point function in the IR region.

Large-Scale Suppression from Stochastic Inflation

We show nonperturbatively that the power spectrum of a self-interacting scalar field in de Sitter space-time is strongly suppressed on large scales. The cutoff scale depends on the strength of the self-coupling, the number of e folds of quasi-de Sitter evolution, and its expansion rate. As a consequence, the two-point correlation function of field fluctuations is free from infrared divergencies.

Fermionic vacuum polarization by a cosmic string in de Sitter spacetime

We investigate the fermionic condensate and the vacuum expectation value of the energy-momentum tensor for a massive spinor field in de Sitter spacetime in the presence of a straight cosmic string. By using the Abel-Plana summation formula, we explicitly extract from the expectation values the contribution associated with purely de Sitter space, thereafter remaining the expectation values induced by the cosmic string alone. Nevertheless, the latter contains information about de Sitter gravity as well. Because the fermionic quantum vacuum fluctuations in de Sitter space have been investigated in literature, here we are mainly interested in the cosmic string-induced contributions. We observe that for a massless field, the fermionic condensate vanishes and the presence of the string does not break chiral symmetry of the massless theory. Unlike the case of a scalar field, for a massive fermionic field the vacuum expectation value of the energymomentum tensor is diagonal and the axial and radial stresses are equal to the energy density. Moreover, at large distances from the string the behavior of the string-induced parts in the vacuum densities is damping oscillatory with the amplitude decaying as the inverse fourth power of the distance. This fact is in contrast to the case of flat spacetime, in which the string-induced vacuum densities for a massive field decay exponentially with distance from the string. In the limit of large curvature radius of de Sitter space we recover the results for a cosmic string in flat spacetime.

Stress tensor fluctuations in de Sitter spacetime

The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m2/H2. In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.

Vacuum polarization by topological defects in de Sitter spacetime

In this paper we investigate the vacuum polarization effects associated with a massive quantum scalar field in de Sitter spacetime in the presence of gravitational topological defects. Specifically we calculate the vacuum expectation value of the field square, (ϕ2). Because this investigation has been developed in a pure de Sitter space, here we are mainly interested on the effects induced by the presence of the defects.

Vacuum polarization by a scalar field in de Sitter spacetime in the presence of a global monopole

In this paper we analyse the vacuum polarization effects associated with massive scalar quantum fields in a higher-dimensional de Sitter space in the presence of a global monopole. Because this analysis has been developed in a pure de Sitter space, here we are mainly interested on the effects induced by the presence of the global monopole. So, in order to achieve this objective we calculate the corresponding Wightman function, which is expressed in an integral representation and explicitly depends on the parameters associated with the presence of the monopole and the cosmological constant. Admitting that the former is closed to the unity, which corresponds to a realistic value predicted by Grand Unified Theories, it is possible to express this function as the sum of two terms: the first one corresponds to the Wightman function on the bulk where the global monopole is absent, and the second one is a contribution induced by the presence of the monopole.