Field In De Sitter Space Research Articles

Entanglement harvesting and quantum discord of alpha vacua in de Sitter space

The CPT invariant vacuum states of a scalar field in de Sitter space, called α-vacua, are not unique. We explore the α-vacua from the quantum information perspective by a pair of static Unruh-DeWitt (UDW) detectors coupled to a scalar field with either monopole or dipole coupling, which are in time-like zero separation or space-like antipodal separation. The analytical form of the reduced final state of the UDW detector is derived. We study the entanglement harvesting and quantum discord of the reduced state, which characterize the quantum entanglement and quantum correlation of the underlying α-vacua, respectively. Our results imply that the quantum entanglement gravitated by de Sitter gravity behaves quite differently for time-like and space-like separations. It experiences “sudden death” for the former and grows for the latter as the measuring time or the value of α increases. This demonstrates the nonlocal nature of quantum entanglement. For the quantum discord, we find no “sudden death” behavior, and it experiences superhorizon suppression, which explains the superhorizon decoherence in the inflationary universe scenario. Overall, the time-like or space-like quantum entanglement and correlation behave differently on their dependence of α, measuring time and spectral gaps, with details discussed in this work.

Positivity from Cosmological Correlators

Effective field theories in flat space and in anti-de Sitter space are constrained by causality and unitarity, often in the form of positivity bounds. Similar bounds have been harder to demonstrate in cosmological backgrounds, where the roles of unitarity and causality are more obscure. Fortunately, the expansion of the universe ensures that late-time cosmological correlators are effectively classical and the role of unitarity is played by classical statistical inequalities. For multi-field inflation, the resulting positivity constraints have long been known in terms of the Suyama-Yamaguchi inequality. In this paper, we demonstrate that similar statistical bounds imply nontrivial constraints for massive fields in the early universe. We show that any real anomalous dimensions for principal series fields in de Sitter space must be positive. We also derive a limit on the amplitude of particular oscillatory signals from inflation, including those arising in cosmological collider physics. Finally, we demonstrate that these constraints manifest themselves directly in the two-point statistics of matter and galaxies that will be measured in upcoming surveys.

Cosmological correlators in massless ϕ4-theory and the method of regions

The calculation of loop corrections to the correlation functions of quantum fields during inflation or in the de Sitter background presents greater challenges than in flat space due to the more complicated form of the mode functions. While in flat space highly sophisticated approaches to Feynman integrals exist, similar tools still remain to be developed for cosmological correlators. However, usually only their late-time limit is of interest. We introduce the method-of-region expansion for cosmological correlators as a tool to extract the late-time limit, and illustrate it with several examples for the interacting, massless, minimally coupled scalar field in de Sitter space. In particular, we consider the in-in correlator 〈ϕ2(η, q)ϕ(η, k1)ϕ(η, k2)〉, whose region structure is relevant to anomalous dimensions and matching coefficients in Soft de Sitter effective theory.

Light scalars at the cosmological collider

We study the self-energies of weakly interacting scalar fields in de Sitter space with one field much lighter than the Hubble scale. We argue that self-energies drastically simplify in this light limit. We illustrate this in theories with two scalar fields, one heavy and one light, interacting with one another through either cubic or quartic interactions. To regulate infrared divergences, we compute these self-energies in Euclidean de Sitter space and then carefully analytically continue to Lorentzian signature. In particular, we do this for the most general renormalizable theory of two scalar fields with even interactions to leading order in the coupling and the mass of the light field. These self-energies are determined by de Sitter sunset diagrams, whose analytic structure and UV divergences we derive. Even at very weak couplings, the light field can substantially change how the heavy field propagates over long distances. The light field’s existence may then be inferred from how it modifies the heavy field’s oscillatory contribution to the primordial bispectrum in the squeezed limit, i.e. its cosmological collider signal.

Late-time correlators and complex geodesics in de Sitter space

We study two-point correlation functions of a massive free scalar field in de Sitter space using the heat kernel formalism. Focusing on two operators in conjugate static patches we derive a geodesic approximation to the two-point correlator valid for large mass and at late times. This expression involves a sum over two complex conjugate geodesics that correctly reproduces the large-mass, late-time limit of the exact two-point function in the Bunch-Davies vacuum. The exponential decay of the late-time correlator is associated to the timelike part of the complex geodesics. We emphasize that the late-time exponential decay is in tension with the finite maximal entropy of empty de Sitter space, and we briefly discuss how non-perturbative corrections might resolve this paradox.

Even the photon propagator must break de Sitter symmetry

The propagator for the massless vector field in de Sitter space cannot maintain de Sitter invariance in the general covariant gauge, except in the exactly transverse limit. This is due to a previously overlooked Ward-Takahashi identity that the propagator must satisfy. We construct the propagator that satisfies all the necessary conditions, and that preserves cosmological symmetries and dilation, but breaks spatial special conformal transformations. Our propagator vanishes in the infrared, contrary to previously reported de Sitter invariant results, which is relevant for loop computations.

Point-splitting regularization of the stress tensor of a coupling scalar field in de Sitter space

We perform the point-splitting regularizationon the vacuum stress tensor of a coupling scalar field in de Sitter spaceunder the guidance from the adiabatically regularized Green's function.For the massive scalar field with the minimal coupling ξ = 0,the 2nd order point-splitting regularizationyields a finite vacuum stress tensorwith a positive, constant energy density,which can be identified as the cosmological constantthat drives de Sitter inflation.For the coupling ξ ≠ 0, we find that,even if the regularized Green's function is continuous, UV and IR convergent,the point-splitting regularization does notautomatically lead to an appropriate stress tensor.The coupling ξ R causes log divergent terms,as well as higher-order finite termswhich depend upon the path of the coincidence limit.After removing these unwanted terms by extra treatments,the 2nd-order regularizationfor small couplings ξ ∈ (0,1/7.04),and respectively the 0th-order regularizationfor the conformal coupling ξ=1/6,yield a finite, constant vacuum stress tensor, in analogy to the case ξ=0.For the massless field with ξ = 0 or ξ = 1/6,the point-splitting regularizationyields a vanishing vacuum stress tensor,and there is no conformal trace anomaly for ξ = 1/6.If the 4th-order regularization were taken,the regularized energy density for general ξ would be negative,which is inconsistent with the de Sitter inflation,and the regularized Green's function would be singular at the zero mass,which is unphysical.In all these cases,the stress tensor from the point-splitting regularization is equal to that from the adiabatic one. We also discuss the issue ofthe adequate order of regularization.

Noncommutative scalar field in de Sitter space–time and pair creation process

In this work, we address the process of pair creation of scalar particles in [Formula: see text] de Sitter space–time in presence of a constant electromagnetic field by applying the noncommutativity on the scalar field up to first-order in [Formula: see text]. We calculate the density of particles created in the vacuum by the mean of the Bogoliubov transformations. In contrast to a previous result, we show that noncommutativity contributes to the pair creation process. We find that the noncommutativity plays the same role of chemical potential and gives an important interest for studies at high energies.

Cosmological Spectrum of Two-Point Correlation Function from Vacuum Fluctuation of Stringy Axion Field in De Sitter Space: A Study of the Role of Quantum Entanglement

In this work, we study the impact of quantum entanglement on the two-point correlation function and the associated primordial power spectrum of mean square vacuum fluctuation in a bipartite quantum field theoretic system. The field theory that we consider is the effective theory of axion field arising from Type IIB string theory compacted to four dimensions. We compute the expression for the power spectrum of vacuum fluctuation in three different approaches, namely (1) field operator expansion (FOE) technique with the quantum entangled state, (2) reduced density matrix (RDM) formalism with mixed quantum state and (3) the method of non-entangled state (NES). For a massless axion field, in all three formalisms, we reproduce, at the leading order, the exact scale invariant power spectrum which is well known in the literature. We observe that due to quantum entanglement, the sub-leading terms for these thee formalisms are different. Thus, such correction terms break the degeneracy among the analysis of the FOE, RDM and NES formalisms in the super-horizon limit. On the other hand, for massive axion field we get a slight deviation from scale invariance and exactly quantify the spectral tilt of the power spectrum in small scales. Apart from that, for massless and massive axion field, we find distinguishable features of the power spectrum for the FOE, RDM, and NES on the large scales, which is the result of quantum entanglement. We also find that such large-scale effects are comparable to or greater than the curvature radius of the de Sitter space. Most importantly, in near future if experiments probe for early universe phenomena, one can detect such small quantum effects. In such a scenario, it is possible to test the implications of quantum entanglement in primordial cosmology.

Adiabatic regularization and Green’s function of a scalar field in de Sitter space: Positive energy spectrum and no trace anomaly

In the conventional adiabatic regularization the vacuum ultraviolet divergences of a quantum field in curved spacetime are removed by subtracting the $k$-mode of the stress tensor to the 4th-order. For a scalar field in de Sitter space, we find that the 4th-order regularized spectral energy density is negative. Moreover, the 2nd-order regularization for minimal coupling ($\xi=0$) and the 0th-order regularization for conformal coupling ($\xi=\frac16$) yield a positive and UV-convergent spectral energy density and power spectrum. The regularized stress tensor in the vacuum is maximally symmetric and can drive inflation, while its $k$-modes representing the primordial fluctuations are nonuniformly distributed. Conventional regularization of a Green's function in position space is generally plagued by a log IR divergence. Only in the massless case with $\xi=0$ or $\frac16$, we can directly regularize the Green's functions and obtain vanishing results that agree with the adiabatic regularization results. In this case, the regularized power spectrum and stress tensor are both zero, and no trace anomaly exists. To overcome the log IR divergence problem in the massive cases with $\xi=0$ and $\frac16$, we perform Fourier transformation of the regularized power spectra and obtain the regularized analytical Green's functions which are IR- and UV-convergent.

Hot cosmic qubits: late-time de Sitter evolution and critical slowing down

Temporal evolution of a comoving qubit coupled to a scalar field in de Sitter space is studied with an emphasis on reliable extraction of late-time behaviour. The phenomenon of critical slowing down is observed if the effective mass is chosen to be sufficiently close to zero, which narrows the window of parameter space in which the Markovian approximation is valid. The dynamics of the system in this case are solved in a more general setting by accounting for non-Markovian effects in the evolution of the qubit state. Self-interactions for the scalar field are also incorporated, and reveal a breakdown of late-time perturbative predictions due to the presence of secular growth.

Quantum steering for continuous variable in de Sitter space

We study the distribution of quantum steerability for continuous variables between two causally disconnected open charts in de Sitter space. It is shown that quantum steerability suffers from “sudden death” in de Sitter space, which is quite different from the behaviors of entanglement and discord because the latter always survives and the former vanishes only in the limit of infinite curvature. It is found that the attainment of maximal steerability asymmetry indicates a transition between unidirectional steerable and bidirectional steerable. Unlike in the flat space, the asymmetry of quantum steerability can be completely destroyed in the limit of infinite curvature for the conformal and massless scalar fields in de Sitter space.

Back(reaction) to the future in the Unruh-de Sitter state

Motivated by black hole physics, we define the Unruh state for a scalar field in de Sitter space. Like the Bunch-Davies state, the Unruh-de Sitter state appears thermal to a static observer. However, it breaks some of the symmetries of de Sitter space. We calculate the expectation value of the energy-momentum tensor in the Unruh-de Sitter state in two dimensions and find a non-vanishing flux of outgoing negative energy. Extrapolating the result to four dimensions, we argue that this backreacts on the initial de Sitter geometry semi-classically. Notably, we estimate that de Sitter space is destabilized on a timescale set by the gravitational entropy; analogous to black hole evaporation, the endpoint of this instability is a singular geometry outside the regime of effective field theory. Finally, we suggest that the Unruh-de Sitter state may be a natural initial state for patches of de Sitter space, and discuss the implications for slow-roll and eternal inflation, and for de Sitter thermodynamics.

Scalar correlation functions in de Sitter space from the stochastic spectral expansion

We consider light scalar fields during inflation and show how the stochastic spectral expansion method can be used to calculate two-point correlation functions of an arbitrary local function of the field in de Sitter space. In particular, we use this approach for a massive scalar field with quartic self-interactions to calculate the fluctuation spectrum of the density contrast and compare it to other approximations. We find that neither Gaussian nor linear approximations accurately reproduce the power spectrum, and in fact always overestimate it. For example, for a scalar field with only a quartic term in the potential, V=λϕ4/4, we find a blue spectrum with spectral index n−1=0.579√λ.

Inflationary stochastic anomalies

The stochastic approach aims at describing the long-wavelength part of quantum fields during inflation by a classical stochastic theory. It is usually formulated in terms of Langevin equations, giving rise to a Fokker–Planck equation for the probability distribution function of the fields, and possibly their momenta. The link between these two descriptions is ambiguous in general, as it depends on an implicit discretisation procedure, the two prominent ones being the Itô and Stratonovich prescriptions. Here we show that the requirement of general covariance under field redefinitions is verified only in the latter case, however at the expense of introducing spurious ‘frame’ dependences. This stochastic anomaly disappears when there is only one source of stochasticity, like in slow-roll single-field inflation, but manifests itself when taking into account the full phase space, or in the presence of multiple fields. Despite these difficulties, we use physical arguments to write down a covariant Fokker–Planck equation that describes the diffusion of light scalar fields in non-linear sigma models in the overdamped limit. We apply it to test scalar fields in de Sitter space and show that some statistical properties of a class of two-field models with derivative interactions can be reproduced by using a correspondence with a single-field model endowed with an effective potential. We also present explicit results in a simple extension of the single-field theory to a hyperbolic field space geometry. The difficulties we describe seem to be the stochastic counterparts of the notoriously difficult problem of maintaining general covariance in quantum theories, and the related choices of operator ordering and path-integral constructions. Our work thus opens new avenues of research at the crossroad between cosmology, statistical physics, and quantum field theory.

The motion of a relativistic charged particle in a homogenous electromagnetic field in De-Sitter space

We discuss the geometric characterization of the trajectoryof a moving charged particle, for the case of a homogeneous electromagnetic eld, in De-Sitter space when the motion is governed by the Lorentz equa-tion. We employ totally relativistic approach during the discussion and itis based on a systematic use of the four-dimensional Frenet-Serret formulae,which is adapted to the De-Sitter space to determine the worldline geometryof the electromagnetic eld acting on the particle in De-Sitter space, and ofthe Faraday antisymmetric tensor properties.

The quantum Fokker-Planck equation of stochastic inflation

We derive the stochastic description of a massless, interacting scalar field in de Sitter space directly from the quantum theory. This is done by showing that the density matrix for the effective theory of the long wavelength fluctuations of the field obeys a quantum version of the Fokker-Planck equation. This equation has a simple connection with the standard Fokker-Planck equation of the classical stochastic theory, which can be generalised to any order in perturbation theory. We illustrate this formalism in detail for the theory of a massless scalar field with a quartic interaction.

Dynamical Casimir effect and loop corrections

We calculate quantum loop corrections to the stress-energy flux caused by moving mirrors. We consider massless, self-interacting, $\phi^4$, real scalar theory. In these calculations we encounter a new and quite unexpected subtleties due to the absence of global hyperbolicity in the presence of mirrors. We attempt to clearly phrase as many as possible hidden assumptions and complications that appear along the course of the solution of the problem in question. On top of that we find that quantum loop corrections to the stress-energy flux are growing with time and are not suppressed in comparison with the semi-classical contributions. Thus, we observe the break down of the perturbation theory, discuss its physical origin and ways to deal with such a situation. As a byproduct we observe a similarity of the problem in question with that for the minimally coupled, massless scalar field in de Sitter space.

Fuzzy Euclidean wormholes in de Sitter space

We investigate Euclidean wormholes in Einstein gravity with a massless scalar field in de Sitter space. Euclidean wormholes are possible due to the analytic continuation of the time as well as complexification of fields, where we need to impose the classicality after the Wick-rotation to the Lorentzian signatures. For some parameters, wormholes are preferred than Hawking-Moss instantons, and hence wormholes can be more fundamental than Hawking-Moss type instantons. Euclidean wormholes can be interpreted in three ways: (1) classical big bounce, (2) either tunneling from a small to a large universe or a creation of a collapsing and an expanding universe from nothing, and (3) either a transition from a contracting to a bouncing phase or a creation of two expanding universes from nothing. These various interpretations shed some light on challenges of singularities. In addition, these will help to understand tensions between various kinds of quantum gravity theories.

Nonperturbative renormalization group for scalar fields in de Sitter space: Beyond the local potential approximation

Nonperturbative renormalization group techniques have recently proven a powerful tool to tackle the nontrivial infrared dynamics of light scalar fields in de Sitter space. In the present article, we develop the formalism beyond the local potential approximation employed in earlier works. In particular, we consider the derivative expansion, a systematic expansion in powers of field derivatives, appropriate for long wavelength modes, that we generalize to the relevant case of a curved metric with Lorentzian signature. The method is illustrated with a detailed discussion of the so-called local potential approximation prime which, on top of the full effective potential, includes a running (but field-independent) field renormalization. We explicitly compute the associated anomalous dimension for O(N) theories. We find that it can take large values along the flow, leading to sizable differences as compared to the local potential approximation. However, it does not prevent the phenomenon of gravitationally induced dimensional reduction pointed out in previous studies. We show that, as a consequence, the effective potential at the end of the flow is unchanged as compared to the local potential approximation, the main effect of the running anomalous dimension being merely to slow down the flow.