The problem of the flat limits of the scalar and spinor fields on the de Sitter expanding universe is considered in the rest frame vacuum where the frequencies are separated in rest frames as in special relativity. The phases of the fundamental solutions of these fields are regularized in order to obtain Minkowskian flat limits. New expressions of scalar mode functions or Dirac spinors reaching natural flat limits are given in the rest frame vacuum and suitable approximate formulas are proposed. In this manner the flat limit is correctly defined for the entire quantum theory since the one-particle operators tend to those of special relativity.
In this letter we show that the ``preferred'' Klein-Gordon Quantum Field Theories (QFT's) on a d-dimensional de Sitter spacetime can be obtained from a Klein-Gordon QFT on a (d+1)-dimensional ``ambient'' Minkowski spacetime satisfying the spectral condition and, conversely, that a Klein-Gordon QFT on a (d+1)-dimensional ``ambient'' Minkowski spacetime satisfying the spectral condition can be obtained as superposition of d-dimensional de Sitter Klein-Gordon fields in the preferred vacuum. These results establish a correspondence between QFT's living on manifolds having different dimensions. The…
We employ gauge-gravity duality to study the backreaction effect of 4-dimensional large-$N$ quantum field theories on constant-curvature backgrounds, and in particular de Sitter space-time. The field theories considered are holographic QFTs, dual to RG flows between UV and IR CFTs. We compute the holographic QFT contribution to the gravitational effective action for 4d Einstein manifold backgrounds. We find that for a given value of the cosmological constant $λ$, there generically exist two backreacted constant-curvature solutions, as long as $λ< λ_{\textrm{max}} \sim M_p^2 / N^2$, otherwise n…
We study the correlators for interacting quantum field theory in the flat chart of de Sitter space at all orders in perturbation. The correlators are calculated in the in-in formalism which are often applied to the calculations in the cosmological perturbation. It is shown that these correlators are de Sitter invariant. They are compared with the correlators calculated based on the Euclidean field theory. We then find that these two correlators are identical. This correspondence has been already shown graph by graph but we give an alternative proof of it by direct calculation.
The density of mass levels ρ(m) and the critical temperature for strings in de Sitter space-time are found. QFT and string theory in de Sitter space are compared. A `Dual'-transform is introduced which relates classical to quantum string lengths, and more generally, QFT and string domains. Interestingly, the string temperature in De Sitter space turns out to be the Dual transform of the QFT-Hawking-Gibbons temperature. The back reaction problem for strings in de Sitter space is addressed selfconsistently in the framework of the `string analogue' model (or thermodynamical approach), which is we…
In recent papers [1,2], it has been shown that the presence of negative norm states or negative frequency solutions are indispensable for a fully covariant quantization of the minimally coupled scalar field in de Sitter space. Their presence, while leaving unchanged the physical content of the theory, offers the advantage of eliminating any ultraviolet divergence in the vacuum energy [2] and infrared divergence in the two point function [3]. We attempt here to extend this method to the interacting quantum field in Minkowski space-time. As an illustration of the procedure, we consider the $λϕ^4…
We show that the Hartle-Hawking vacuum for theories of interacting massive scalars in de Sitter space is both perturbatively well-defined and stable in the IR. Correlation functions in this state may be computed on the Euclidean section and Wick-rotated to Lorentz-signature. The results are manifestly de Sitter-invariant and contain only the familiar UV singularities. More importantly, the connected parts of all Lorentz-signature correlators decay at large separations of their arguments. Our results apply to all cases in which the free Euclidean vacuum is well defined, including scalars with m…
We describe the dynamics of strongly coupled field theories in de Sitter spacetime using the holographic gauge/gravity duality. The main motivation for this is to explore the possibility of dynamical phase transitions during cosmological evolution. Specifically, we study two classes of theories: (i) conformal field theories on de Sitter in the static patch which are maintained in equilibrium at temperatures that may differ from the de Sitter temperature and (ii) confining gauge theories on de Sitter spacetime. In the former case we show the such states make sense from the holographic viewpoint…
We study bosonic Quantum Field Theory on the double covering $\widetilde{dS}_{2}$ of the 2-dimensional de Sitter universe, identified to a coset space of the group $SL(2,{\Bbb R})$. The latter acts effectively on $\widetilde{dS}_{2}$ and can be interpreted as it relativity group. The manifold is locally identical to the standard the Sitter spacetime ${dS}_2$; it is globally hyperbolic, geodesically complete and an inertial observer sees exactly the same bifurcate Killing horizons as in the standard one-sheeted case. The different global Lorentzian structure causes however drastic differences b…
In this paper we study various aspects of entanglement entropy in strongly-coupled de Sitter quantum field theories in various dimensions. We find gravity solutions that are dual to field theories in a fixed de Sitter background, both in equilibrium and out-of-equilibrium configurations. The latter corresponds to the Vaidya generalization of the AdS black hole solutions with hyperbolic topology. We compute analytically the entanglement entropy of spherical regions and show that there is a transition when the sphere is as big as the horizon. We also explore thermalization in time-dependent situ…
We study the relation between two sets of correlators in interacting quantum field theory on de Sitter space. The first are correlators computed using in-in perturbation theory in the expanding cosmological patch of de Sitter space (also known as the conformal patch, or the Poincaré patch), and for which the free propagators are taken to be those of the free Euclidean vacuum. The second are correlators obtained by analytic continuation from Euclidean de Sitter; i.e., they are correlators in the fully interacting Hartle-Hawking state. We give an analytic argument that these correlators coincide…
We compute the quantum string entropy S_s(m, H) from the microscopic string density of states of mass m in Anti de Sitter space-time. For high m, (high Hm -->c/α'), no phase transition occurs at the Anti de Sitter string temperature T_{s} which is higher than the flat space (Hagedorn) temperature t_{s}. (the Hubble constant H acts as producing a smaller string constant and thus, a higher tension). T_s is the precise quantum dual of the semiclassical (QFT) Anti de Sitter temperature scale . We compute the quantum string emission by a black hole in Anti de Sitter space-time (bhAdS). In the early…
We analyze the model of a self-interacting $ϕ^4_{\star}$ scalar field theory in Snyder-de Sitter space. After analytically computing the one-loop beta functions {in the small noncommutativity and curvature limit}, we solve numerically the corresponding system of differential equations, showing that in this limit the model possesses at least one regime in which the theory is asymptotically free. Moreover, in a given region of the parameter space we also observe a peculiar running of the parameter associated to the curvature, which changes its sign and therefore can be interpreted as a transitio…
Using the dS/QFT correspondence in the context of inflation allows for the study of interesting, otherwise inaccessible physics. In particular, by studying inflation via its dual field theory at the boundary of the de Sitter space, it may be possible to study a regime of strongly coupled gravity at early times. The purpose of this work is to completely express cosmological observables in terms of the free parameters of a dual field theory and to compare them with CMB data. In this way, constraints on the observational parameters constrains the validity of the strongly coupled inflation picture…
This work uses Lorentz-signature in-in perturbation theory to analyze the late-time behavior of correlators in time-dependent interacting massive scalar field theory in de Sitter space. We study a scenario recently considered by Krotov and Polyakov in which the coupling $g$ turns on smoothly at finite time, starting from $g=0$ in the far past where the state is taken to be the (free) Bunch-Davies vacuum. Our main result is that the resulting correlators (which we compute at the one-loop level) approach those of the interacting Hartle-Hawking state at late times. We argue that similar results s…
We show that a particular set of global modes for the massive de Sitter scalar field (the de Sitter waves) allows to manage the group representations and the Fourier transform in the flat (Minkowskian) limit. This is in opposition to the usual acceptance based on a previous result, suggesting the appearance of negative energy in the limit process. This method also confirms that the Euclidean vacuum, in de Sitter spacetime, has to be preferred as far as one wishes to recover ordinary QFT in the flat limit.
We explicitly describe the last stages of black hole evaporation in the context of string theory : the combined study of Quantum Field Theory (QFT) and String Theory (ST) in curved backgrounds allows us to go further in the understanding of quantum gravity effects. The string ``analogue model''(or thermo-dynamical approach) is a well suited framework for this purpose.The results also apply to another physically relevant case: de Sitter background. Semiclassical (QFT) and quantum gravity (String) phases or regimes are properly determined (back reaction effects included). The Hawking-Gibbons tem…
We study some kinematical aspects of quantum fields on causal sets. In particular, we are interested in free scalar fields on a fixed background causal set. We present various results building up to the study of the entanglement entropy of de Sitter horizons using causal sets. We begin by obtaining causal set analogs of Green functions for this field. First we construct the retarded Green function in a Riemann normal neighborhood (RNN) of an arbitrary curved spacetime. Then, we show that in de Sitter and patches of anti-de Sitter spacetimes the construction can be done beyond the RNN. This all…
It is shown that the Nachtmann boosting method of introducing coordinates on de Siter manifolds can be completed with suitable gauge transformations able to keep under control the transformation under isometries of the conserved quantities. With this method, the rest local charts (or natural frames) are defined pointing out the role of the conserved quantities in investigating the relative geodesic motion. The advantages of this approach can be seen from the applications presented here. For the first time, the simple kinematic effects, the electromagnetic field of a free falling charge and the…
We compute the quantum string entropy S_s(m, H) from the microscopic string density of states rho_s (m,H) of mass m in de Sitter space-time. We find for high m, a {\bf new} phase transition at the critical string temperature T_s= (1/2 pi k_B)L c^2/alpha', higher than the flat space (Hagedorn) temperature t_s. (L = c/H, the Hubble constant H acts at the transition as producing a smaller string constant alpha' and thus, a higher tension). T_s is the precise quantum dual of the semiclassical (QFT Hawking-Gibbons) de Sitter temperature T_sem = hbar c /(2πk_B L). We find a new formula for the full …
The general plane wave solutions of the Proca field in conformal charts of the de Sitter expanding universe are derived for arbitrary polarizations showing how the frequencies can be separated in rest frames, defining thus the rest frame vacuum of this field.
We explicitly show that the one loop IR correction to the two--point function in de Sitter space scalar QFT does not reduce just to the mass renormalization. The proper interpretation of the loop corrections is via particle creation revealing itself through the generation of the quantum averages $<a^+_p a_p>$, $<a_p a_{-p}>$ and $<a^+_p a^+_{-p}>$, which slowly change in time. We show that this observation in particular means that loop corrections to correlation functions in de Sitter space can not be obtained via analytical continuation of those calculated on the sphere. We find harmonics for…
The covariantly constant spacetime torsion is one of the fields which may break Lorentz and CPT symmetry. We review the previous works on the dynamical torsion in the framework of effective quantum field theory (QFT). It turns out that the existence of propagating torsion is strongly restricted by the QFT principles. In particular, the torsion mass must be much greater than the masses of all fermionic particles. In this situation, the main chance to observe torsion is due to some symmetry breaking which may, in principle, produce almost constant background torsion field.
We numerically compute renormalized expectation values of quadratic operators in a quantum field theory (QFT) of free Dirac fermions in curved two-dimensional (Lorentzian) spacetime. First, we use a staggered-fermion discretization to generate a sequence of lattice theories yielding the desired QFT in the continuum limit. Numerically-computed lattice correlators are then used to approximate, through extrapolation, those in the continuum. Finally, we use so-called point-splitting regularization and Hadamard renormalization to remove divergences, and thus obtain finite, renormalized expectation …
We show that there is only one physically acceptable vacuum state for quantum fields in de Sitter space-time which is left invariant under the action of the de Sitter-Lorentz group $SO(1,d)$ and supply its physical interpretation in terms of the Poincare invariant quantum field theory (QFT) on one dimension higher Minkowski spacetime. We compute correlation functions of the generalized vertex operator $:e^{i\hat{S}(x)}:$, where $\hat{S}(x)$ is a massless scalar field, on the $d$-dimensional de Sitter space and demonstrate that their limiting values at timelike infinities on de Sitter space rep…
Upper limits for the mass-radius ratio are derived for arbitrary general relativistic matter distributions in the presence of a cosmological constant. General restrictions for the red shift and total energy (including the gravitational contribution) for compact objects in the Schwarzschild-de Sitter geometry are also obtained in terms of the cosmological constant and of the mean density of the star.
The Nachtmann boosting method is completed with gauge transformations in order to be applied to the study of the relative geodesic motion on the de Sitter spacetimes, finding how the conserved quantities transform under isometries and defining the rest frames of massive mobiles.
New spherical scalar modes on the expanding part of Sitter spacetime, eigenfunctions of a conserved Hamiltonian-like operator are found by solving the Klein-Gordon equation in the appropriate coordinate chart, with the help of a time evolution picture technique specially developed for spatially flat FLRW charts. Transition coefficients are computed between these modes and the rest of the scalar spherical and plane wave modes, either momentum or energy eigenfunctions on the spatially flat FLRW chart.
We propose a complete microscopic definition of the Hilbert space of minimal higher spin de Sitter quantum gravity and its Hartle-Hawking vacuum state. The fundamental degrees of freedom are $2N$ bosonic fields living on the future conformal boundary, where $N$ is proportional to the de Sitter horizon entropy. The vacuum state is normalizable. The model agrees in perturbation theory with expectations from a previously proposed dS-CFT description in terms of a fermionic Sp(N) model, but it goes beyond this, both in its conceptual scope and in its computational power. In particular it resolves t…
We analyze families of particle detector models that linearly couple to different kinds of fermionic and bosonic fields. We also study the response of these detectors to particle and anti-particle excitations of the field. We propose a simple linear complex scalar particle detector model that captures the fundamental features of fermionic field detectors similarly to how the Unruh-DeWitt model captures the features of the light matter interaction. We also discuss why we do not need to limit ourselves to quadratic models commonly employed in past literature. Namely, we provide a physically moti…
It is shown that on the de Sitter manifolds the tachyonic geodesics are restricted such that the classical tachyons cannot exist on this manifold at any time. On the contrary, the theory of the scalar quantum tachyons is free of any restriction. The tachyonic scalar and Dirac plane waves are deduced in this geometry, pointing out that these are well-defined, behaving as tempered distributions at any moment.
The scalar mode functions on the spatially flat FLRW chart of the de Sitter spacetime are redefined in order to obtain a natural frequencies separation in the special local charts where the momentum vanishes, called here (natural) rest frames. This can be done since in such frames the mode functions are eigenfunctions of the energy operator. Moreover, the most general criteria for choosing the suitable phase factors of the mode functions able to simultaneously determine the correct rest and flat limits are established. These results are compared to the different original choices from the liter…
We show explicitly that free quantum field theory in de Sitter background restricted on the cosmological horizon produces another quantum field theory unitarily equivalent with the original one. Symmetry properties descending from the dual theory are also remarked. In the restricted theory the thermal properties, known for de Sitter quantum field theory, can be proved straightforwardly.
Landauer's principle has seen a boom of interest in the last few years due to the growing interest in quantum information sciences. However, its relevance and validity in the contexts of quantum field theory (QFT) remain surprisingly unexplored. In the present paper, we consider Landauer's principle in qubit-cavity QFT interaction perturbatively, in which the initial state of the cavity QFT is chosen to be a vacuum or thermal state. In the vacuum case, the QFT always absorbs heat and jumps to excited states. For the qubit at rest, its entropy decreases, whereas if the qubit accelerates, it may…
We study the space of Killing fields on the four dimensional AdS spacetime $AdS^{3,1}$. Two subsets $\mathcal{S}$ and $\mathcal{O}$ are identified: $\mathcal{S}$ (the spinor Killing fields) is constructed from imaginary Killing spinors, and $\mathcal{O}$ (the observer Killing fields) consists of all hypersurface orthogonal, future timelike unit Killing fields. When the cosmology constant vanishes, or in the Minkowski spacetime case, these two subsets have the same convex hull in the space of Killing fields. In presence of the cosmology constant, the convex hull of $ \mathcal{O}$ is properly co…
We obtain spacetimes generated by static and spinning magnetic string sources in Einstein Relativity with negative cosmological constant. Since the spacetime is asymptotically a cylindrical anti-de Sitter spacetime, we will be able to calculate the mass, momentum, and electric charge of the solutions. We find two families of solutions, one with longitudinal magnetic field and the other with angular magnetic field. The source for the longitudinal magnetic field can be interpreted as composed by a system of two symmetric and superposed electrically charged lines with one of the electrically char…
We propose a new propagation formula for the Maxwell field in de Sitter space which exploit the conformal invariance of this field together with a conformal gauge condition. This formula allows to determine the classical electromagnetic field in the de Sitter space from given currents and initial data. It only uses the Green's function of the massless Minkowskian scalar field. This leads to drastic simplifications in practical calculations. We apply this formula to the classical problem of the two charges of opposite signs at rest at the North and South Poles of the de Sitter space.
We study non-interacting automorphic quantum scalar fields with positive mass in two-dimensional de Sitter space. We find that there are no Hadamard states which are de Sitter invariant except in the periodic case, extending the result of Epstein and Moschella for the anti-periodic case. We construct the two-point Wightman functions for the non-Hadamard de Sitter-invariant states by exploiting the fact that they are functions of the geodesic distance between the two points satisfying an ordinary differential equation. We then examine a certain Hadamard state, which is not de Sitter invariant, …
Starting from an (unknown) quantum gravitational model, one can invoke a sequence of approximations to progressively arrive at quantum field theory (QFT) in curved spacetime, QFT in flat spacetime, nonrelativistic quantum mechanics and newtonian mechanics. The more exact theory can put restrictions on the range of possibilities allowed for the approximate theory which are not derivable from the latter - an example being the symmetry restrictions on the wave function for a pair of electrons. We argue that the choice of vacuum state at low energies could be such a `relic' arising from combining …
We construct explicit mode expansions of various tree-level propagators in the Rindler -- de Sitter universe, also known as the static (or compact) patch of the de Sitter spacetime. We construct in particular the Wightman functions for thermal states having a generic temperature $T$. We give a fresh simple proof that the only thermal Wightman propagator that respects the de Sitter isometry is the restriction to the Rindler -- de Sitter wedge of the propagator for the Bunch--Davies state. It is the thermal state with $T = (2 π)^{-1}$ in the units of de Sitter curvature. We show that propagators…
It has been shown that the Strong Cosmic Censorship (SCC) can be violated by a scalar field in a near-extremal Reissner-Nordstrom-de Sitter black hole. In this paper, we investigate the Strong Cosmic Censorship in a Born-Infeld-de Sitter black hole by a scalar perturbation field with/without a charge. When the Born-Infeld parameter b becomes small, the nonlinear electrodynamics effect starts to play an important role and tends to rescue SCC. Specifically, we find that the SCC violation region decreases in size with decreasing b. Moreover, for a sufficiently small b, SCC can always be restored …
