De Sitter Background Research Articles

Can all the infrared secular growth really be understood as increase of classical statistical variance?

It is known that in the theory of light scalar fields during inflation, correlation functions suffer from infrared (IR) divergences or large IR loop corrections, leading to the breakdown of perturbation theory. In order to understand the physical meaning of such IR enhancement, we investigate the stochastic properties of an effective equation of motion (EoM) for long-wavelength modes of a canonically normalized light scalar field ϕ with a general sufficiently flat interaction potential on de Sitter background. Firstly, we provide an alternative refined derivation of the effective action for long-wavelength modes which leads to the effective EoM that correctly reproduces all the IR correlation functions in a good approximation at a late time, by integrating out short-wavelength modes. Next, under the assumption that one can neglect non-local correlations in the influence functional exceeding the coarse-graining scale, we show that the effective EoM for IR modes of the “average field” in Schwinger-Keldysh formalism ϕc< can be interpreted as a classical stochastic process in the present model.

Schwinger mechanism on de Sitter background

In this paper, incorporating the effect of the deformed commutation relation on de Sitter background, we studied the deformed Schwinger mechanism in (1[Formula: see text]+[Formula: see text]1) dimensions for scalars particle of spin-0 in a constant electric field. The Klein–Gordon equation is solved exactly and the wave function is given in term of hypergeometric functions. The canonical method based on a Bogoliubov transformation is applied. The pair creation probability and the density number of created particles are calculated.

Gravitational radiation in infinite derivative gravity and connections to effective quantum gravity

The Hulse-Taylor binary provides possibly the best test of GR to date. We find the modified quadrupole formula for infinite derivative gravity (IDG). We investigate the backreaction formula for propagation of gravitational waves, found previously for effective quantum gravity (EQG) for a flat background and extend this calculation to a de Sitter background for both EQG and IDG. We put tighter constraints on EQG using new LIGO data. We also find the power emitted by a binary system within the IDG framework for both circular and elliptical orbits and use the example of the Hulse-Taylor binary to show that IDG is consistent with GR.

Schrödinger field theory in curved spacetime: In-in formalism and three-point function for the inflationary background

We review the Schrödinger picture of field theory in curved spacetime and using this formalism, the power spectrum of massive noninteracting, minimally coupled scalars in a fixed de Sitter background is obtained. To calculate the [Formula: see text]-point function in Schrödinger field theory, the in-in formalism is extended in the Friedmann–Lemaître–Robertson–Walker (FLRW) universe. We compute the three-point function for primordial scalar field fluctuation in the single field inflation by this in-in formalism. The results are the same as the three-point function in the Heisenberg picture.

Infrared modified gravity with propagating torsion: Instability of torsionfull de Sitter-like solutions

We continue the exploration of the consistency of a modified-gravity theory that generalizes General Relativity by including a dynamical torsion in addition to the dynamical metric. The six-parameter theory we consider was found to be consistent around arbitrary torsionless Einstein backgrounds, in spite of its containing a (notoriously delicate) massive spin-2 excitation. At zero bare cosmological constant, this theory was found to admit a self-accelerating solution whose exponential expansion is sustained by a non-zero torsion background. The scalar-type perturbations of the latter torsionfull self-accelerating solution were recently studied and were found to preserve the number of propagating scalar degrees of freedom, but to exhibit, for some values of the torsion background some exponential instabilities (of a rather mild type). Here, we study the tensor-type and vector-type perturbations of the torsionfull self-accelerating solution, and of its deformation by a non-zero bare cosmological constant. We find strong, "gradient" instabilities in the vector sector. No tuning of the parameters of the theory can kill these instabilities without creating instabilities in the other sectors. Further work is needed to see whether generic torsionfull backgrounds are prone to containing gradient instabilities, or if the instabilities we found are mainly due to the (generalized) self-accelerating nature of the special de Sitter backgrounds we considered.

Gibbons-Hawking radiation of gravitons in the Poincaré and static patches of de Sitter spacetime

We discuss the quantization of linearized gravity in the background de Sitter spacetime using a gauge-invariant formalism to write the perturbed gravitational field in the static patch. This field is quantized after fixing the gauge completely. The response rate of this field to monochromatic multipole sources is then computed in the thermal equilibrium state with the well known Gibbons-Hawking temperature. We compare this response rate with the one obtained in the Bunch-Davies-like vacuum state defined in the Poincar\'e patch. These response rates are found to be the same as expected. This agreement serves as a verification of the infrared finite graviton two-point function in the static patch of de Sitter spacetime found previously.

Brane SUSY breaking and the gravitino mass

Supergravity models with spontaneously broken supersymmetry have been widely investigated over the years, together with some notable non-linear limits. Although in these models the gravitino becomes naturally massive absorbing the degrees of freedom of a Nambu-Goldstone fermion, there are cases in which the naive counting of degrees of freedom does not apply, in particular because of the absence of explicit gravitino mass terms in unitary gauge. The corresponding models require non-trivial de Sitter-like backgrounds, and it becomes of interest to clarify the fate of their Nambu-Goldstone modes. We elaborate on the fact that these non-trivial backgrounds can accommodate, consistently, gravitino fields carrying a number of degrees of freedom that is intermediate between those of massless and massive fields in a flat spacetime. For instance, in a simple supergravity model of this type with de Sitter background, the overall degrees of freedom of gravitino are as many as for a massive spin-3/2 field in flat spacetime, while the gravitino remains massless in the sense that it undergoes null-cone propagation in the stereographic picture. On the other hand, in the ten-dimensional USp(32) Type I Sugimoto model with “brane SUSY breaking”, which requires a more complicated background, the degrees of freedom of gravitino are half as many of those of a massive one, and yet it somehow behaves again as a massless one.

On the ghost-induced instability on de Sitter background

It is known that the perturbative instability of tensor excitations in higher derivative gravity may not take place if the initial frequency of the gravitational waves is below the Planck threshold. One can assume that this is a natural requirement if the cosmological background is sufficiently mild, since in this case the situation is qualitatively close to the free gravitational wave in flat space. Here, we explore the opposite situation and consider the effect of a very far from Minkowski radiation-dominated or de Sitter cosmological background with a large Hubble rate, e.g., typical of an inflationary period. It turns out that, then, for initial Planckian or even trans-Planckian frequencies, the instability is rapidly suppressed by the very fast expansion of the Universe.

Spectator electric fields, de Sitter spacetime, and the Schwinger effect

During a de Sitter stage of expansion the spectator fields of different spin are constrained by the critical density bound and by further requirements determined by their specific physical nature. The evolution of spectator electric fields in conformally flat background geometries is occasionally concocted by postulating the existence of ad hoc currents but this apparently innocuous trick violates the second law of thermodynamics. Such a problem occurs, in particular, for those configurations (customarily employed for the analysis of the Schwinger effect in four-dimensional de Sitter backgrounds) leading to an electric energy density which is practically unaffected by the expansion of the underlying geometry. The obtained results are compared with more mundane situations where Joule heating develops in the early stages of a quasi-de Sitter phase.

Revealing infinite derivative gravity’s true potential: The weak-field limit around de Sitter backgrounds

General Relativity is known to produce singularities in the potential generated by a point source. Our universe can be modelled as a de Sitter (dS) metric and we show that ghost-free Infinite Derivative Gravity (IDG) produces a non-singular potential around a dS background, while returning to the GR prediction at large distances. We also show that although there are an apparently infinite number of coefficients in the theory, only a finite number actually affect the predictions. By writing the linearised equations of motion in a simplified form, we find that at distances below the Hubble length scale, the difference between the IDG potential around a flat background and around a de Sitter background is negligible.

Electromagnetic fields with vanishing quantum corrections

We show that a large class of null electromagnetic fields are immune to any modifications of Maxwell's equations in the form of arbitrary powers and derivatives of the field strength. These are thus exact solutions to virtually any generalized classical electrodynamics containing both non-linear terms and higher derivatives, including, e.g., non-linear electrodynamics as well as QED- and string-motivated effective theories. This result holds not only in a flat or (anti-)de Sitter background, but also in a larger subset of Kundt spacetimes, which allow for the presence of aligned gravitational waves and pure radiation.

Cosmological stealths with nonconformal couplings

In this paper we reconsider the existence of stealth fields during the evolution of our Universe by admitting more realistic nonminimal couplings to gravity than the conformal one. In the framework of the FRW cosmology we found that inhomogeneous stealths, as those enabled in the conformal case, are only allowed in de Sitter backgrounds. In particular, it is shown that the homogeneous stealths resulting from nonconformal couplings can coexist with each kind of matter dominant in the several phases characterizing the evolution of our Universe according to the $\Lambda$CDM model.

Statistical nature of infrared dynamics on de Sitter background

In this study, we formulate a systematic way of deriving an effective equation of motion(EoM) for long wavelength modes of a massless scalar field with a general potential V(ϕ) on de Sitter background, and investigate whether or not the effective EoM can be described as a classical stochastic process. Our formulation gives an extension of the usual stochastic formalism to including sub-leading secular growth coming from the nonlinearity of short wavelength modes. Applying our formalism to λ ϕ4 theory, we explicitly derive an effective EoM which correctly recovers the next-to-leading secularly growing part at a late time, and show that this effective EoM can be seen as a classical stochastic process. Our extended stochastic formalism can describe all secularly growing terms which appear in all correlation functions with a specific operator ordering. The restriction of the operator ordering will not be a big drawback because the commutator of a light scalar field becomes negligible at large scales owing to the squeezing.

Schwinger pair production by electric field coupled to inflaton

We analytically investigate the Schwinger pair production in the de Sitter background by using the uniform asymptotic approximation method, and show that the equation of motion in general has two turning points, and the nature of these points could be single, double, real or complex, depending on the choice of the free parameters involved in the theory. Different natures of these points lead to different electric currents. In particular, when β ≡ m2/H2−9/4 is positive, both turning points are complex, and the electric current due to the Schwinger process is highly suppressed, where m and H denote, respectively, the mass of the particle and the Hubble parameter. For the turning points to be real, it is necessary to have β < 0, and the more negative of β, the easier to produce particles. In addition, when β < 0, we also study the particle production when the electric field E is very weak. We find that the electric current in this case is proportional to E1/2 − √|β|, which is strongly enhanced in the weak electric field limit when m < √2 H.

Standard model vacuum decay in a de Sitter background

We present a calculation of thick-wall Coleman-de-Luccia (CdL) bounces in the Standard Model effective potential in a de Sitter background. The calculation is performed including the effect of the bounce back-reaction on the metric, which we compare with the case of a fixed de-Sitter background, and with similar full-backreaction calculation in a model polynomial potential. The results show that the Standard Model potential exhibits non-trivial behavior: rather than a single CdL solution, there are multiple (non-oscillating) bounce solutions which may contribute to the decay rate. All the extra solutions found have higher actions than the largest amplitude solution, and thus would not contribute significantly to the decay rate, but their existence demonstrates that CdL solutions in the Standard Model potential are not unique, and the existence of additional, lower action, solutions cannot be ruled out. This suggests that a better understanding of the appearance and disappearance of CdL solutions in de Sitter space is needed to fully understand the vacuum instability issue in the Standard Model.

Linear waves on constant radius limits of cosmological black hole spacetimes

In this paper we consider the Klein-Gordon equation on spherically symmetric background spacetimes with a constant area radius. The spacetimes under consideration are Nariai and Plebanski-Hacyan, and can be considered constant radius limits of Reissner-Nordstrom-de Sitter spacetimes. We prove boundedness in the case of a non-negative Klein Gordon mass and decay unless the mass is zero. In the latter case we prove decay of solutions that are supported on all harmonic modes with angular momentum l greater or equal to 1. We show that the l=0 modes of solutions to the massless Klein-Gordon equation do not decay. They are subject to conservation laws along degenerate Killing horizons. We apply the estimates in Nariai to give decay of solutions to the massive Klein-Gordon equation on an n-dimensional de Sitter background, using only the vector field method and with no restrictions on the positive Klein-Gordon mass.

Condition on Ramond-Ramond fluxes for factorization of worldsheet scattering in anti–de Sitter space

Factorization of scattering is the hallmark of integrable $1+1$ dimensional quantum field theories. For factorization of scattering to be possible the set of masses and momenta must be conserved in any two-to-two scattering process. We use this fact to constrain the form of the Ramond-Ramond fluxes for integrable supergravity anti--de Sitter (AdS) backgrounds by analyzing tree-level scattering of two AdS bosons into two fermions on the worldsheet of a Berenstein-Maldacena-Nastase string. We find a condition which can be efficiently used to rule out integrability of AdS strings and therefore of the corresponding AdS/conformal field theory dualities, as we demonstrate for some simple examples.

De Sitter symmetries and inflationary correlators in parity violating scalar-vector models

In this paper we use conformal field theory techniques to constrain the form of the correlations functions of an inflationary scalar-vector model described by the interaction term f1(ϕ)Fμ νFμ ν + f2(ϕ)̃Fμ νFμ ν. We use the fact that the conformal group is the relevant symmetry group acting on super horizon scales in an inflationary de Sitter background. As a result, we find that super horizon conformal symmetry, constraints the form of the coupling functions f1, f2 to be homogeneous functions of the same degree. We derive the general form of the correlators involving scalar and vector perturbations in this model and determine its squeezed limit scaling behaviour for super horizon scales. The approach followed here is useful to constraint the shape of scalar-vector correlators, and our results agree with recent literature on the subject, but don't allow us to determine amplitude factors of the correlators.

Impulsive gravitational waves in general massive 3D gravity

Impulsive, non-diverging, Petrov-Segre type N gravitational wave solutions to a general massive three-dimensional gravity in the de Sitter, anti-de Sitter and flat Minkowski backgrounds are constructed in a unified manner by using the exterior algebra of differential forms.

De Sitter spacetime with a Becchi–Rouet–Stora quartet

We generalize the topological model recently proposed and investigate the cosmological perturbations of the model. The model has an exact de Sitter background solution associated with the Becchi–Rouet–Stora (BRS) quartet terms which are regarded as the Lagrangian density of the topological field theory. The de Sitter solution can be selected without spontaneously breaking the BRS symmetry, and be interpreted as a gauge fixing of de Sitter spacetime. The BRS symmetry is preserved for the perturbations around the de Sitter background before we solve the constraints of general relativity. We derive action to the second-order of the perturbations and confirm that even after solving the constraints, we have the BRS symmetry at least for the second-order action. We construct the cosmological perturbation theory involving the BRS sector, and obtain the two-point correlation functions for the curvature perturbation and the isocurvature perturbations which compose the BRS sector. Our result gives a new description for de Sitter spacetime and the quantum field theory in de Sitter spacetime.