We investigate the decay rate of a false vacuum state in de Sitter space at high Hubble rates, using two methods: the Hawking-Moss instanton method which is fully quantum mechanical but relies on the saddle-point approximation, and the Starobinsky-Yokoyama stochastic approach which is non-perturbative but does not include quantum effects. We use the flux-over-population method to compute the Hawking-Moss decay rate at one-loop order, and demonstrate that in its domain of validity, it is reproduced by the stochastic calculation using the one-loop constraint effective potential. This suggests that the stochastic approach together with the constraint effective potential can be used to accurately describe vacuum decay beyond the saddle-point approximation.
We employ a recent, general gauge computation of the one loop graviton contribution to the vacuum polarization on de Sitter to solve for one loop corrections to the photon mode function. The vacuum polarization takes the form of a gauge independent, spin 2 contribution and a gauge dependent, spin 0 contribution. We show that the leading secular corrections derive entirely from the spin 2 contribution.
A dynamical aspect of quantum gravity on de Sitter spacetime is investigated by holography or the dS/CFT correspondence. We show that de Sitter spacetime emerges from a free Sp(N) vector model by complexifying the ghost fields and flowing them in parallel to the imaginary axis. We confirm that the emergence of de Sitter spacetime is ensured by conformal symmetry. We also compute the quantum corrections to the cosmological constant up to the next-to-leading order of the 1/N expansion in a proposed holographic approach. As a result the sub-leading corrections have the opposite sign to the classi…
The higher-derivative $α'$ corrections consistent with $O(d,d)$ duality invariance can be completely classified for cosmological, purely time-dependent backgrounds. This result is used to show that there are duality invariant theories featuring string-frame de Sitter vacua as solutions that are non-perturbative in $α'$, thus suggesting that classical string theory may realize de Sitter solutions in an unexpected fashion.
We compute the one-loop photon contribution to the graviton self-energy on a de Sitter background and use it to solve the linearized Einstein equation for a point mass. Our results show that a comoving observer sees a logarithmic spatial running Newton's constant. Equivalently, a static observer reports a secular suppression of the Newtonian potential.
We investigate the combined effect of fluxes and higher-order curvature corrections, in the form of the Gauss-Bonnet term, on the existence of de Sitter vacua in a heterotic string inspired framework, compactified on spheres and tori. We first gain some intuition on the effects of these corrections by studying a perturbative expansion in the small Gauss-Bonnet coupling. Then, for choices of potential closer to the string theory predictions, we show that the inclusion of quadratic curvature corrections actually reduces the parametric likelihood of de Sitter solutions.
The rôle of string loop corrections on the existence of de Sitter vacua and the moduli stabilization problem is examined in type IIB effective theories. The fundamental building blocks are a minimum of three intersecting D7 brane stacks, three Kähler moduli, and a novel Einstein-Hilbert term associated with higher derivative terms of the 10-dimensional effective action. It was shown in previous works that loop corrections appear which induce novel logarithmic volume-dependent terms in the effective potential. When D-term contributions are considered, all Kähler moduli are stabilized and de Sit…
We use the Hartree approximation to the Einstein equation on de Sitter background to solve for the one loop correction to the graviton mode function. This should give a reasonable approximation to how the ensemble of inflationary gravitons affects a single external graviton. At late times we find that the one loop correction to the plane wave mode function $u(η,k)$ goes like $G H^2 \ln(a)/a^2$, where $a$ is the inflationary scale factor. One consequence is that the one loop corrections to the "electric" components of the linearized Weyl tensor grow compared to the tree order result.
We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions. Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been …
We first briefly discuss the relation between black hole thermodynamics and the entropy function formalism. We find that an equation which governs the relationship between Sen's entropy function and black hole entropy, can quickly give higher order corrections to entropy of pure (anti-) de Sitter space without knowing the corrected metric. We also show that near horizon geometry and the entropy function extremization is no longer required for pure (anti-)de Sitter space. The entropy of (anti-)de Sitter space and Schwarzschild-(anti-) de Sitter black holes together with Gauss-Bonnet terms, $R^2…
We consider single graviton loop corrections to the effective field equation of a massless, minimally coupled scalar on de Sitter background in the simplest gauge. We find a large temporal logarithm in the approach to freeze-in at late times, but no correction to the feeze-in amplitude. We also find a large spatial logarithm (at large distances) in the scalar potential generated by a point source, which can be explained using the renormalization group with one of the higher derivative counterterms regarded as a curvature-dependent field strength renormalization. We discuss how these results se…
Higher-derivative corrections to cosmological effective actions in string theory are largely constrained by T-duality, but have been computed hitherto only to the first few orders in the string scale $α'$. The functional renormalization group, in conjunction with the strong constraints imposed by T-duality, allows to derive cosmological effective actions to all orders in $α'$ while avoiding "truncations" of the theory space. We show that the resulting higher-derivative $α'$-corrections forbid the existence of de Sitter vacua, at least in regimes where string-loop corrections can be neglected. …
We discuss the de Sitter swampland and trans-Planckian censorship conjectures (TCC) from the entropy bound with quantum corrections, namely quantum version of Bousso bound and energy conditions. We include the typical contributions from the entanglement entropy in quasi-de Sitter spacetime. The TCC is not much corrected, whereas the bounds on de Sitter swampland conjecture from energy conditions can be relaxed due to quantum corrections.
From the partition function of canonical ensemble we derive the entropy of the de Sitter space by anti-Wick rotation. And then from the one-loop bubble $S^2\times S^2$ created from vacuum fluctuation in de Sitter background space, we obtain the one-loop quantum correction to the entropy of de Sitter space.
We employ the graviton self-energy induced by a massless, minimally coupled (MMC) scalar on de Sitter background to compute the quantum corrections to the gravitational potentials of a static point particle with a mass $M$. The Schwinger-Keldysh formalism is used to derive real and causal effective field equations. When evaluated at the one-loop order, the gravitational potentials exhibit a secular decrease in the observed gravitational coupling $G$. This can also be interpreted as a (time dependent) anti-screening of the mass $M$.
We study the effects of a fixed de Sitter geometry background in scenarios of false vacuum decay. It is currently understood that bubble nucleation processes associated with first order phase transitions are particularly important in cosmology. The geometry of spacetime complicates the interpretation of the decay rate of a metastable vacuum. However, the effects of curvature can still be studied in the particular case where backreaction is neglected. We compute the imaginary part of the action in de Sitter space, including the one-loop and the gradient corrections. We use two independent metho…
We study string loop corrections to the gravity kinetic terms in type IIB compactifications on Calabi-Yau threefolds or their orbifold limits, in the presence of $D7$-branes and orientifold planes. We show that they exhibit in general a logarithmic behaviour in the large volume limit transverse to the $D7$-branes, induced by a localised four-dimensional Einstein-Hilbert action that appears at a lower order in the closed string sector, found in the past. Here, we compute the coefficient of the logarithmic corrections and use them to provide an explicit realisation of a mechanism for Kähler modu…
We exploit a recent computation of one graviton loop corrections to the self-mass [1] to quantum-correct the field equation for a massless, conformally coupled scalar on a de Sitter background. With the obvious choice for the finite part of the $R^2 ϕ^2$ counterterm, we find that neither plane wave mode functions nor the response to a point source acquires large infrared logarithms. However, we do find a decaying logarithmic correction to the mode function and a short distance logarithmic running of the potential in addition to the power-law effect inherited from flat space.
We compute 1-loop corrections to Lorentz-signature de Sitter-invariant 2-point functions defined by the interacting Euclidean vacuum for massive scalar quantum fields with cubic and quartic interactions. Our results apply to all masses for which the free Euclidean de Sitter vacuum is well-defined, including values in both the complimentary and the principal series of SO(D,1). In dimensions where the interactions are renormalizeable we provide absolutely convergent integral representations of the corrections. These representations suffice to analytically extract the leading behavior of the 2-po…
In this paper, we show the equivalence between a classical static scalar field theory and the (closed) de Sitter cosmological model whose potential represents shape invariance property. Based on this equivalence, we calculate the one-loop quantum cosmological correction to the ground state energy of the kink-like solution in the (closed) de Sitter cosmological model in which the fluctuation potential $V^{\prime\prime}$ has a shape invariance property. It is shown that this type of correction, which yields a renormalized mass in the case of scalar field theory, may be {\it interpreted} as a ren…
We compute the radiative corrections to the mass of a test boson field in an inflating space-time. The calculations are carried out in case of a boson part of a supersymmetric chiral multiplet. We show that its mass is preserved up to logarithmic divergences both in ultraviolet and infrared domains. Consequences of these results for inflationary models are discussed.
We find a coordinate-independent wave-packet solution of the massive Klein-Gordon equation with the conformal coupling to gravity in the de-Sitter universe. This solution can locally be represented through the superposition of positive-frequency plane waves at any space-time point, assuming that the scalar-field mass $M$ is much bigger than the de-Sitter Hubble constant $H$. The solution is also shown to be related to the two-point function in the de-Sitter quantum vacuum. Moreover, we study the wave-packet propagation over cosmological times, depending on the ratio of $M$ and $H$. In doing so…
We compute the one-loop quantum corrections to the gravitational potentials of a spinning point particle in a de Sitter background, due to the vacuum polarisation induced by conformal fields in an effective field theory approach. We consider arbitrary conformal field theories, assuming only that the theory contains a large number $N$ of fields in order to separate their contribution from the one induced by virtual gravitons. The corrections are described in a gauge-invariant way, classifying the induced metric perturbations around the de Sitter background according to their behaviour under tra…
We calculate IR divergent graviton one-loop corrections to scalar correlators in de Sitter space, and show that the leading IR contribution may be reproduced via simple semiclassical consistency relations. One can likewise use such semiclassical relations to calculate leading IR corrections to correlators in slow-roll inflation. The regulated corrections shift the tensor/scalar ratio and consistency relation of single field inflation, and non-gaussianity parameters averaged over very large distances. For inflation of sufficient duration, for example arising from a chaotic inflationary scenario…
The Riemann correlator with appropriately raised indices characterizes in a gauge-invariant way the quantum metric fluctuations around de Sitter spacetime including loop corrections from matter fields. Specializing to conformal fields and employing a method that selects the de Sitter-invariant vacuum in the Poincaré patch, we obtain the exact result for the Riemann correlator through order $H^4/m_\mathrm{p}^4$. The result is expressed in a manifestly de Sitter-invariant form in terms of maximally symmetric bitensors. Its behavior for both short and long distances (sub- and superhorizon scales)…
Universal Secular External Leg Corrections for Gauge Independent Scalar Self-Mass on de Sitter
CEICO, FZU — Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Department of Physics, National Cheng Kung University（国立成功大学物理系）；ITP, EMMEPH and Spinoza Institute, Utrecht University（乌得勒支大学）；Department of Physics, University of Florida（佛罗里达大学）
本文提出在 de Sitter 背景上通过组合图并添加外部腿修正，消除引力子对无质量标量自质量修正中的局域长期规范依赖性，从而获得 1 圈阶完全规范无关的有效场方程。
We revisit the classical theory of ten-dimensional two-derivative gravity coupled to fluxes, scalar fields, D-branes, anti D-branes and Orientifold-planes. We show that such set-ups do not give rise to a four-dimensional positive curvature spacetime with the isometries of de Sitter spacetime. We further argue that a de Sitter solution in type IIB theory may still be achieved if the higher-order curvature corrections are carefully controlled. Our analysis relies on the derivation of the de Sitter condition from an explicit background solution by going beyond the supergravity limit of type IIB t…
The local and global thermal phase structure for asymptotically anti-de Sitter black holes charged under an abelian gauge group, with both Gauss-Bonnet and quartic field strength corrections, is mapped out for all parameter space. We work in the grand canonical ensemble where the external electric potential is held fixed. The analysis is performed in an arbitrary number of dimensions, for all three possible horizon topologies - spherical, flat or hyperbolic. For spherical horizons, new metastable configurations are exhibited both for the pure Gauss-Bonnet theory as well as the pure higher deri…
During inflation, the geometry of spacetime is described by a (quasi-)de Sitter phase. Inflationary observables are determined by the underlying (softly broken) de Sitter isometry group SO(1, 4) which acts like a conformal group on R^3: when the fluctuations are on super-Hubble scales, the correlators of the scalar fields are constrained by conformal invariance. Heavy fields with mass m larger than the Hubble rate H correspond to operators with imaginary dimensions in the dual Euclidean three-dimensional conformal field theory. By making use of the dS/CFT correspondence we show that, besides t…
We derive the leading quantum corrections to the gravitational potentials in a de Sitter background, due to the vacuum polarization from loops of conformal fields. Our results are valid for arbitrary conformal theories, even strongly interacting ones, and are expressed using the coefficients $b$ and $b'$ appearing in the trace anomaly. Apart from the de Sitter generalization of the known flat-space results, we find two additional contributions: one which depends on the finite coefficients of terms quadratic in the curvature appearing in the renormalized effective action, and one which grows lo…
In Vaidya-Bonner de Sitter Black hole space-time, the tunneling radiation characteristics of fermions and bosons are corrected by taking Lorentz symmetry breaking theory into account. The corresponding gamma matrices and ether-like field vectors of the black hole are constructed, then the new modified form of Dirac equation for the fermion with spin 1/2 and the new modified form of Klein-Gordon equation for boson in the curved space-time of the black hole are obtained. Through solving the two equations, new and corrected expressions of surface gravity, Hawking temperature and tunneling rate of…
We derive the effects of the scalar particle production on the physical graviton operator in the de Sitter space. Our analysis is done for the sub-horizon modes at large values of the conformal time. In this limit, we completely determine the correction to the scalar energy-momentum tensor at the first order in the WKB iteration. Also, we calculate the corresponding correction to the graviton operator for a single sub-horizon mode.
Recently a swampland criterion has been proposed that rules out de Sitter vacua in string theory. Such a criterion should hold at all points in the field space and especially at points where the system is on-shell. However there has not been any attempt to examine the swampland criterion against explicit equations of motion. In this paper we study four-dimensional de Sitter and quasi-de Sitter solutions using dimensionally reduced M-theory. While on one hand all classical sources that could allow for solutions with de Sitter isometries are ruled out, the quantum corrections, on the other hand,…
Since trans-Planckian considerations can be associated with the re-definition of the initial vacuum, we investigate further the influence of trans-Planckian physics on the spectra produced by the initial quasi-de Sitter (dS) state during inflation. We use the asymptotic-dS mode to study the trans-Planckian correction of the power spectrum to the quasi-dS inflation. The obtained spectra consist of higher order corrections associated with the type of geometry and harmonic terms sensitive to the fluctuations of space-time (or gravitational waves) during inflation. As an important result, the ampl…
We evaluate one loop quantum gravity corrections to the conformally coupled (CC) scalar self-mass-squared on a locally de Sitter background. In this paper we consider only the conformal-conformal interaction part of the self-mass-squared. This complements the minimal-minimal part worked out in the previous paper [E. O. Kahya and R. P. Woodard, Phys. Rev. D 76, 124005 (2007), arXiv: 0709.0536], and we will add the minimal-conformal part in a follow-up paper to complete the full self-mass-squared at one loop order. The computation is performed using dimensional regularization and the results are…
The microscopic structure of black holes remains a challenging subject. In this paper, based on the well-accepted fact that black holes can be mapped to thermodynamic systems, we make a preliminary exploration of the microscopic structure of the thermodynamically stable Schwarzschild anti-de-Sitter (SAdS) black hole. In accordance with the number density and thermodynamic scalar curvature, we give the interaction potential among the molecules of thermodynamically stable SAdS black holes and analyze its effectiveness. Moreover, we derive the thermo-correction to the equation of state for such b…
We have estimated higher order quantum gravity corrections to de~Sitter spacetime. Our results suggest that, while the classical spacetime metric may be distorted by the graviton self-interactions, the corrections are relatively weaker than previously thought, possibly growing like a power rather than exponentially in time.
The correction of Hawking temperature of Schwarzschild-de Sitter (SdS) black hole is investigated using the generalized Klein-Gordon equation and the generalized Dirac equation by taking the quantum gravity effects into account. We derive the corrected Hawking temperatures for scalar particles and fermions crossing the event horizon. The quantum gravity effects prevent the rise of temperature in the SdS black hole. Besides correction of Hawking temperature, the Hawking radiation of SdS black hole is also investigated using massive particles tunneling method. By considering self gravitation eff…
The stochastic spectral expansion method offers a simple framework for calculations in de Sitter spacetimes. We show how to extend its reach to metastable vacuum states, both in the case when the potential is bounded from below, and when it is unbounded from below and therefore no stable vacuum state exists. In both cases, the decay rate of the metastable vacuum is given by the lowest non-zero eigenvalue associated to the Fokker-Planck equation. We show how the corresponding eigenfunction determines the field probability distribution which can be used to compute correlation functions and other…
We define a perturbative S-matrix in a local patch of de Sitter background in the limit when the curvature length scale ($\ell$) is large and study the 'soft' behavior of the scalar QED amplitudes in de Sitter spacetime in generic dimensions. We obtain the leading and subleading perturbative corrections to flat space soft photon theorems in the large $\ell$ limit, and comment on the universality of these corrections. We compare our results with the electromagnetic memory tails obtained earlier in $d=4$ using classical radiation analysis.
We present detailed calculations for quantum-gravitational corrections to the power spectra of gauge-invariant scalar and tensor perturbations during inflation. This is done by performing a semiclassical Born-Oppenheimer type of approximation to the Wheeler-DeWitt equation, from which we obtain a Schroedinger equation with quantum-gravitational correction terms. As a first step, we perform our calculation for a de Sitter universe and find that the correction terms lead to an enhancement of power on the largest scales.
Therotationofthecosmicobjectsisauniversalphenomenonanditsoriginisstillanopenquestion.Here a model for the origin of rotation is presented. After an investigation of the phase transition of a scalar field in de Sitter and Gödel backgrounds, the motion of a test particle during the phase transitions is studied. Then using computer simulation for a congruence of particles, we show that although the local induced rotation is nonzero, the global rotation is below the observational limit.
We study whether the Hawking-Page phase transition may occur in topological de Sitter spaces (TdS) and Schwarzschild-de Sitter black hole (SdS). We show that at the critical temperature $T=T_1$, TdS with hyperbolic cosmological horizon can make the Hawking-Page transition from the zero mass de Sitter space to TdS. It is also shown that there is no Hawking-Page transition for TdS with Ricci-flat and spherical horizons, when the zero mass de Sitter space is taken as the thermal background. Also we find that the SdS undergoes a different phase transition at T=0 which the Nariai black hole is form…
The present work is the second part of a series of computations for the self-mass-squared of the conformally coupled (CC) scalar interacting with gravitons. This work includes the kinetic-kinetic and kinetic-conformal parts, and thus completes the full scalar self-mass squared at one loop order in de Sitter background when combined with the conformal-conformal part previously evaluated. We use dimensional regularization and renormalize the results by subtracting appropriate counterterms. The self-mass squared is finally ready to quantum-correct the CC scalar field equation so that one can stud…
According to a corrected dispersion relation proposed in the study on string theory and quantum gravity theory, Rarita-Schwinger equation has been precisely modified, which results in a Rarita-Schwinger-Hamilton-Jacobi equation, and through which, the characteristics of arbitrary spin fermions quantum tunneling radiation from non-stationary Kerr-de Sitter black hole are researched. A series of accurately corrected physical quantities such as surface gravity, chemical potential, tunneling probability and Hawking temperature that describe the properties of the black hole are derived. This resear…
Graviton loop corrections to observables in de Sitter space often lead to infrared divergences. We show that these infrared divergences are resolved by the spontaneous breaking of de Sitter invariance.
In this note, we consider confining gauge theories in $D=2,3,4$ defined by $S^2$ or $T^2$ compactification of higher-dimensional conformal field theories with gravity duals. We investigate the behavior of these theories on de Sitter spacetime as a function of the Hubble parameter. We find that in each case, the de Sitter vacuum state of the field theory (defined by Euclidian continuation from a sphere) undergoes a deconfinement transition as the Hubble parameter is increased past a critical value. In each case, the corresponding critical de Sitter temperature is smaller than the corresponding …
We obtain microstates accounting for the Gibbons-Hawking entropy in $dS_3$, along with a subleading logarithmic correction, from the solvable $T\bar T+Λ_2$ deformation of a seed CFT with sparse light spectrum. The microstates arise as the dressed CFT states near dimension $Δ=c/6$, associated with the Hawking-Page transition; they dominate the real spectrum of the deformed theory. We exhibit an analogue of the Hawking-Page transition in de Sitter. Appropriate generalizations of the $T\bar T+Λ_2$ deformation are required to treat model-dependent local bulk physics (subleading at large central ch…
The effect of string and quantum gravity inspired minimum-length deformed quantization on a free, massless scalar field is studied on de Sitter background at the level of second quantization. Analytic solution of a field operator is obtained to the first order in deformation parameter. Using this solution we then estimate the two point and four point correlation functions (with respect to the Bunch-Davies vacuum). The field operator shows up a non-linear dependence on creation and annihilation operators, therefore the perturbation spectrum proves to be non-Gaussian. The correction to the power…
This work applies the formalism developed in our earlier paper to de Sitter space. After exactly solving the relevant Heisenberg equations of motion we give a detailed discussion of the subtleties associated with defining physical states and the emergence of the classical theory. This computation provides the striking result that quantum corrections to this long wavelength limit of gravity eliminate the problem of the big crunch. We also show that the same corrections lead to possibly measureable effects on the CMB radiation. Finally, for the sake of completeness we discuss the special case, $…
We consider three dimensional gravity with a positive cosmological constant and non- zero gravitational Chern-Simons term. This theory has inflating de Sitter solutions and local metric degrees of freedom. The Euclidean signature partition function of the theory is evaluated including both perturbative and non-perturbative corrections. The perturbative one-loop correction is computed using heat kernel techniques. The non- perturbative corrections come from gravitational instantons with non-trivial topology which can be enumerated explicitly. We compute the sum over an infinite class of ge- ome…
