We find that the amplitude of quantum fluctuations of the invariant de Sitter vacuum coincides exactly with that of the vacuum of a comoving observer for a massless scalar (inflaton) field. We propose redefining the actual physical power spectrum as the difference between the amplitudes of the above vacua. An inertial particle detector continues to observe the Gibbons-Hawking temperature. However, although the resulting power spectrum is still scale-free, its amplitude can be drastically reduced since now, instead of the Hubble's scale at the inflationary period, it is determined by the square of the mass of the inflaton fluctuation field.
We develop a nonperturbative quantum scalar field formalism from a noncompact Kaluza-Klein (KK) theory using the induced-matter theory of gravity during inflation. We study the particular case of a de Sitter expansion for the universe.
We use Heun type solutions given in \cite{Suzuki} for the radial Teukolsky equation, written in the background metric of the Kerr-Newman-de Sitter geometry, to calculate the quasinormal frequencies for polynomial solutions and the reflection coefficient for waves coming from the de Sitter horizon and reflected at the outer horizon of the black hole.
It has recently been suggested that Planck scale physics may effect the evolution of cosmological fluctuations in the early stages of cosmological inflation in a non-trivial way, leading to an excited state for modes whose wavelength is super-Planck but sub-Hubble. In this case, the issue of how this excited state back-reacts on the background space-time arises. In fact, it has been suggested that such back-reaction effects may lead to tight constraints on the magnitude of possible deviations from the usual predictions of inflation. In this note we discuss some subtle aspects of this back-reac…
We consider the quasi-de Sitter geometry of the inflationary universe. We calculate the energy flux of the slowly rolling background scalar field through the quasi-de Sitter apparent horizon and set it equal to the change of the entropy (1/4 of the area) multiplied by the temperature, dE=TdS. Remarkably, this thermodynamic law reproduces the Friedmann equation for the rolling scalar field. The flux of the slowly rolling field through the horizon of the quasi-de Sitter geometry is similar to the accretion of a rolling scalar field onto a black hole, which we also analyze. Next we add inflaton f…
In this short note, we verify explicitly in static coordinates that the non trivial asymptotic Killing vectors at spatial infinity for anti-de Sitter space-times correspond one to one to the conformal Killing vectors of the conformally flat metric induced on the boundary. The fall-off conditions for the metric perturbations that guarantee finiteness of the associated conserved charges are derived.
In this letter we study the generation of gravitational waves during inflation from a 5D vacuum theory of gravity. Within this formalism, on an effective 4D de Sitter background, we recover the typical results obtained with 4D inflationary theory in general relativity, for the amplitude of gravitational waves generated during inflation. We also obtain a range of values for the amplitude of tensor to scalar ratio which is in agreement with COBE observations.
We interpret the cosmological constant as the energy of the vacuum, and under a minimum amount of assumptions, we show that it is deformed in the vicinity of a black hole. This leads us to reexamine the Kerr-de Sitter solution. We provide a new solution, simpler and geometrically richer, which shows the impact of the rotation in form of a warped curvature. We carry out a detailed and exact study on the new black hole solution, and we conclude with a conjecture regarding the possible impact of our results on alternative theories.
We calculate the one-loop vacuum polarization tensor of scalar electrodynamics in a locally de Sitter space-time, endowed with a nearly minimally coupled, light scalar field. We show that the photon dynamics is well approximated by a (local) Proca Lagrangean. Since the photon mass can be much larger than the Hubble parameter, the photons may propagate slowly during inflation. Finally, we briefly discuss magnetic field generation on cosmological scales, and point out that, while the spectrum of the magnetic field is identical to that obtained from the massless scalar, B_l ~ B_0/l, the amplitude…
We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of the comoving curvature perturbation and discuss the slow-roll order of the n-point correlation function.
In this paper, we revisit brane inflation models with the WMAP five-year results. The WMAP five-year data favor a red-tilted power spectrum of primordial fluctuations at the level of two standard deviations, which is the same as the WMAP three-year result qualitatively, but quantitatively the spectral index is slightly greater than the three-year value. This result can bring impacts on brane inflation models. According to the WMAP five-year data, we find that the KKLMMT model can survive at the level of one standard deviation, and the fine-tuning of the parameter $β$ can be alleviated to a cer…
We consider the semiclassical Einstein equations (SEE) in the presence of a quantum scalar field with self-interaction $λϕ^4$. Working in the Hartree truncation of the two-particle irreducible (2PI) effective action, we compute the vacuum expectation value of the energy-momentum tensor of the scalar field, which act as a source of the SEE. We obtain the renormalized SEE by implementing a consistent renormalization procedure. We apply our results to find self-consistent de Sitter solutions to the SEE in situations with or without spontaneous breaking of the $Z_2$-symmetry.
It is possible to associate temperatures with the non-extremal horizons of a large class of spherically symmetric spacetimes using periodicity in the Euclidean sector and this procedure works for the de Sitter spacetime as well. But, unlike e.g., the black hole spacetimes, the de Sitter spacetime also allows a description in Friedmann coordinates. This raises the question of whether the thermality of the de Sitter horizon can be obtained, working entirely in the Friedmann coordinates, without reference to the static coordinates or using the symmetries of de Sitter spacetime. We discuss several…
We generalize the stochastic approach to quasi-power-law inflationary Universes,obtain the corresponding Langevin and Fokker-Planck equations for the scalar field driving inflation and find stationary solutions to the above FP equation.
This paper represents an in-depth treatment of the chain inflation scenario. We fully determine the evolution of the universe in the model, the necessary conditions in order to have a successful inflationary period, and the matching with the observational results regarding the cosmological perturbations. We study in great detail, and in general, the dynamics of the background, as well as the mechanism of generation of the perturbations. We also find an explicit formula for the spectrum of adiabatic perturbations. Our results prove that chain inflation is a viable model for solving the horizon,…
A semi-classical analysis of vacuum energy in the expanding spacetime suggests that the cosmological term decays with time, with a concomitant matter production. For early times we find, in Planck units, $Λ\approx H^4$, where H is the Hubble parameter. The corresponding cosmological solution has no initial singularity, existing since an infinite past. During an infinitely long period we have a quasi-de Sitter, inflationary universe, with $H \approx 1$. However, at a given time, the expansion undertakes a phase transition, with H and $Λ$ decreasing to nearly zero in a few Planck times, producin…
We consider a quantum scalar field with λϕ^4 interaction in curved spacetimes. The quantum effects are taken into account nonperturbatively using the Hartree approximation to the 2PI effective action. Although this approximation has been considered in many previous works, we reconsider it using a consistent nonperturbative renormalization procedure, which we extend to general curved spacetimes. We obtain the renormalized equations for the mean field and for the propagator of the fluctuations, showing explicitly their independence on the arbitrary scale introduced by the regularization scheme. …
We continue studying the zero mass limit of the Kerr- (Anti) de Sitter space-times by investigating the possibility of special values of the frequencies to have polynomial solutions for the radial wave equation, compute reflection coefficient for waves coming from and going to the cosmological horizon and see whether there is Hawking radiation for de Sitter geometry. We used the Parikh-Wilczek method to study this property and could not find Hawking radiation.
It is widely believed that in the presence of a positive cosmological constant, heavy black holes can exhibit non-standard behaviour, namely there is a possibility that such objects would grow instead of evaporating. We point out that all those results (obtained in different frameworks) rely heavily upon the identification of the Nariai spacetime with the Schwarzschild--de Sitter (Kottler) black hole. In this note we argue that it is an incorrect assumption. As a result, previous treatments need revisiting. In particular, we show that within effective action approach, there is no solution corr…
We discuss under which conditions multi-field cold and warm inflationary models with canonical kinetic energy terms are compatible with the swampland conjectures about the emergence of de Sitter solutions in string theory. We find that under quite general conditions the slow-roll conditions for multi-field cold inflation are at odds with the swampland conjectures for an arbitrary number of scalar fields driving inflation. However, slow-roll conditions can be reconciled with the swampland conjectures in the strong dissipative regime of warm inflation.
Stochastic inflation describes the global structure of the inflationary universe by modeling the super-Hubble dynamics as a system of matter fields coupled to gravity where the sub-Hubble field fluctuations induce a stochastic force into the equations of motion. The super-Hubble dynamics are ultralocal, allowing us to neglect spatial derivatives and treat each Hubble patch as a separate universe. This provides a natural framework in which to discuss probabilities on the space of solutions and initial conditions. In this article we derive an evolution equation for this probability for an arbitr…
In this short note, we pointed out that Warm inflationary scenario remains to be favoured over its cold counterpart by the recently proposed conjectures, which aim to overrule de Sitter like constructions in String Landscapes. On the other hand, the canonical cold (single-field slow-roll) inflationary models, which were in tension with the previously proposed de Sitter conjecture, have now become even more unlikely to realise in String Landscapes as these scenarios fail to cope up with both the conjectures, de Sitter and trans-Planckian censorship, at one go.
In this work, we revisit the perturbations that are generated in the bounce inflation scenario constructed within the framework of $f(T)$ theory. It has been well known that pure $f(T)$ theory cannot give rise to bounce inflation behavior, so aside from the gravity part, we also employ a canonical scalar field for minimal extension. We calculate the perturbations in $f(T)$ theory using the well-established ADM formalism, and find various conditions to avoid their pathologies. We find that it is indeed very difficult to obtain a healthy model without those pathologies, however, one may find a w…
We explore trace-anomaly driven inflation in modified gravity. It is explicitly shown that in $T^2$ teleparallel gravity, the de Sitter inflation can occur, although quasi de Sitter inflation happens in $R^2$ gravity. Furthermore, we investigate the influence of the trace anomaly on inflation. It is found that in $f(T)$ gravity, the de Sitter inflation can end because it becomes unstable due to the trace anomaly, whereas also in higher derivative gravity, the de Sitter inflation can be realized and it will be over thanks to the trace anomaly for smaller parameter regions in comparison with tho…
The "de Sitter constraint" on the space of effective scalar field theories consistent with superstring theory provides a lower bound on the slope of the potential of a scalar field which dominates the evolution of the Universe, e.g., a hypothetical inflaton field. Whereas models of single scalar field inflation with a canonically normalized field do not obey this constraint, it has been claimed recently in the literature that models of warm inflation can be made compatible with it in the case of large dissipation. The de Sitter constraint is known to be derived from entropy considerations. Sin…
We briefly revisit the Schwarzschild-de Sitter solution in the context of five-dimensional general relativity. We obtain a class of five-dimensional solutions of Einstein vacuum field equations into which the four-dimensional Schwarzschild-de Sitter space can be locally and isometrically embedded. We show that this class of solutions is well-behaved in the limit of lambda approaching zero. Applying the same procedure to the de Sitter cosmological model in five dimensions we obtain a class of embedding spaces which are similarly well-behaved in this limit. These examples demonstrate that the pr…
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 study the structure of two-point correlators of the inflationary field fluctuations in order to improve the accuracy and efficiency of the existing methods to calculate primordial spectra. We present a description motivated by the separation of the fast and slow evolving components of the spectrum which is based on Cholesky decomposition of the field correlator matrix. Our purpose is to rewrite all the relevant equations of motion in terms of slowly varying quantities. This is important in order to consider the contribution from high-frequency modes to the spectrum without affecting computa…
We study the Einstein-singleton theory during de Sitter inflation since it provides a way of degenerate fourth-order scalar theory. We obtain an exact solution expressed in terms of the exponential-integral function by solving the degenerate fourth-order scalar equation in de Sitter spacetime. Furthermore, we find that its power spectrum blows negatively up in the superhorizon limit, while it is negatively scale-invariant in the subhorizon limit. This suggests that the Einstein-singleton theory contains the ghost-instability and thus, it is not suitable for developing a slow-roll inflation mod…
We calculate the probability distribution for the volume of the Universe after slow-roll inflation both in the eternal and in the non-eternal regime. Far from the eternal regime the probability distribution for the number of e-foldings, defined as one third of the logarithm of the volume, is sharply peaked around the number of e-foldings of the classical inflaton trajectory. At the transition to the eternal regime this probability is still peaked (with the width of order one e-folding) around the average, which gets twice larger at the transition point. As one enters the eternal regime the pro…
We revisit phenomenological as well as string-theoretical aspects of D-brane inflation cosmological models. Phenomenologically these models stand out on par with $α$-attractors, as models with Planck-compatible values of $n_s$, moving down to the sweet spot in the data with decreasing value of $r$. On the formal side we present a new supersymmetric version of these models in the context of de Sitter supergravity with a nilpotent multiplet and volume modulus stabilization. The geometry of the nilpotent multiplet is evaluated in the framework of string theory.
The methods of supergravity allow us to derive a multi-field F-term potential. Using this, we denote a generic and non-positive single-field F-term potential. We insert our theory into the scalar-gravity part of the $SU(2,1|1)$ invariant superconformal action. That action leads us to a de Sitter solution at the inflationary trajectory. One can denote stabilization of fields in terms of the Kähler kinetic terms and single-field slow-roll inflation parameters. We combine these with the de Sitter swampland conjecture to generate a bounded conjecture. This approach allowed us to show that the sing…
We develop a stochastic approach to a non de Sitter Universe in a gauge-invariant way and obtain a system of Langevin-type equations which may be considered to be renormalization group equations for the long wave parts of the scalar fields and metric. We investigate in detail the case of generalized power-law inflation that appears in the model of the deflationary exit from the inflationary stage. For this case the above system is simplified greatly, we derive a Fokker-Planck equation for the scalar field driving inflation, find its stationary solutions and solve the FP equation for a delta-fu…
We revisit gravitino production following inflation. As a first step, we review the standard calculation of gravitino production in the thermal plasma formed at the end of post-inflationary reheating when the inflaton has completely decayed. Next we consider gravitino production prior to the completion of reheating, assuming that the inflaton decay products thermalize instantaneously while they are still dilute. We then argue that instantaneous thermalization is in general a good approximation, and also show that the contribution of non-thermal gravitino production via the collisions of inflat…
A new gauge-invariant criterion for stability against inhomogeneous perturbations of de Sitter space is applied to scenarios of dark energy and inflation in scalar-tensor gravity. The results extend previous studies.
We compute the mass and the temperature of third order Lovelock black holes with negative Gauss-Bonnet coefficient $α_2<0$ in anti-de Sitter space and perform the stability analysis of topological black holes. When $k=-1$, the third order Lovelock black holes are thermodynamically stable for the whole range $r_+$. When $k=1$, we found that the black hole has an intermediate unstable phase for $D=7$. In eight dimensional spacetimes, however, a new phase of thermodynamically unstable small black holes appears if the coefficient $\tildeα$ is under a critical value. For $D\geq 9$, black holes have…
Variation of the 4-D string cosmology action with dynamical torsion and massless dilatons lead to an expression of torsion in terms of massless dilatons in the case of de Sitter inflation.The solution is approximated according to the COBE data.
We consider an inflationary universe model in which the phase of accelerated expansion was preceded by a non-singular bounce and a period of contraction which involves a phase of deceleration. We follow fluctuations which exit the Hubble radius in the radiation-dominated contracting phase as quantum vacuum fluctuations, re-enter the Hubble radius in the deflationary period and re-cross during the phase of inflationary expansion. Evolving the fluctuations using the general relativistic linear perturbation equations, we find that they exit the Hubble radius during inflation not with a scale-inva…
In this work we re-investigate pros and cons of mutated hilltop inflation. Applying Hamilton-Jacobi formalism we solve inflationary dynamics and find that inflation goes on along the ${\cal W}_{-1}$ branch of the Lambert function. Depending on the model parameter mutated hilltop model renders two types of inflationary solutions: one corresponds to small inflaton excursion during observable inflation and the other describes large field inflation. The inflationary observables from curvature perturbation are in tune with the current data for a wide range of the model parameter. The small field br…
We reconsider an inflationary model that inflaton field is non-minimally coupled to gravity. We study parameter space of the model up to the second ( and in some cases third ) order of the slow-roll parameters. We calculate inflation parameters in both Jordan and Einstein frames and the results are compared in these two frames and also with observations. Using the recent observational data from combined WMAP5+SDSS+SNIa datasets, we study constraint imposed on our model parameters especially the nonminimal coupling $ξ$.
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.
Earlier it was shown that the entropy of an ideal gas, contained in a box and moving in a gravitational field, develops an area dependence when it approaches the horizon of a static, spherically symmetric spacetime. Here we extend the above result in two directions; viz., to (a) the stationary axisymmteric spacetimes and (b) time dependent cosmological spacetimes evolving asymptotically to the de Sitter or the Schwarzschild de Sitter spacetimes. While our calculations are exact for the stationary axisymmetric spacetimes, for the cosmological case we present an analytical expression of the entr…
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…
When the slow-roll parameter $ε_H$ is smaller than $H^2/M_{\rm Pl}^2$, the quantum fluctuations of the inflaton after the horizon crossing are large enough to realize eternal inflation. Whereas they do not generate a sufficient amount of density fluctuation of the inflaton to produce the black hole in quasi-de Sitter space, they can also generate the sizeable density fluctuation of the radiation when the number of degrees of freedom increases rapidly in time, as predicted by the distance conjecture. We argue that the condition that the density fluctuation of the radiation is not large enough t…
Out-of-time-ordered Correlators in de Sitter Revisited
Department of Physics and Astronomy, University of Kentucky（肯塔基大学物理与天文学系）；Racah Institute of Physics, The Hebrew University of Jerusalem（耶路撒冷希伯来大学拉卡物理研究所）；ORFE Department, Princeton University（普林斯顿大学运筹工程金融系）；Department of Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校物理系）
We study the multifield inflationary models where the cosmological perturbation is sourced by light scalar fields other than the inflaton. We exploit the operator product expansion and partly the symmetries present during the de Sitter epoch to characterize the non-Gaussian four-point correlator in the squeezed limit. We point out that the contribution to it from the intrinsic non-Gaussianity of the light fields at horizon crossing can be larger than the usually studied contribution arising on superhorizon scales and it comes with a different shape. Our findings indicate that particular attent…
The measured Standard Model parameters lie in a range such that the Higgs potential, once extrapolated up to high scales, develops a minimum of negative energy density. This has important cosmological implications. In particular, during inflation, quantum fluctuations could have pushed the Higgs field beyond its potential barrier, triggering the formation of anti-de Sitter regions, with fatal consequences for our universe. By requiring that this did not happen, one can in principle connect (and constrain) Standard Model parameters with the energy scale of inflation. In this context, we highlig…
Motivated by issues on inflation, a generalized modified gravity model is investigated, where the model Lagrangian is described by a smooth function $f(R, K, ϕ)$ of the Ricci scalar $R$, the kinetic term $K$ of a scalar field $ϕ$. In particular, the one-loop effective action in the de Sitter background is examined on-shell as well as off-shell in the Landau gauge. In addition, the on-shell quantum equivalence of $f(R)$ gravity in the Jordan and Einstein frames is explicitly demonstrated. Furthermore, we present applications related to the stability of the de Sitter solutions and the one-loop q…
We revisit inflation with non-canonical scalar fields by applying deformed-steepness exponential potentials. We show that the resulting scenario can lead to inflationary observables, and in particular to scalar spectral index and tensor-to-scalar ratio, in remarkable agreement with observations. Additionally, a significant advantage of the scenario is that the required parameter values, such as the non-canonicality exponent and scale, as well as the potential exponent and scale, do not need to acquire unnatural values and hence can accept a theoretical justification. Hence, we obtain a signifi…
Criteria for the existence of de Sitter inflation with dilaton fields in four-dimensional space-times with torsion is discussed.The relation between matter density perturbation and the spin-density perturbation is stablished based on this criteria.From COBE data it is shown that there is a linear relationship between the spin-torsion density and temperature of the Universe for the case where matter density dominates the kinetic part of dilaton fields.
We revisit the constraints on inflation models by using the current cosmological observations involving the latest local measurement of the Hubble constant ($H_{0} = 73.00\pm 1.75$ km s $^{-1}$ Mpc$^{-1}$). We constrain the primordial power spectra of both scalar and tensor perturbations with the observational data including the Planck 2015 CMB full data, the BICEP2 and Keck Array CMB B-mode data, the BAO data, and the direct measurement of $H_0$. In order to relieve the tension between the local determination of the Hubble constant and the other astrophysical observations, we consider the add…
In this paper, we study the correspondence between a field theory in de Sitter space in $D$-dimensions and a dual conformal field theory in a euclidean space in $(D-1)$-dimensions. In particular, we investigate the form in which this correspondence is established for a system of interacting scalar and a vector fields propagating in de Sitter space. We analyze some necessary (but not sufficient) conditions for which conformal symmetry is preserved in the dual theory in $(D-1)$-dimensions, making possible the establishment of the correspondence. The discussion that we address on this paper is fr…
We compute the one loop self-mass of a charged massless, minimally coupled scalar in a locally de Sitter background geometry. The computation is done in two different gauges: the noninvariant generalization of Feynman gauge which gives the simplest expression for the photon propagator and the de Sitter invariant gauge of Allen and Jacobson. In each case dimensional regularization is employed and fully renormalized results are obtained. By using our result in the linearized, effective field equations one can infer how the scalar responds to the dielectric medium produced by inflationary particl…
