We use the spectral representation of the stochastic Starobinsky-Yokoyama approach to compute correlation functions in de Sitter space for a scalar field with a symmetric or asymmetric double-well potential. The terms in the spectral expansion are determined by the eigenvalues and eigenfunctions of the time-independent Fokker-Planck differential operator, and we solve them numerically. The long-distance asymptotic behaviour is given by the lowest state in the spectrum, but we demonstrate that the magnitude of the coeffients of different terms can be very different, and the correlator can be dominated by different terms at different distances. This can give rise to potentially observable cosmological signatures. In many cases the dominant states in the expansion do not correspond to small fluctuations around a minimum of the potential and are therefore not visible in perturbation theory. We discuss the physical interpretation these states, which can be present even when the potential has only one minimum.
An exact de Sitter solution of scalar-tensor gravity is found, in which the non-minimal coupling scalar is rolling along a non-constant potential. Based on this solution, a dust-filled FRW universe is explored in frame of scalar-tensor gravity. The effective dark energy induced by the sole non-minimal scalar can be quintessence-like, phantom-like, and more significantly, can cross the phantom divide. The rich and varied properties of scalar-tensor gravity even with only one scalar is shown in this article.
We calculate quantum fluctuations of a free scalar field in the Schwarzschild-de Sitter space-time, adopting the planar coordinates that is pertinent to the presence of a black hole in an inflationary universe. In a perturbation approach, doing expansion in powers of a small black hole event horizon compared to the de Sitter cosmological horizon, we obtain time evolution of the quantum fluctuations and then derive the scalar power spectrum.
The infrared dynamics of a minimally coupled scalar field in de Sitter spacetime can be described as Brownian motion of a particle in a medium of de Sitter temperature $T_{DS}=\frac{H}{2π}$. The system obeys a fluctuation-dissipation relation and its equilibrium distribution is Maxwell-Boltzmann, implying kinetic and potential energies of comparable magnitudes. The transition to equilibrium is a semi-classical process beyond the scope of perturbation theory for interacting fields. The stochastic kinetic energy of the field causes de Sitter spacetime to cool down slowly with a corresponding dec…
We develop the general reconstruction scheme in two scalar model. The quintom-like theory which may describe (different) non-singular Little Rip or de Sitter cosmology is reconstructed. (In)stability of such dark energy cosmologies as well as the flow to fixed points is studied. The stability of Little Rip universe which leads to dissolution of bound objects sometime in future indicates that no classical transition to de Sitter space occurs.
We compute the greybody factors for non-minimally coupled scalar fields in four-dimensional Schwarzschild-de Sitter spacetime. In particular, we demonstrate that the zero-angular-momentum greybody factor generically tends to zero in the zero-frequency limit like frequency squared if there is non-vanishing coupling to the scalar curvature. This is in contrast with the minimally coupled case, where the greybody factor is known to tend to a finite constant. We also study the Hawking radiation for non-minimally coupled massless scalar fields in Schwarzschild-de Sitter spacetime, formulate a sensib…
We consider light scalar fields during inflation and show how the stochastic spectral expansion method can be used to calculate two-point correlation functions of an arbitrary local function of the field in de Sitter space. In particular, we use this approach for a massive scalar field with quartic self-interactions to calculate the fluctuation spectrum of the density contrast and compare it to other approximations. We find that neither Gaussian nor linear approximations accurately reproduce the power spectrum, and in fact always overestimate it. For example, for a scalar field with only a qua…
We investigate in detail the mechanism of superradiance to render the instability of Kerr-de Sitter black holes in scalar-tensor gravity. Our results provide more clues to examine the scalar-tensor gravity in the astrophysical black holes in the universe with cosmological constant. We also discuss the spontaneous scalarization in the de Sitter background and find that this instability can also happen in the spherical de Sitter configuration in a special style.
The behaviour of a massive, non-interacting and non-minimally coupled quantised scalar field in an expanding de Sitter background is investigated by solving the field evolution for an arbitrary initial state. In this approach there is no need to choose a vacuum in order to provide a definition for particle states. We conclude that the expanding de Sitter space is a stable equilibrium configuration under small perturbations of the initial conditions. Depending on the initial state, the energy density can approach its asymptotic value from above or below, the latter of which implies a violation …
In the semiclassical limit of de Sitter gravity a separation of scales takes place that divides the theory into a "cosmic" sector and a "microscopic" sector. A similar separation takes place in the double-scaled limit of SYK theory. We examine the scaling behaviors that accompany these limits and find parallels that support the previously conjectured duality between Jackiw-Teitelboim gravity (with positive cosmological constant), and double-scaled SYK. This paper is a companion to "dS JT Gravity and Double-Scaled SYK" by Adel Rahman, to appear simultaneously with this paper.
In this work, we investigate inflationary cosmology using scalar field theory deformed by the generalized uncertainty principle (GUP) containing a linear momentum term. Apart from being consistent with the existence of a minimum measurable length scale, this GUP is also consistent with doubly special relativity and hence with the existence of maximum measurable momentum. We use this deformed scalar field theory to analyze the tensor and scalar mode equations in a de Sitter background, and to calculate modifications to the tensor-to-scalar ratio. Finally, we compare our results for the tensor-t…
Inertial observers in de Sitter are surrounded by a horizon and see thermal fluctuations. To them, a massless scalar field appears to follow a random motion but any attractive potential, no matter how weak, will eventually stabilize the field. We study this thermalization process in the static patch (the spacetime region accessible to an individual observer) via a truncation to the low frequency spectrum. We focus on the distribution of the field averaged over a subhorizon region. At timescales much longer than the inverse temperature and to leading order in the coupling, we find the evolution…
We construct a perturbative S-matrix for interacting massive scalar fields in global de Sitter space. Our S-matrix is formulated in terms of asymptotic particle states in the far past and future, taking appropriate care for light fields whose wavefunctions decay only very slowly near the de Sitter conformal boundaries. An alternative formulation expresses this S-matrix in terms of residues of poles in analytically-continued Euclidean correlators (computed in perturbation theory), making it clear that the standard Minkowski-space result is obtained in the flat-space limit. Our S-matrix transfor…
Casimir effect for massless minimally coupled scalar field is studied. An explicit answer for de Sitter spacetime is obtained and analized. Cosmological implications of the result are discussed.
It is shown that the isometry group of the de Sitter spacetime includes two different three-dimensional Abelian subgroups which transform between themselves through a discrete isometry corresponding to the time reversal in the five-dimensional Minkowski spacetime embedding the de Sitter one. The eigenfunctions of the generators of these Abelian subgroups form two different sets of quantum modes correlated by the mentioned isometry.
We present new solutions of warped compactifications in the higher-dimensional gravity coupled to the scalar and the form field strengths. These solutions are constructed in the D-dimensional spacetime with matter fields, with the internal space that has a finite volume. Our solutions give explicit examples where the cosmological constant or 0-form field strength leads to a de Sitter spacetime in arbitrary dimensions.
We study the superradiance instability of charged massive scalar field in the background of Kerr-Newman-anti-de Sitter black hole. By employing the asymptotic matching technique to solve Klein-Gordon equation analytically, the complex parts of quasinormal frequencies are shown to be positive in the regime of superradiance. Because the calculation is performed in the approximation of small black hole, the result indicates that small Kerr-Newman-anti-de Sitter black hole is unstable against the massive scalar field perturbation with small charge.
We study the response of a classical massless minimally coupled scalar to a static point scalar charge on de Sitter. By considering explicit solutions of the problem we conclude that -- even though the dynamics formally admits dilatation (scaling) symmetry -- the physical scalar field profile necessarily breaks the symmetry. This is an instance of symmetry breaking in classical physics due to large infrared effects. The gravitational backreaction, on the other hand, does respect dilatation symmetry, making this an example of symmetry non-inheritance phenomenon.
We investigate the weak cosmic censorship conjecture in extremal and near-extremal Kerr-Newman-(anti-)de Sitter black holes by the scattering of a massive scalar field with an electric charge. Under this scattering, the scalar field fluxes change the black hole state, as determined by the mass, angular momentum, and electric charge. The black hole may exceed its extremal condition because of these changes. However, we find that the black hole cannot be overcharged or overspun by the scattering. In particular, although the fluxes are closely associated with the asymptotic boundary conditions al…
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 …
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, …
In this work we investigate the quantum theory of scalar fields propagating in a $D-$dimensional de Sitter spacetime. The method of dynamic invariants is used to obtain the solution of the time-dependent Schrödinger equation. The quantum behavior of the scalar field in this background is analyzed, and the results generalize previous ones found in the literature. We point that the Bunch-Davies thermal bath depends on the choice of $D$ and the conformal parameter $ξ$. This is important in extra dimension physics, as in the Randall-Sundrum model.
We study the greybody factor and power spectra of Hawking radiation for the minimally or nonminimally coupled scalar field with exact numerical method in spherically symmetric Einstein-Gauss-Bonnet-de Sitter black hole spacetime. The effects of scalar coupling constant, angular momentum number of scalar, spacetime dimension, cosmological constant and Gauss-Bonnet coupling constant on the Hawking radiation are studied in detail. Specifically, the Gauss-Bonnet coupling constant always increases the greybody factor in the entire energy regime. Different from the case of Schwarzschild-de Sitter bl…
We study the backreaction of superhorizon fluctuations of a light quantum scalar field on a classical de Sitter geometry by means of the Wilsonian renormalisation group. This allows us to treat the gravitationally amplified fluctuations in a nonperturbative manner and to analytically follow the induced renormalisation flow of the spacetime curvature as long wavelength modes are progressively integrated out. Unbounded loop corrections in the deep infrared are eventually screened by nonperturbative effects which stabilise the geometry.
In this paper, we study spontaneous scalarization of asymptotically anti-de Sitter charged black holes in the Einstein-Maxwell-scalar model with a non-minimal coupling between the scalar and Maxwell fields. In this model, Reissner-Nordström-AdS (RNAdS) black holes are scalar-free black hole solutions, and may induce scalarized black holes due to the presence of a tachyonic instability of the scalar field near the event horizon. For RNAdS and scalarized black hole solutions, we investigate the domain of existence, perturbative stability against spherical perturbations and phase structure. In a …
We present spinning Q-balls and boson stars in four dimensional anti-de Sitter spacetime. These are smooth, horizonless solutions for gravity coupled to a massive complex scalar field with a harmonic dependence on time and the azimuthal angle. Similar to the flat spacetime configurations, the angular momentum is quantized. We find that a class of solutions with a self-interaction potential has a limit corresponding to static solitons with axial symmetry only. An exact solution describing spherically symmetric Q-balls in a fixed AdS background is also discussed.
We derive the response function for a comoving, pointlike Unruh-DeWitt particle detector coupled to a complex scalar field $ϕ$, in the $(3+1)$-dimensional cosmological de Sitter spacetime. The field-detector coupling is taken to be proportional to $ϕ^{\dagger} ϕ$. We address both conformally invariant and massless minimally coupled scalar field theories, respectively in the conformal and the Bunch-Davies vacuum. The response function integral for the massless minimal complex scalar, not surprisingly, shows divergences and accordingly we use suitable regularisation scheme to find out well behav…
We find a new instability in the four-dimensional Reissner-Nordstrom-de Sitter black holes against charged scalar perturbations with vanishing angular momentum, $l=0$. We show that such an instability is caused by superradiance. The instability does not occur for an larger angular index, as explicitely proven for $l=1$. Our results are obtained from a numerical investigation of the time domain profiles of the perturbations.
In this work we derive a general expression for the greybody factor of non-minimally coupled scalar fields in Reissner-Nordström-de Sitter spacetime in low frequency approximation. In particular case of zero momentum, greybody factor tends to zero in low frequency limit as frequency squared goes to zero for non-vanishing coupling. We also elaborate the significance of the results by giving formulae of differential energy rate and general absorption cross section. The greybody factor gives insight into the spectrum of Hawking radiations.
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 consider the massless minimally coupled scalar field in the de Sitter ambient space formalism as a gauge potential or connection field. We construct the scalar gauge theory by helping an arbitrary constant five-vector field $B^α$ analogous to the standard gauge theory. The Lagrangian density of the interaction between the scalar and spinor fields is presented in this framework. The Yukawa potential can be extracted from this Lagrangian density at the null curvature limit by an appropriate choice of a constant five-vector field. It is shown that the de Sitter ambient space formalism permits …
We investigate the thermodynamic properties of 3+1 dimensional black holes in asymptotically de Sitter spacetimes, conformally coupled to a real scalar field. We use a Euclidean action approach, where boundary value data is specified at a finite radius `cavity' outside the black hole, working in the extended phase space where the cosmological constant is treated as a thermodynamic pressure. We examine the phase structure of these black holes through their free energy. For the MTZ subclass of solutions, we find Hawking-Page-like phase transitions from a black hole spacetime to thermal de Sitter…
We study spatially localized, time-periodic solutions (breathers) of scalar field theories with various self-interacting potentials on Anti-de Sitter (AdS) spacetimes in $D$ dimensions. A detailed numerical study of spherically symmetric configurations in $D=3$ dimensions is carried out, revealing a rich and complex structure of the phase-space (bifurcations, resonances). Scalar breather solutions form one-parameter families parametrized by their amplitude, $\varepsilon$, while their frequency, $ω=ω(\varepsilon)$, is a function of the amplitude. The scalar breathers on AdS we find have a small…
We study the quantum theory of an O(N) scalar field on de Sitter geometry at leading order in a nonperturbative 1/N-expansion. This resums the infinite series of so-called superdaisy loop diagrams. We obtain the de Sitter symmetric solutions of the corresponding, properly renormalized, dynamical field equations and compute the complete effective potential. Because of its self-interactions, the field acquires a strictly positive square mass which screens potential infrared divergences. Moreover, strongly enhanced ultralong-wavelength fluctuations prevent the existence of a spontaneously broken …
Assuming both that our Universe is evolving into a de Sitter space and a vanishing cosmological constant, leaves only the option that the observed acceleration is provided by a "kinetic" energy of a scalar field. From an effective field theory point of view, the absence of Ostrogradsky instabilities restricts the choice to shift-symmetric Horndeski theories. Within these theories, we find the conditions for the existence of a de Sitter critical point in a universe filled by matter, radiation and a Horndeski scalar. Moreover, we show that this point is a universal attractor and we provide the t…
In this letter we will study the cosmological dynamical system of an $f(R)$ gravity in the presence of a canonical scalar field $ϕ$ with an exponential potential, by constructing the dynamical system in a way that it is render autonomous. This feature is controlled by a single variable $m$, which when it is constant, the dynamical system is autonomous. We focus on the $m=0$ case which, as we demonstrate by using a numerical analysis approach, leads to an unstable de Sitter attractor, which occurs after $N\sim 60$ $e$-foldings. This instability can be viewed as a graceful exit from inflation, w…
Equipped with new powerful and efficient methods for computing quantum expectation values in static-spherically symmetric spacetimes in arbitrary dimensions, we perform an in-depth investigation of how the quantum vacuum polarization varies with the parameters in the theory. In particular, we compute and compare the vacuum polarization for a quantum scalar field in the Schwarzschild anti-de Sitter black hole spacetime for a range of values of the field mass and field coupling constant as well as the black hole mass and number of spacetime dimensions. In addition, a new approximation for the va…
We investigate the thermodynamics and stability of the horizons in warped anti-de Sitter black holes of the new massive gravity under the scattering of a massive scalar field. Under scattering, conserved quantities can be transferred from the scalar field to the black hole, which change the state of the black hole. We determine that the changes in the black hole are well coincident with the laws of thermodynamics. In particular, the Hawking temperature of the black hole cannot be zero in the process as per the third law of thermodynamics. Furthermore, the black hole cannot be overspun beyond t…
Scalar-tensor gravity is one of the most competitive gravity theory to Einstein's relativity. We reconstruct the exact de Sitter solution in scalar-tensor gravity, in which the non-minimal coupling scalar is rolling along the potential. This solution may have some relation to the early inflation and present acceleration of the universe. We investigated its primordial quantum perturbation around the adiabatic vacuum. We put forward for the first time that exact de Sitter generates non-exactly scale invariant perturbations. In the conformal coupling case, this model predicts that the tensor mode…
We study the phi^4 scalar field theory in de Sitter space using the 2PI effective action formalism. This formalism enables us to investigate the nonperturbative quantum effects. We use the mean field and gap equations and calculate the physical mass and effective potential. We find that nonperturbative infrared effects on de Sitter space produce a curvature-induced mass and work to restore the broken Z_2 symmetry.
It has been shown recently that the strong cosmic censorship conjecture is violated by near-extremal Reissner-Nordström-de Sitter black holes. We investigate whether the introduction of a charged scalar field can rescue strong cosmic censorship. We find that such a field improves the situation but there is always a neighbourhood of extremality in which strong cosmic censorship is violated by perturbations arising from smooth initial data.
We analytically investigate the quasinormal modes of the massive scalar field with a nonminimal coupling in the higher-dimensional de Sitter black hole with a single rotation. According to the separated scalar field equation, the boundary conditions of quasinormal modes are well constructed at the outer and cosmological horizons. Then, under near-extremal conditions, where the outer horizon closes to the cosmological horizon, the quasinormal frequencies are obtained and generalized to universal form in the higher-dimensional spacetime. Here, the real part of the frequency includes the scalar f…
We study scalar condensations around asymptotically Anti-de Sitter(AdS) regular reflecting shells. We show that the charged scalar field can condense around charged reflecting shells with both Dirichlet and Neumann boundary conditions. In particular, the radii of the asymptotically AdS hairy shells are discrete, which is similar to cases in asymptotically flat spacetimes. We also provide upper bounds for the radii of the hairy Dirichlet reflecting shells and above the bound, the scalar field cannot condense around the shell.
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…
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.
