De Sitter Solution Research Articles

Cosmological solutions with time-delay

We introduce a time-delay function in bulk viscosity cosmology. Even for bulk viscosity functions where closed-form solutions are known, because of the time-delay term, the exact solutions are lost. Therefore in order to study the cosmological evolution of the resulting models we perform a detailed analysis of the stability of the critical points, which describe de Sitter solutions, by using Lindstedt’s method. We find that for the stability of the critical points it depends also on the time-delay parameter, where a critical time-delay value is found which plays the role of a bifurcation point. For time-delay values near the critical value, the cosmological evolution has a periodic evolution, this oscillating behavior is because of the time-delay function. We find a new behavior near the exponential expansion point, which can be seen also as an alternative way to exit the exponential inflation.

Exploring the landscape of (anti-) de Sitter and Minkowski solutions: group manifolds, stability and scale separation

We classified in [1] certain 10d supergravity solutions with a 4d de Sitter, Minkowski or anti-de Sitter spacetime. We then found new solutions in previously unexplored classes. In this paper we study their properties, compare them to swampland conjectures, and make new observations.Using new numerical tools, we first identify all Lie algebras underlying the 6d group manifolds, allowing us to discuss their compactness. We then investigate scale separation, and prove related no-go theorems. Last but not least, we automatize and analyze the stability of all solutions. This leads us to propose the Massless Minkowski Conjecture, claiming the systematic presence of a 4d flat direction.

The spectral geometry of de Sitter space in asymptotic safety

Within the functional renormalization group approach to Background Independent quantum gravity, we explore the scale dependent effective geometry of the de Sitter solution dS4. The investigation employs a novel approach whose essential ingredient is a modified spectral flow of the metric dependent d’Alembertian, or of similar hyperbolic kinetic operators. The corresponding one-parameter family of spectra and eigenfunctions encodes information about the nonperturbative backreaction of the dynamically gravitating vacuum fluctuations on the mean field geometry of the quantum spacetime. Used as a diagnostic tool, the power of the spectral flow method resides in its ability to identify the scale dependent subsets of field modes that supply the degrees of freedom which participate in the effective field theory description of the respective scale. A central result is that the ultraviolet of Quantum Einstein Gravity comprises far less effective degrees of freedom than predicted (incorrectly) by background dependent reasoning. The Lorentzian signature of dS4 is taken into account by selecting a class of renormalization group trajectories which are known to apply to both the Euclidean and a Lorentzian version of the approach. Exploring the quantum spacetime’s spatial geometry carried by physical fields, we find that 3-dimensional space disintegrates into a collection of coherent patches which individually can, but in their entirety cannot be described by one of the effective average actions occurring along the renormalization group trajectory. A natural concept of an entropy is introduced in order to quantify this fragmentation effect. Tentatively applied to the real Universe, surprising analogies to properties of the observed cosmic microwave background are uncovered. Furthermore, a set of distinguished field modes is found which, in principle, has the ability to transport information about the asymptotic fixed point regime from the ultraviolet, across almost the entire “scale history”, to cosmological distances in the observed Universe.

Charting the landscape of (anti-) de Sitter and Minkowski solutions of 10d supergravities

We classify solutions of 10d type IIA/B supergravities with orientifolds, on a 4d maximally symmetric spacetime times a 6d group manifold. We then look for new solutions in previously unexplored solution classes, and find some: (anti-) de Sitter solutions with intersecting O4, O6 and D6, or Minkowski solutions with 3 intersecting O5, among others. We provide the numerical code that we developed for this purpose. We also prove new no-go theorems against (anti-) de Sitter solutions. We finally conjecture the absence of de Sitter solution for 2 or less intersecting source sets, implying that a 4d effective theory with de Sitter is at most mathcal{N} = 1 supersymmetric.

STAROBINSKY MODEL WITH A VISCOUS FLUID

The article considers some cosmological solutions of the Starobinsky model for a flat inhomogeneous viscous Universe. The first section contains a brief of the F(R)  theory of gravity. One of the most common examples of F(R) gravity with a high degree of curvature is the Starobinsky model. For the Starobinsky  F(R)=aR+bR2 model, the cosmological model of a flat and homogeneous Universe is considered. For the Friedmann-Robertson-Walker metric, the Lagrange function is defined, and the corresponding equations are determined by the Euler-Lagrange equations and the Hamilton energy condition. Using the equation of state for inhomogeneous viscous fluid, we considered two cases of the viscosity parameter when the state parameter is constant. Next, using the results obtained, we determined the dynamics of the Hubble parameter H. At constant viscosity,  has a negative value of the Hubble parameter and decreases with time along a hyperbola, while the viscosity parameter with proportional dependence on H has a positive value that decreases along a hyperbola. If we compare it with the well-known de Sitter solution describing the accelerated expansion of the Universe and take into account that time in physics should only be positive, then the change in the Hubble parameter for the viscosity with proportional dependence on H occurs later. An analysis of this solution shows that at a certain point in time the acceleration of the Universe turns into a process of instantaneous compression. However, in the end, the result is similar to the de Sitter solution tends to zero, i.e. the Universe stops accelerating. Based on the results obtained, a graph was constructed with respect to the de Sitter solution. The analysis was carried out according to the graph. These results are useful for describing the accelerated expansion of the modern Universe and do not contradict modern astronomical observations.

RG-induced modulus stabilization: perturbative de Sitter vacua and improved D3- overline{mathrm{D}3} inflation

We propose a new mechanism that adapts to string theory a perturbative method for stabilizing moduli without leaving the domain of perturbative control, thereby evading the ‘Dine-Seiberg’ problem. The only required nonperturbative information comes from the standard renormalization-group resummation of leading logarithms that allow us simultaneously to work to a fixed order in the perturbative parameter α and to all orders in α ln τ where τ is a large extra-dimensional modulus. The resulting potential is naturally minimized for moduli of order τ ~ e1/α and so can be exponentially large given mathcal{O} (10) input parameters. The mechanism relies on accidental low-energy scaling symmetries known to be generic and so is robust against UV details. The resulting compactifications generically break supersymmetry and 4D de Sitter solutions are relatively easy to achieve without additional uplifting. Variations on the theme lead to inflationary scenarios for which the size of the stabilized moduli differ significantly before and after inflation and so provide a dynamical mechanism whereby inflationary scales are much larger than late-time physical (e.g. supersymmetry breaking) scales, with this hierarchy contingent on past cosmic evolution with the inflaton playing a secondary late-time role as a relaxation field. We apply this formalism to warped D3- overline{mathrm{D}3} inflation using non-linearly realized supersymmetry to describe the antibrane tension and the Coulomb interaction, and show how doing so our perturbative modulus stabilization mechanism evades the η-problem that usually plagues this scenario. We speculate about the relevance of our formalism to tachyon condensation at later stages of brane-antibrane annihilation.

A systematic approach to find solutions of the Einstein–Maxwell field equations for static spherically symmetric spacetimes using Segre classification

In the literature, several spherically symmetric static solutions of the Einstein–Maxwell field equations (EMFEs) have been obtained by taking assumptions/ansatz on the parameters involved, like electric field intensity, gravitational potential, equation of state, etc. In this paper, using the Segre classification, we present a systematic scheme that limits the number of assumptions/ansatz required to be taken. It is found that the static spherically symmetric solutions of the EMFEs can only be of Segre types [Formula: see text], [Formula: see text], [Formula: see text], or [Formula: see text]. It is also shown that the type [Formula: see text] leads to the Schwarzschild de-Sitter/anti de-Sitter solutions.

Cosmology in scalar-tensor f(R, T) gravity

In this work, we use reconstruction methods to obtain cosmological solutions in the recently developed scalar-tensor representation of $f(R,T)$ gravity. Assuming that matter is described by an isotropic perfect fluid and the spacetime is homogeneous and isotropic, i.e., the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) universe, the energy density, the pressure, and the scalar field associated with the arbitrary dependency of the action in $T$ can be written generally as functions of the scale factor. We then select three particular forms of the scale factor: an exponential expansion with $a(t)\ensuremath{\propto}{e}^{t}$ (motivated by the de Sitter solution); and two types of power-law expansion with $a(t)\ensuremath{\propto}{t}^{1/2}$ and $a(t)\ensuremath{\propto}{t}^{2/3}$ (motivated by the behaviors of radiation- and matter-dominated universes in general relativity, respectively). A complete analysis for different curvature parameters $k={\ensuremath{-}1,0,1}$ and equation of state parameters $w={\ensuremath{-}1,0,1/3}$ is provided. Finally, the explicit forms of the functions $f(R,T)$ associated with the scalar-field potentials of the representation used are deduced.

Quadratic curvature corrections to stringy effective actions and the absence of de Sitter vacua

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.

Estimating the Cosmological Constant from Shadows of Kerr–de Sitter Black Holes

The Event Horizon Telescope collaboration has revealed the first direct image of a black hole, as per the shadow of a Kerr black hole of general relativity. However, other Kerr-like rotating black holes of modified gravity theories cannot be ignored, and they are essential as they offer an arena in which these theories can be tested through astrophysical observation. This motivates us to investigate asymptotically de Sitter rotating black holes wherein interpreting the cosmological constant Λ as the vacuum energy leads to a deformation in the vicinity of a black hole—new Kerr–de Sitter solution, which has a richer geometric structure than the original one. We derive an analytical formula necessary for the shadow of the new Kerr–de Sitter black holes and then visualize the shadow of black holes for various parameters for an observer at given coordinates (r0,θ0) in the domain (r0,rc) and estimate the cosmological constant Λ from its shadow observables. The shadow observables of the new Kerr–de Sitter black holes significantly deviate from the corresponding observables of the Kerr–de Sitter black hole over an appreciable range of the parameter space. Interestingly, we find a finite parameter space for (Λ, a) where the observables of the two black holes are indistinguishable.

Constant‐Roll Inflation in the Generalized SU(2) Proca Theory

AbstractThe generalized SU(2) Proca theory (GSU2P) is a variant of the well known generalized Proca theory where the vector field belongs to the Lie algebra of the SU(2) group of global transformations under which the action is made invariant. New interesting possibilities arise in this framework because of the existence of new interactions of purely non‐Abelian character and new configurations of the vector field resulting in spatial spherical symmetry and the cosmological dynamics being driven by the propagating degrees of freedom. We study the 2D phase space of the system that results when the cosmic triad configuration is employed in the Friedmann–Lemaitre–Robertson–Walker background and find an attractor curve whose attraction basin both covers almost all the allowed region and does not include a Big‐Bang singularity. Such an attractor curve corresponds to a primordial inflationary solution that has the following characteristic properties: 1) it is a de Sitter solution whose Hubble parameter is regulated by a generalized version of the SU(2) group coupling constant, 2) it is constant‐roll including, as a limiting case, the slow‐roll variety, 3) a number of e‐folds is easily reached, 4) it has a graceful exit into a radiation dominated period powered by the canonical kinetic term of the vector field and the Einstein–Hilbert term. The free parameters of the action are chosen such that the tensor sector of the theory is the same as that of general relativity at least up to second‐order perturbations, thereby avoiding the presence of ghost and Laplacian instabilities in the tensor sector as well as making the gravity waves propagate at light speed. This is a proof of concept of the interesting properties that could be found in this scenario when the coupling constants be replaced by general coupling functions and more terms be discovered in the GSU2P.

Barrow Entropy Cosmology: an observational approach with a hint of stability analysis

In this work, we use an observational approach and dynamical system analysis to study the cosmological model recently proposed by Saridakis (2020), which is based on the modification of the entropy-area black hole relation proposed by Barrow (2020). The Friedmann equations governing the dynamics of the Universe under this entropy modification can be calculated through the gravity-thermodynamics conjecture. We investigate two models, one considering only a matter component and the other including matter and radiation, which have new terms compared to the standard model sourcing the late cosmic acceleration. A Bayesian analysis is performed in which using five cosmological observations (observational Hubble data, type Ia supernovae, HII galaxies, strong lensing systems, and baryon acoustic oscillations) to constrain the free parameters of both models. From a joint analysis, we obtain constraints that are consistent with the standard cosmological paradigm within 2σ confidence level. In addition, a complementary dynamical system analysis using local and global variables is developed which allows obtaining a qualitative description of the cosmology. As expected, we found that the dynamical equations have a de Sitter solution at late times.

A new de Sitter solution with a weakly warped deformed conifold

We revisit moduli stabilisation for type IIB flux compactifications that include a warped throat region corresponding to a warped deformed conifold, with an anti-D3-brane sitting at its tip. The warping induces a coupling between the conifold’s deformation modulus and the bulk volume modulus in the Kähler potential. Previous works have studied the scalar potential assuming a strong warping such that this coupling term dominates, and found that the anti-D3-brane uplift may destabilise the conifold modulus and/or volume modulus, unless flux numbers within the throat are large, which makes tadpole cancellation a challenge. We explore the regime of parameter space corresponding to a weakly-but-still warped throat, such that the coupling between the conifold and volume moduli is subdominant. We thus discover a new metastable de Sitter solution within the four-dimensional effective field theory. We discuss the position of this de Sitter vacuum in the string theory landscape and swampland.

On one integrable cosmological model of the flat universe in k-essence

The study of the origin and evolution of our Universe is one of the interesting and actual directions in modern physics and astrophysics. This paper considers the cosmological model of the Universe in the Einstein's theory of gravity and -essence, where the gravitational field interacts in a non-minimal way with the scalar field . That is, in action, in the role of the matter field, we consider the special case of the Lagrange function for the essence. The corresponding field equations of the considered model are obtained. Also, particular solutions for the scale factor  were obtained in the form of de Sitter's solution. Two solutions were found, for the potential energy  and the scalar field , and their graphical solutions were also built. The analytical solutions obtained in this work are solutions of the considered integrable systems. These solutions are in good agreement with the available observational data and are able to describe the modern dynamics of the expansion of the Universe.

De Sitter braneworld and gravitational waves

We study the braneworld theory constructed by multi-scalar fields. The model contains a smooth and infinitely large extra dimension, allowing background fields to propagate in it. We give a de Sitter solution for the four-dimensional cosmology as a good approximation to the early universe inflation. We show that the graviton has a localizable massless mode, and a series of continuous massive modes, separated by a mass gap. There could be a normalizable massive mode, depending on the background solution. The gravitational waves of the massless mode evolve as in the four-dimensional theory, while those of the massive modes evolve very differently from the massless mode.

The unbearable lightness of charged gravitini

We prove that charged gravitini cannot have parametrically small or vanishing Lagrangian mass in de Sitter vacua of extended supergravity while respecting the magnetic weak gravity conjecture. This places large classes of de Sitter solutions of gauged supergravity in the swampland, including all known stable solutions of the N=2 theory. We illustrate this result by analyzing a variety of de Sitter critical points of N=2 matter-coupled supergravity that also include new stable de Sitter solutions. Our results provide concrete evidence that (quasi) de Sitter with charged light gravitini should belong to the swampland, which also strongly resonates with the “festina lente” bound.

Averaging generalized scalar-field cosmologies III: Kantowski\u2013Sachs and closed Friedmann\u2013Lema\xeetre\u2013Robertson\u2013Walker models

Scalar-field cosmologies with a generalized harmonic potential and matter with energy density rho _m, pressure p_m, and barotropic equation of state (EoS) p_m=(gamma -1)rho _m, ; gamma in [0,2] in Kantowski–Sachs (KS) and closed Friedmann–Lemaître–Robertson–Walker (FLRW) metrics are investigated. We use methods from non-linear dynamical systems theory and averaging theory considering a time-dependent perturbation function D. We define a regular dynamical system over a compact phase space, obtaining global results. That is, for KS metric the global late-time attractors of full and time-averaged systems are two anisotropic contracting solutions, which are non-flat locally rotationally symmetric (LRS) Kasner and Taub (flat LRS Kasner) for 0le gamma le 2, and flat FLRW matter-dominated universe if 0le gamma le frac{2}{3}. For closed FLRW metric late-time attractors of full and averaged systems are a flat matter-dominated FLRW universe for 0le gamma le frac{2}{3} as in KS and Einstein–de Sitter solution for 0le gamma <1. Therefore, a time-averaged system determines future asymptotics of the full system. Also, oscillations entering the system through Klein–Gordon (KG) equation can be controlled and smoothed out when D goes monotonically to zero, and incidentally for the whole D-range for KS and closed FLRW (if 0le gamma < 1) too. However, for gamma ge 1 closed FLRW solutions of the full system depart from the solutions of the averaged system as D is large. Our results are supported by numerical simulations.

The Study of the Energy Conditions of the Universe and Unique Solutions of the Einstein’s Field Equations in the Lights of the Theory of General Relativity

Objectives: To study the energy conditions of the universe and to find unique solutions of the Einstein’s field equations. Methods: A mathematical formulation developed to study the energy conditions of the universe and a new way of unique solutions of the famous Einstein’s field equations with appropriate theoretical and mathematical analysis of the theory of general relativity. Findings: With the reference to the power series expansion of the mass function ˆM(u; r) developed by Wang and Wu (1999), we have derived two new ways to solve Einstein’s field equations by introducing new values of n as n=2 and n=-2. Novelty: With the reference to the power series expansion of the mass function ˆM(u; r), we have found new ways to solve Einstein’s field equations with n=2 and n=-2. And we have derived a total of four new solutions of the Einstein’s field equations. And the solutions are very innovative and different from (i) Schwarzschild solution and (ii) de Sitter solution. The solutions own (i) the first solution with the line element in the equation (11) describes a stationary solution. It has coordinate singularity at r = (2m)􀀀1 . (ii) The second solution with the line element in the equation (14) will be reduced to those Schwarzschild black holes when m=0 with singularities at r=2M. Also, it will be that dark energy when M=0 with singularities at r = (2m)􀀀1 . (iii) The third solution with the line element in the equation (17) describes a stationary solution. It has coordinate singularity at r = (2m)13 (iv) The fourth solution with the line element in the equation (20) describes a stationary solution. It has coordinate singularity at r = (2m)13. Keywords: The Mass Function; Schwarzschild Solution; Einstein’s Field Equation; The Theory of General Relativity; Space - time Curvature

Swampland de Sitter conjectures in no-scale supergravity models

It is challenging to construct explicit and controllable models that realize de Sitter solutions in string compactifications. This difficulty is the main motivation for the refined de Sitter conjecture and the trans-Planckian censorship conjecture which forbid stable de Sitter solutions but allow metastable, unstable and rolling solutions in a theory consistent with quantum gravity. Inspired by this, we first study a toy de Sitter no-scale supergravity model and show that for particular choices of parameters it can be consistent with the refined de Sitter conjecture and the trans-Planckian censorship conjecture. Then we modify the model by adding rolling dynamics and show that the theory can become stable along the imaginary direction, where it would otherwise be unstable. We extend the model to multifield rolling and de Sitter fields, finding the parameter space where they can be compatible with the refined de Sitter conjecture. The modified models with rolling fields can be used to construct quintessence models to accommodate the accelerating expansion of the Universe.

Nonsingular extension of the Kerr-NUT–(anti–)de Sitter spacetimes

In 1963 Ezra Ted Newman and his two students Louis A. Tamburino, and Theodore W. J. Unti, proposed a deformation of the Shwarzschild spacetime that made it twisting. In the cosmological context, an equivalent solution had been found earlier, in 1951, by Abraham Haskel Taub. The problem that these solutions have is a conical singularity along the symmetry axis at all distances from the origin. In 1969 Misner proposed a non-singular interpretation of Taub-NUT spacetimes. We extend and refine his method to include a broader family of solutions and completely solve the outstanding issue of a non-singular extension of the Kerr-NUT- (anti) de Sitter solutions to Einstein's equations. Our approach relies on an observation that in 2 dimensional algebra of Killing vector fields there exist 2 distinguished vector fields that may be used to define $U(1)$-principal bundle structure over the non-singular spaces of non-null orbits. For all admissible parameters we derive appropriate Killing vector fields and discuss limits to spacetimes with less parameters. The global structure of spacetime, together with non-singular conformal geometry of the infinities is presented and (possibly also projectively non-singular) Killing horizons is presented.