De Sitter State Research Articles

Spacetime Symmetry and LemaîTre Class Dark Energy Models

We present the regular cosmological models of the Lemaître class with time-dependent and spatially inhomogeneous vacuum dark energy, which describe relaxation of the cosmological constant from its value powering inflation to the final non-zero value responsible for the present acceleration in the frame of one self-consistent theoretical scheme based on the algebraic classification of stress-energy tensors and spacetime symmetry directly related to their structure. Cosmological evolution starts with the nonsingular non-simultaneous de Sitter bang, followed by the Kasner-type anisotropic expansion, and goes towards the present de Sitter state. Spacetime symmetry provides a mechanism of reducing cosmological constant to a certain non-zero value involving the holographic principle which singles out the special class of the Lemaître dark energy models with the global structure of the de Sitter spacetime. For this class cosmological evolution is guided by quantum evaporation of the cosmological horizon whose dynamics entirely determines the final value of the cosmological constant. For the choice of the density profile modeling vacuum polarization in a spherical gravitational field and the GUT scale for the inflationary value of cosmological constant, its final value agrees with that given by observations. Anisotropy grows quickly at the postinflationary stage, then remains constant and decreases to A < 10 − 6 when the vacuum density starts to dominate.

The dark-baryonic matter mass relation for observational verification in Verlinde’s emergent gravity

Recently, a new interesting idea of origin of gravity has been developed by Verlinde. In this scheme of emergent gravity, where horizon entropy, microscopic de Sitter states and relevant contribution to gravity are involved, an entropy displacement resulting from matter behaves as a memory effect and can be exhibited at sub-Hubble scales, namely, the entropy displacement and its “elastic” response would lead to emergent gravity, which gives rise to an extra gravitational force. Then galactic dark matter effects may origin from such extra emergent gravity. We discuss some concepts in Verlinde’s theory of emergent gravity and point out some possible problems or issues, e.g., the gravitational potential caused by Verlinde’s emergent apparent dark matter may no longer be continuous in spatial distribution at ordinary matter boundary (such as a massive sphere surface). In order to avoid the unnatural discontinuity of the extra emergent gravity of Verlinde’s apparent dark matter, we suggest a modified dark-baryonic mass relation (a formula relating Verlinde’s apparent dark matter mass to ordinary baryonic matter mass) within this framework of emergent gravity. The modified mass relation is consistent with Verlinde’s result at relatively small scales (e.g., $$R<3h_{70}^{-1}$$ Mpc). However, it seems that, compared with Verlinde’s relation, at large scales (e.g., gravitating systems with $$R>3h_{70}^{-1}$$ Mpc), the modified dark-baryonic mass relation presented here might be in better agreement with the experimental curves of weak lensing analysis in the recent work of Brouwer et al. Galactic rotation curves are compared between Verlinde’s emergent gravity and McGaugh’s recent model of MOND (Modified Newtonian Dynamics established based on recent galaxy observations). It can be found that Verlinde rotational curves deviate far from those of McGaugh MOND model when the MOND effect (or emergent dark matter) dominates. Some applications of the modified dark-baryonic mass relation inspired by Verlinde’s emergent gravity will be addressed for galactic and solar scales. Potential possibilities to test this dark-baryonic mass relation as well as apparent dark matter effects, e.g., planetary perihelion precession at Solar System scale, will be considered. This may enable to place some constraints on the magnitudes of the MOND characteristic acceleration at the small solar scale.

Gravitational entropy and the cosmological no-hair conjecture

The gravitational entropy and no-hair conjectures seems to predict contradictory future states of our Universe. The growth of the gravitational entropy is associated with the growth of inhomogeneity, while the no-hair conjecture argues that a universe dominated by dark energy should asymptotically approach a homogeneous and isotropic de Sitter state. The aim of this paper is to study these two conjectures. The investigation is based on the Simsilun simulation, which simulates the universe using the approximation of the Silent Universe. The Silent Universe is a solution to the Einstein equations that assumes irrotational, non-viscous, and insulated dust, with vanishing magnetic part of the Weyl curvature. The initial conditions for the Simsilun simulation are sourced from the Millennium simulation, which results with a realistically appearing but relativistic at origin simulation of a universe. The Simsilun simulation is evolved from the early universe (t = 25 Myr) till far future (t = 1000 Gyr). The results of this investigation show that both conjectures are correct. On global scales, a universe with a positive cosmological constant and non-positive spatial curvature does indeed approach the de Sitter state. At the same time it keeps generating the gravitational entropy.

Self-acceleration and matter content in bicosmology from Noether symmetries

In bigravity, when taking into account the potential existence of matter fields minimally coupled to the second gravitation sector, the dynamics of our Universe depends on some matter that cannot be observed in a direct way. In this paper, we assume the existence of a Noether symmetry in bigravity cosmologies in order to constrain the dynamics of that matter. By imposing this assumption we obtain cosmological models with interesting phenomenology. In fact, considering that our universe is filled with standard matter and radiation, we show that the existence of a Noether symmetry implies that either the dynamics of the second sector decouples, being the model equivalent to general relativity (GR), or the cosmological evolution of our universe tends to a de Sitter state with the vacuum energy in it given by the conserved quantity associated with the symmetry. The physical consequences of the genuine bigravity models obtained are briefly discussed. We also point out that the first model, which is equivalent to GR, may be favored due to the potential appearance of instabilities in the second model.

Generalization of the de Sitter Cosmos

First of all, we investigate whether the transformation of Lemaitre inevitably leads from the static de Sitter cosmos to an expanding cosmos. A Lorentz transformation which can be assigned to the Lemaitre transformation results in a frame of reference that moves relatively to the static dS system. Because of the homogeneity of space, this applies to every point in the space which does not itself undergo any change. We interpret the “expansion” of the cosmos Milne-like. It is not the space that expands, but the mesh of the Lemaitre coordinate system. The velocity parameter of the associated Lorentz transformation is geometrically based and shows that the joined observer systems are moving in free fall. We also discuss the question of whether the speed of light for free-falling observers in the universe can be reached or can be exceeded, respectively. We raise the question of whether the model can be extended in such a way that the motions take place with a velocity that is lower than the one of the free fall. We believe that the method we have derived can be generalized to models with genuine expansion.

Dark Energy and Inflation from Gravitational Waves

In this seven-part paper, we show that gravitational waves (classical and quantum) produce the accelerated de Sitter expansion at the start and at the end of the cosmological evolution of the Universe. In these periods, the Universe contains no matter fields but contains classical and quantum metric fluctuations, i.e., it is filled with classical and quantum gravitational waves. In such evolution of the Universe, dominated by gravitational waves, the de Sitter state is the exact solution to the self-consistent equations for classical and quantum gravitational waves and background geometry for the empty space-time with FLRW metric. In both classical and quantum cases, this solution is of the instanton origin since it is obtained in the Euclidean space of imaginary time with the subsequent analytic continuation to real time. The cosmological acceleration from gravitational waves provides a transparent physical explanation to the coincidence, threshold and “old cosmological constant” paradoxes of dark energy avoiding recourse to the anthropic principle. The cosmological acceleration from virtual gravitons at the start of the Universe evolution produces inflation, which is consistent with the observational data on CMB anisotropy. Section 1 is devoted to cosmological acceleration from classical gravitational waves. Section 2 is devoted to the theory of virtual gravitons in the Universe. Section 3 is devoted to cosmological acceleration from virtual gravitons. Section 4 discusses the consistency of the theory with observational data on dark energy and inflation. The discussion of mechanism of acceleration and cosmological scenario are contained in Sections 5 and 6. Appendix contains the theory of stochastic nonlinear gravitational waves of arbitrary wavelength and amplitude in an isotropic Universe.

A simple all-time model for the birth, big bang, and death of the universe

We model the standard [Formula: see text]CDM model of the universe by the spatially flat FLRW line element [Formula: see text] which we extend for all time [Formula: see text]. Although there is a cosmological singularity at the big bang [Formula: see text], since the spatial part of the metric collapses to zero, nevertheless, this line element is defined for all time [Formula: see text], is [Formula: see text] for all [Formula: see text], is [Formula: see text] differentiable at [Formula: see text], and is non-degenerate and solves Friedmann’s equation for all [Formula: see text]. Thus, we can use this extended line element to model the universe from its past-asymptotic initial state [Formula: see text] at [Formula: see text], through the big bang at [Formula: see text], and onward to its future-asymptotic final state [Formula: see text] at [Formula: see text]. Since in this model the universe existed before the big bang, we conclude that (1) the universe was not created de novo at the big bang and (2) cosmological singularities such as black holes or the big bang itself need not be an end to spacetime. Our model shows that the universe was asymptotically created de novo out of nothing at [Formula: see text] from an unstable vacuum negative half de Sitter [Formula: see text] initial state and then dies asymptotically at [Formula: see text] as the stable positive half de Sitter [Formula: see text] final state. Since the de Sitter states are vacuum matter states, our model shows that the universe was created from nothing at [Formula: see text] and dies at [Formula: see text] to nothing.

De Sitter limit analysis for dark energy and modified gravity models

The effective field theory of dark energy and modified gravity is supposed to well describe, at low energies, the behaviour of the gravity modifications due to one extra scalar degree of freedom. The usual curvature perturbation is very useful when studying the conditions for the avoidance of ghost instabilities as well as the positivity of the squared speeds of propagation for both the scalar and tensor modes, or the St\"uckelberg field performs perfectly when investigating the evolution of linear perturbations. We show that the viable parameters space identified by requiring no-ghost instabilities and positive squared speeds of propagation does not change by performing a field redefinition, while the requirement of the avoidance of tachyonic instability might instead be different. Therefore, we find interesting to associate to the general modified gravity theory described in the effective field theory framework, a perturbation field which will inherit the whole properties of the theory. In the present paper we address the following questions: 1) how can we define such a field? and 2) what is the mass of such a field as the background approaches a final de Sitter state? We define a gauge invariant quantity which identifies the density of the dark energy perturbation field valid for any background. We derive the mass associated to the gauge invariant dark energy field on a de Sitter background, which we retain to be still a good approximation also at very low redshift ($z\simeq 0$). On this background we also investigate the value of the speed of propagation and we find that there exist classes of theories which admit a non-vanishing speed of propagation, even among the Horndeski model, for which in literature it has previously been found a zero speed. We finally apply our results to specific well known models.

Quantum break-time of de Sitter

The quantum break-time of a system is the time-scale after which its true quantum evolution departs from the classical mean field evolution. For capturing it, a quantum resolution of the classical background—e.g., in terms of a coherent state—is required. In this paper, we first consider a simple scalar model with anharmonic oscillations and derive its quantum break-time. Next, following [1], we apply these ideas to de Sitter space. We formulate a simple model of a spin-2 field, which for some time reproduces the de Sitter metric and simultaneously allows for its well-defined representation as quantum coherent state of gravitons. The mean occupation number N of background gravitons turns out to be equal to the de Sitter horizon area in Planck units, while their frequency is given by the de Sitter Hubble parameter. In the semi-classical limit, we show that the model reproduces all the known properties of de Sitter, such as the redshift of probe particles and thermal Gibbons-Hawking radiation, all in the language of quantum S-matrix scatterings and decays of coherent state gravitons. Most importantly, this framework allows to capture the 1/N-effects to which the usual semi-classical treatment is blind. They violate the de Sitter symmetry and lead to a finite quantum break-time of the de Sitter state equal to the de Sitter radius times N. We also point out that the quantum-break time is inversely proportional to the number of particle species in the theory. Thus, the quantum break-time imposes the following consistency condition: older and species-richer universes must have smaller cosmological constants. For the maximal, phenomenologically acceptable number of species, the observed cosmological constant would saturate this bound if our Universe were 10100 years old in its entire classical history.

Emergent Gravity and the Dark Universe

Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional ‘dark’ gravitational force describing the ‘elastic’ response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton’s constant and the Hubble acceleration scale a_0 =cH_0a0=cH0, and provide evidence for the fact that this additional ‘dark gravity force’ explains the observed phenomena in galaxies and clusters currently attributed to dark matter.

Phantom dark ghost in Einstein\u2013Cartan gravity

A class of dynamical dark energy models is constructed through an extended version of fermion fields corresponding to phantom dark ghost spinors, which are spin 1/2 with mass dimension 1. We find that if these spinors interact with torsion fields in a homogeneous and isotropic universe, then it does not imply any future dark energy singularity or any abrupt event, though the fermion has a negative kinetic energy. In fact, the equation of state of this dark energy model will asymptotically approach the value w=-1 from above without crossing the phantom divide and inducing therefore a de Sitter state. Consequently, we expect the model to be stable because no real phantom fields will be created. At late time, the torsion fields will vanish as the corresponding phantom dark ghost spinors dilute. As would be expected, intuitively, this result is unaffected by the presence of cold dark matter although the proof is not as straightforward as in general relativity.

Inflationary α -attractor cosmology: A global dynamical systems perspective

We study flat FLRW $\alpha$-attractor $\mathrm{E}$- and $\mathrm{T}$-models by introducing a dynamical systems framework that yields regularized unconstrained field equations on two-dimensional compact state spaces. This results in both illustrative figures and a complete description of the entire solution spaces of these models, including asymptotics. In particular, it is shown that observational viability, which requires a sufficient number of $e$-folds, is associated with a solution given by a one-dimensional center manifold of a past asymptotic de Sitter state, where the center manifold structure also explains why nearby solutions are attracted to this `inflationary attractor solution.' A center manifold expansion yields a description of the inflationary regime with arbitrary analytic accuracy, where the slow-roll approximation asymptotically describes the tangency condition of the center manifold at the asymptotic de Sitter state.

Anisotropic deformations of spatially open cosmology in massive gravity theory

We combine analytical and numerical methods to study anisotropic deformations of the spatially open homogeneous and isotropic cosmology in the ghost free massive gravity theory with flat reference metric. We find that if the initial perturbations are not too strong then the physical metric relaxes back to the isotropic de Sitter state. However, the dumping of the anisotropies is achieved at the expense of exciting the Stueckelberg fields in such a way that the reference metric changes and does not share anymore with the physical metric the same rotational and translational symmetries. As a result, the universe evolves towards a fixed point which does not coincide with the original solution, but for which the physical metric is still de Sitter. If the initial perturbation is strong, then its evolution generically leads to a singular anisotropic state or, for some parameter values, to a decay into flat spacetime. We also present an infinite dimensional family of new homogeneous and isotropic cosmologies in the theory.

Dynamical system approach to scalar–vector–tensor cosmology

Using scalar-vector-tensor Brans Dicke (VBD) gravity [3] in presence of self interaction BD potential $V(\phi)$ and perfect fluid matter field action we solve corresponding field equations via dynamical system approach for flat Friedmann Robertson Walker metric (FRW). We obtained 3 type critical points for $\Lambda CDM$ vacuum de Sitter era where stability of our solutions are depended to choose particular values of BD parameter $\omega.$ One of these fixed points is supported by a constant potential which is stable for $\omega<0$ and behaves as saddle (quasi stable) for $\omega\geq0.$ Two other ones are supported by a linear potential $V(\phi)\sim\phi$ which one of them is stable for $\omega=0.27647.$ For a fixed value of $\omega$ there is at least 2 out of 3 critical points reaching to a unique critical point. Namely for $\omega=-0.16856(-0.56038)$ the second (third) critical point become unique with the first critical point. In dust and radiation eras we obtained 1 critical point which never become unique fixed point. In the latter case coordinates of fixed points are also depended to $\omega.$ To determine stability of our solutions we calculate eigenvalues of Jacobi matrix of 4D phase space dynamical field equations for de Sitter, dust and radiation eras. We should be point also potentials which support dust and radiation eras must be similar to $V(\phi)\sim\phi^{-\frac{1}{2}}$ and $V(\phi)\sim\phi^{-1}$ respectively. In short our study predicts that radiation and dust eras of our VBD-FRW cosmology transmit to stable de Sitter state via non-constant potential (effective variable cosmological parameter) by choosing $\omega=0.27647$.

What ξ? Cosmological constraints on the non-minimal coupling constant

In dynamical system describing evolution of universe with the flat Friedmann–Robertson–Walker symmetry filled with barotropic dust matter and non-minimally coupled scalar field with a constant potential function an invariant manifold of the de Sitter state is used to obtain exact solutions of the reduced dynamics. Using observational data coming from distant supernovae type Ia, the Hubble function H(z) measurements and information coming from the Alcock–Paczyński test we find cosmological constraints on the non-minimal coupling constant ξ between the scalar curvature and the scalar field. For all investigated models we can exclude negative values of this parameter at the 68% confidence level. We obtain constraints on the non-minimal coupling constant consistent with condition for conformal coupling of the scalar field in higher dimensional theories of gravity.

Towards Generic Cosmological Evolution Without Singularity and Fundamental Symmetry of Space-time

Dynamical systems methods are used to investigate cosmological model with non-minimally coupled scalar field. Existence of an asymptotically unstable de Sitter state distinguishes values of the non-minimal coupling constant parameter $\frac{3}{16}\le\xi<\frac{1}{4}$, which correspond to conformal coupling in higher dimensional theories of gravity.

Instability of the de Sitter Reissner–Nordstrom black hole in the expansion

We study the large D effective theory for D dimensional charged (Anti) de Sitter black holes. Then we show that the de Sitter Reissner–Nordstrom black hole becomes unstable against gravitational perturbations at larger charge than a critical charge in a higher dimension. Furthermore, we find that there is a nontrivial zero-mode static perturbation at the critical charge. The existence of static perturbations suggests the appearance of non-spherical symmetric solution branches of static charged de Sitter black holes. This expectation is confirmed by constructing the non-spherical symmetric static solutions of large D effective equations.

Dark energy and inflation in a gravitational wave dominated universe

The empty space (with no matter fields) is not really empty because of natural metric fluctuations, quantum and classical. We show that gravitons as well as classical gravitational waves of super-horizon wavelengths are able to form the de Sitter state of the empty homogeneous isotropic Universe. This state is the exact solution to the self-consistent equations of one-loop quantum gravity for gravitons in the empty FLRW space. It also is the exact solution to the self-consistent equations of back reaction for classical gravitational waves. Technically, to get this de Sitter solution in both quantum and classical cases, it is necessary to make the transition to imaginary time and then come back to real time which is possible because this de Sitter state is invariant with respect to Wick rotation. Such a procedure means that the time was used as a complex variable, and this fact has a deep but still not understood meaning. De Sitter accelerated expansion of the empty Universe naturally explains the origin of dark energy and inflation because the Universe is empty at the start and by the end of its evolution. This theory is consistent with the existing observational data. The CMB anisotropy of the order of 10^-5 is produced by fluctuations in the number of gravitons. The existence of a threshold and unique coincidence of topologically impenetrable barriers for tunneling takes place for the matter-dominated epoch and De Sitter State only. These facts provide a solution to the coincidence problem. The theoretical prediction that the equation-of-state parameter should be w>-1 for inflation and w<-1 for dark energy is consistent with observational data. To provide the reader with a complete picture, this paper gather together new and some published results of the graviton theory of the origin of inflation and dark energy

Effect of a cosmological constant on propagation of vacuum polarized photons in stationary spacetimes

Consideration of vacuum polarization in quantum electrodynamics may affect the momentum dispersion relation for photons for a non-trivial background, due to the appearance of curvature dependent terms in the effective action. We investigate the effect of a positive cosmological constant $$\Lambda $$ on this at one-loop order for stationary $$\Lambda $$ -vacuum spacetimes. To the best of our knowledge, so far it only has been shown that $$\Lambda $$ affects the propagation in a time dependent black hole spacetime. Here we consider the static de Sitter cosmic string and the Kerr–de Sitter spacetime to show that there might occur a non-vanishing effect due to $$\Lambda $$ for physical polarizations. The consistency of these results with the polarization sum rule is discussed.

Self tuning scalar fields in spherically symmetric spacetimes

We search for self tuning solutions to the Einstein-scalar field equations for the simplest class of `Fab-Four' models with constant potentials. We first review the conditions under which self tuning occurs in a cosmological spacetime, and by introducing a small modification to the original theory—introducing the second and third Galileon terms—show how one can obtain de Sitter states where the expansion rate is independent of the vacuum energy. We then consider whether the same self tuning mechanism can persist in a spherically symmetric inhomogeneous spacetime. We show that there are no asymptotically flat solutions to the field equations in which the vacuum energy is screened, other than the trivial one (Minkowski space). We then consider the possibility of constructing Schwarzschild de Sitter spacetimes for the modified Fab Four plus Galileon theory. We argue that the only model that can successfully screen the vacuum energy in both an FLRW and Schwarzschild de Sitter spacetime is one containing `John' ∼ Gμν ∂μϕ∂νϕ and a canonical kinetic term ∼ ∂αϕ ∂αϕ. This behaviour was first observed in [1]. The screening mechanism, which requires redundancy of the scalar field equation in the `vacuum', fails for the `Paul' term in an inhomogeneous spacetime.