Positive Cosmological Constant Research Articles

The Equation of the Universe (According to the Theory of Relation)

A new equation is found in which the concept of matter-space-time is mathematically connected; gravitation and electromagnetism are also bound by space-time. A mechanism is described showing how velocity, time, distance, matter, and energy are correlated. We are led to ascertain that gravity and electricity are two distinct manifestations of a single underlying process: electro-gravitation. The force of gravitation arises of electromagnetism—inherently much stronger—divided by the cosmological space-time. The radius of space-time belongs to the family of electromagnetic waves: the wavelength is the radius (1026 m) of the universe and the period (1017 s) is its cosmological age. For the first time, the cosmological time, considered as a real physical object, is integrated into a “cosmological equation” which makes coherent what we know regarding the time (its origin, its flow …), the matter, and space. It sets up a mathematical model allowing us to interpret dark energy (or cosmological constant) as being both “negative” and “tired” energy. After an introduction with a brief history of unifications and the presentation of two roughly equal ratios arising out from Dirac’s large-number hypotheses which relate to the ratio of electric force to gravitational force and the ratio of the age of the universe to the atomic time unit associated with atomic processes, we present in §2 this new equation of quantum cosmology which operates the reconciliation between the macrocosm and the microcosm. In §3 and §4, we discuss the irreversible cosmological time resulting from the equation, as well as the role of the mass (heavy) relative to the gravitational constant G. In §5 we discuss the links that the equation establishes between gravitation (structure of condensation) and electromagnetism (structure of expansion), between relativity and quantum theory. We apply the formula to Planck’s time. We speak of the new essential variable , and briefly of a new principle, the principle of compensation. In §6 we discuss the negative energy solutions banned by physics, and we deplore that half of the universe escapes us. We present the electro-gravitation in §7, from the equation which represents a super hydrogen atom. In § 8 we show that the global mass (gravitational) is variable: it increases during the expansion while the mass of the elementary particles decreases. In §9 we approach the spontaneous symmetry breaking; when it occurs, the arrows of the equation are momentarily reversed: such a mechanism would apply to the Allais effect, also mentioned in §6.4. §10 and §11 deal with the energy linked by the equation to matter through expansive space-time. The equation transforms electromagnetic kinetic energy into a gravitational mass, considered as a potential energy. Entropy increases according to the arrow of time towards the future. In §12 we discuss of the prevailing theory of inflation. We note the similarity between the proclaimed acceleration of current expansion and inflation. Physicists have interpreted the positive cosmological constant in terms of vacuum energy which would be 10120 times higher than the dark energy density deduced from the astronomical measurements. However, the high theoretical value of the vacuum energy (and the cosmological constant) has no observable pending in the cosmos. In §13 we suggest that these several orders of magnitude difference problem are solved by the theory of relation, which indicates a deceleration of the expansion. Finally, in § 14, we close by speaking of a model of cyclic universe and about the object of this paper, a dynamic equation that allows to build a quantum cosmology.

On Exclusion of Positive Cosmological Constant

AbstractSome time ago we have suggested that positive vacuum energy exhibits a finite quantum break time, which can be a signal that a positive cosmological constant is inconsistent. From the requirement that the Universe never undergoes through quantum breaking, we have derived an absolute lower bound on the speed of variation of positive vacuum energy. The same suggestion about exclusion of positive cosmological constant was made recently. We show that the new bound represents a particular string theoretic version of the old bound, which is more general. In this light, we show that the existing window still provides a large room for the inflationary and dark energy model building. In particular, the inflationary models with gravitational strength interactions, are protected against fast quantum breaking.

Bounding Horizon Area by Angular Momentum, Charge, and Cosmological Constant in 5-Dimensional Minimal Supergravity

We establish a class of area-angular momentum-charge inequalities satisfied by stable marginally outer trapped surfaces in 5-dimensional minimal supergravity which admit a $U(1)^2$ symmetry. A novel feature is the fact that such surfaces can have the nontrivial topologies $S^1 \times S^2$ and $L(p,q)$. In addition to two angular momenta, they may be characterized by `dipole charge' as well as electric charge. We show that the unique geometries which saturate the inequalities are the horizon geometries corresponding to extreme black hole solutions. Analogous inequalities which also include contributions from a positive cosmological constant are also presented.

Dark energy in the swampland

In this Letter, we study the implications of string Swampland criteria for dark energy in view of ongoing and future cosmological observations. If string theory should be the ultimate quantum gravity theory, there is evidence that exact de Sitter solutions with a positive cosmological constant cannot describe the fate of the late-time universe. Even though cosmological models with dark energy given by a scalar field $\pi$ evolving in time are not in direct tension with string theory, they have to satisfy the Swampland criteria $|\Delta\pi|<d\sim\mathcal{O}(1)$ and $|V'|/V>c\sim\mathcal{O}(1)$, where $V$ is the scalar field potential. In view of the restrictive implications that the Swampland criteria have on dark energy, we investigate the accuracy needed for future observations to tightly constrain standard dark-energy models. We find that current 3-$\sigma$ constraints with $c \lesssim 1.35$ are still well in agreement with the string Swampland criteria. However, Stage-4 surveys such as Euclid, LSST and DESI, tightly constraining the equation of state $w(z)$, will start putting surviving quintessence models into tensions with the string Swampland criteria by demanding $c<0.4$. We further investigate whether any idealised futuristic survey will ever be able to give a decisive answer to the question whether the cosmological constant would be preferred over a time-evolving dark-energy model within the Swampland criteria. Hypothetical surveys with a reduction in the uncertainties by a factor of $\sim20$ compared to Euclid would be necessary to reveal strong tension between quintessence models obeying the string Swampland criteria and observations by pushing the allowed values down to $c<0.1$. In view of such perspectives, there will be fundamental observational limitations with future surveys.

Killing horizons: Negative temperatures and entropy super-additivity

Many discussions in the literature of spacetimes with more than one Killing horizon note that some horizons have positive and some have negative surface gravities, but assign to all a positive temperature. However, the first law of thermodynamics then takes a non-standard form. We show that if one regards the Christodoulou and Ruffini formula for the total energy or enthalpy as defining the Gibbs surface, then the rules of Gibbsian thermodynamics imply that negative temperatures arise inevitably on inner horizons, as does the conventional form of the first law. We provide many new examples of this phenomenon, including black holes in STU supergravity. We also give a discussion of left and right temperatures and entropies, and show that both the left and right temperatures are non-negative. The left-hand sector contributes exactly half the total energy of the system, and the right-hand sector contributes the other half. Both the sectors satisfy conventional first laws and Smarr formulae. For spacetimes with a positive cosmological constant, the cosmological horizon is naturally assigned a negative Gibbsian temperature. We also explore entropy-product formulae and a novel entropy-inversion formula, and we use them to test whether the entropy is a super-additive function of the extensive variables. We find that super-additivity is typically satisfied, but we find a counterexample for dyonic Kaluza-Klein black holes.

Strong cosmic censorship in charged black-hole spacetimes: Still subtle

It was recently shown that Strong Cosmic Censorship may be violated in highly charged black-hole spacetimes living in a universe with a positive cosmological constant. Several follow-up works have since suggested that such result, while conceptually interesting, cannot be upheld in practice. We focus here on the claim that the presence of charged massive scalars suffices to save Strong Cosmic Censorship. To the contrary, we show that there still exists a finite region in parameter space where Strong Cosmic Censorship is expected to be violated.

A stable flat universe with variable cosmological constant in f(R, T) gravity

In this paper, a general FRW cosmological model has been constructed in f(R,T) gravity reconstruction with variable cosmological constant. A number of solutions to the field equations has been generated by utilizing a form for the Hubble parameter that leads to Berman’s law of constant deceleration parameter q = m − 1. The possible decelerating and accelerating solutions have been investigated. For (q > 0) we get a stable flat decelerating radiation-dominated universe at q = 1. For (q < 0) we get a stable accelerating solution describing a flat universe with positive energy density and negative cosmological constant. Nonconventional mechanisms that are expected to address the late-time acceleration with negative cosmological constant have been discussed.

On causality violation on a Kerr-de Sitter spacetime

The causal properties of the family of Kerr-de Sitter spacetimes are analyzed and compared to those of the Kerr family. At first we show that a Kerr-de Sitter spacetime can be viewed as an assembly of Carter's blocks i.e. four dimensional spacetime regions contained within Killing horizons or a Killing horizon and the asymptotic de Sitter region. From this perspective and leaving aside topological identifications, the causal properties of a Kerr de Sitter spacetime are determined by the causal properties of the individual Carter's blocks viewed as spacetimes in their own right. We show that any Carter's block is stably causal except for the blocks that contain the ring singularity. The latter are vicious sets: any two events within such block can be connected by a future (respectively past) directed timelike curve. This behavior is identical to the causal behavior of the Boyer-Lindquist blocks that contains the Kerr ring singularity which are also vicious sets. On the other hand, while for the case of a naked Kerr singularity the entire spacetime is a vicious set and thus closed timelike curves pass through any event including events lying in the asymptotic region, for the case of a Kerr-de Sitter spacetime the cosmological horizons imply that the asymptotic de Sitter region is causally well behaved. In that regard a positive cosmological constant appears to improve the causal behavior of the underlying spacetime.

Antigravitating braneworld solutions for a de Sitter brane in scalar-tensor gravity

In the context of a five-dimensional theory with a scalar field nonminimally coupled to gravity, we look for solutions that describe novel black-string or maximally symmetric solutions in the bulk. The brane line element is found to describe a Schwarzschild--(anti)--de Sitter spacetime, and, here, we choose to study solutions with a positive four-dimensional cosmological constant. We consider two different forms of the coupling function of the scalar field to the bulk scalar curvature, a linear one and a quadratic one. In the linear case, we find solutions where the theory, close to our brane, mimics an ordinary gravitational theory with a minimally coupled scalar field giving rise to an exponentially decreasing warp factor in the absence of a negative bulk cosmological constant. The solution is characterized by the presence of a normal gravity regime around our brane and an antigravitating regime away from it. In the quadratic case, there is no normal-gravity regime at all; however, scalar field and energy-momentum tensor components are well defined and an exponentially decreasing warp factor emerges again. We demonstrate that, in the context of this theory, the emergence of a positive cosmological constant on our brane is always accompanied by an antigravitating regime in the five-dimensional bulk.

On the CMC-Einstein-Λ flow

We complement a recent work on the stability of fixed points of the CMC-Einstein-Λ flow. In particular, we modify the utilized gauge for the Einstein equations and remove a restriction on the fixed points whose stability we are able to prove by this method, and thereby generalize the stability result. In addition, we consider the notion of the reduced Hamiltonian, originally introduced by Fischer and Moncrief for the standard CMC-Einstein flow. For the analog version of the flow in the presence of a positive cosmological constant we identify the stationary points and relate them to the long-time behavior of the flow on manifolds of different Yamabe types. This entails conjectures on the asymptotic behaviour and potential attractors.

The cosmological constant in supergravity

We propose a supersymmetrisation of the cosmological constant in ordinary N=1 supergravity that breaks supersymmetry spontaneously by a constant Fayet-Iliopoulos (FI) term associated to a U(1) symmetry. This term is a variation of a new gauge invariant FI term proposed recently, which is invariant under Kähler transformations and can be written even for a gauged R-symmetry on top of the standard FI contribution. The two terms are the same in the absence of matter but differ in its presence. The proposed term is reduced to a constant FI-term up to fermion interactions that disappear in the unitary gauge in the absence of any F-term supersymmetry breaking. The constant FI term leads to a positive cosmological constant, uplifting the vacuum energy from the usual anti-de Sitter supergravity to any higher value.

Geometric and physical properties of closed ever expanding dust models

Current observations suggest that our Universe is not incompatible with a small positive spatial curvature that can be associated with rest frames having a "closed" standard topology. We examine a toy model generalisation of the $\Lambda$CDM model in the form of ever expanding Lema\^{i}tre-Tolman-Bondi (LTB) models with positive spatial curvature. It is well known that such models with $\Lambda=0$ exhibit a thin layer distribution at the turning values of the area distance that must be studied through the Israel-Lanczos formalism. We find that this distributional source exhibits an unphysical behaviour for large cosmic times and its presence can be detected observationally. However, these unphysical features can always be avoided by assuming $\Lambda >0$. While these LTB models are very simplified, we believe that these results provide a simple argument favouring the assumption of a nonzero positive cosmological constant in cosmological models.

The Dirac Equation in the Kerr-de Sitter Metric

We consider a Fermion in the presence of a rotating BH immersed in a universe with a positive cosmological constant. After presenting a rigorous classification of the number and type of the horizons, we adopt the Carter tetrad to separate the aforementioned equation into radial and angular equations. We show how the Chandrasekhar ansatz leads to the construction of a symmetry operator that in the limit of a vanishing cosmological constant reproduces the square root of the squared total angular momentum operator for a Dirac particle in the Kerr metric. Furthermore, we prove that the the spectrum of the angular operator is discrete and consists of simple eigenvalues, and by means of the functional Bethe ansatz method we also derive a set of necessary and sufficient conditions for the angular operator to have polynomial solutions. Finally, we show that there exist no bound states for the Dirac equation in the non-extreme case.

Quasinormal modes of black strings in de Rham\u2013Gabadadze\u2013Tolley massive gravity

The effect of massive scalar perturbations on neutral black string in de Rham–Gabadadze–Tolley (dRGT) massive gravity is investigated through the study of the quasi-normal modes (QNMs). Due to the similarity between the equation of motion of the field in the black-string and black-hole background, similar numerical and analytical techniques can be used to explore the behaviour of the QNMs. We use the asymptotic iteration method (AIM) and the WKB method to numerically calculate the QNMs of scalar perturbation in the black string background with positive cosmological constant. High-momentum behaviour of such QNMs can be analytically approximated by the first-order WKB method with excellent accuracy. For near-extremal black string with event horizon very close to the cosmological horizon, the Pöschl–Teller technique gives accurate analytic formula for the QNMs. When massive-gravity-parameter gamma increases, we found that the scalar modes oscillate with higher frequencies and decay faster. The QNMs of black string in spacetime with negative cosmological constant are explored in all range of possible gamma using the spectral method. We found the movement of the holographic sound poles to collide and form diffusive poles as gamma changes from positive to negative values. We observe no evidence of instability of neutral black string in both positive and negative cosmological constant cases.

Rotating Bowen–York initial data with a positive cosmological constant

A generalization of the Bowen–York initial data to the case with a positive cosmological constant is investigated. We follow the construction presented recently by Bizoń, Pletka and Simon, and solve numerically the Lichnerowicz equation on a compactified domain . In addition to two branches of solutions depending on the polar variable on that were already known, we find branches of solutions depending on two variables: the polar variable on and the coordinate on . Using Vanderbauwhede’s results concerning bifurcations from symmetric solutions, we show the existence of the corresponding bifurcation points. By linearizing the Lichnerowicz equation and solving the resulting eigenvalue problem, we collect numerical evidence suggesting the absence of additional branches of solutions.

Some results on a black hole with a global monopole in Poincar\xe9 gravity

The aim of this work is to study the thermodynamics and spin current of a system corresponding to a black hole containing a global monopole in the context of Poincaré gravity theory which is an extension of general relativity, in the sense that the intrinsic angular momentum of matter is also a source of gravitational interaction. Thus, in this work we find the solution corresponding to the spacetime under consideration by taking into account that the action which describes this system contains terms corresponding to the curvature and torsion. The metric obtained is a function of mass, solid angle deficit and the coupling constants of the quadratic terms of the curvature and torsion. In this model, the stability of the system is studied through the analysis of the Hawking temperature and the specific heat. In this context it was also studied the critical temperatures of the system considering positive or negative cosmological constant. In the vicinity of the black hole with a global monopole, where there is a logarithmic correction due to the relationship between the torsion and curvature fields, some analysis were done. We also study the AdS/dS limit where the black hole is analyzed from the topological point of view. Although the effect of spin current density at low energies is negligible, in the vicinity of strong gravitational fields it can generate an appreciable effect due to spin gravity coupling.

Weakly trapped surfaces in asymptotically de Sitter spacetimes

It is a standard fact that trapped or marginally trapped surfaces are not visible from conformal infinity, under the usual set of conditions on matter fields and the conformal completion, provided that the cosmological constant is non-positive. In this note we show that the situation is more delicate in the presence of a positive cosmological constant: we present examples of visible marginally trapped surfaces, and we provide a set of natural conditions which guarantee non-visibility.

On the mass of static metrics with positive cosmological constant: I

In this paper we prove a new uniqueness result for the de Sitter solution. Our theorem is based on a new notion of mass, whose well-posedness is discussed and established in the realm of static spacetimes with positive cosmological constant that are bounded by Killing horizons. This new definition is formulated in terms of the surface gravities of the Killing horizons and agrees with the usual notion when the Schwarzschild–de Sitter solutions are considered. A positive mass statement is also shown to hold in this context. The corresponding rigidity statement coincides with the above mentioned characterization of the de Sitter solution as the only static vacuum metric with zero mass. Finally, exploiting some particular features of our formalism, we show how the same analysis can be fruitfully employed to treat the case of negative cosmological constant, leading to a new uniqueness theorem for the anti-de Sitter spacetime, which holds under a very feeble assumption on the asymptotic behavior of the solution.

On the holographic basis of loop quantum cosmology

In this work, we obtain the loop quantum cosmology dynamical equations, plus a positive cosmological constant, from the Bekenstein–Hawking entropy-area relation given by Loop Quantum Black Holes, by the use of the Jacobson formalism (Phys Rev Lett 75:1260, 1995). The results found out may set a still absent connection between holography and the description of the cosmos given by loop quantum cosmology.

Kerr-de Sitter spacetime, Penrose process, and the generalized area theorem

We investigate various aspects of energy extraction via the Penrose process in the Kerr-de Sitter spacetime. We show that the increase in the value of a positive cosmological constant, $\mathrm{\ensuremath{\Lambda}}$, always reduces the efficiency of this process. The Kerr-de Sitter spacetime has two ergospheres associated with the black hole and the cosmological event horizons. We prove by analyzing turning points of the trajectory that the Penrose process in the cosmological ergoregion is never possible. We next show that in this process both the black hole and cosmological event horizons' areas increase, and the latter becomes possible when the particle coming from the black hole ergoregion escapes through the cosmological event horizon. We identify a new, local mass function instead of the mass parameter, to prove this generalized area theorem. This mass function takes care of the local spacetime energy due to the cosmological constant as well, including that which arises due to the frame-dragging effect due to spacetime rotation. While the current observed value of $\mathrm{\ensuremath{\Lambda}}$ is quite small, its effect in this process could be considerable in the early Universe scenario where its value is much larger, where the two horizons could have comparable sizes. In particular, the various results we obtain here are also evaluated in a triply degenerate limit of the Kerr-de Sitter spacetime we find, in which radial values of the inner, the black hole and the cosmological event horizons are nearly coincident.