Case Of Cosmological Constant Research Articles

Semiclassical saddles of three-dimensional gravity via holography

We find out the complex geometries corresponding to the semiclassical saddles of three-dimensional quantum gravity by making use of the known results of dual conformal field theory (CFT), which is effectively given by Liouville field theory. We examine both the cases with positive and negative cosmological constants. We determine the set of semiclassical saddles to choose from the homotopy argument in the Chern-Simons formulation combined with CFT results and provide strong supports from the minisuperspace approach to the quantum gravity. For the case of positive cosmological constant, partial results were already obtained in our previous works, and they are consistent with the current ones. For the case of negative cosmological constant, we identify the geometry corresponding a semiclassical saddle with three-dimensional Euclidean anti–de Sitter space dressed with imaginary radius three-dimensional spheres. The geometry is generically unphysical, but the fact itself should not lead to any problems as derived from consistent dual CFT. We thus find an intriguing example, where the gravity path integral is performed over unphysical geometries. Published by the American Physical Society 2024

A note on no-hair properties of static black holes in four and higher dimensional spacetimes with cosmological constant

We study no-hair properties of static black holes in four and higher dimensional spacetimes with a cosmological constant. For the vanishing cosmological constant case, we show a no-hair theorem and also a no-short-hair theorem under certain conditions for the energy-momentum of matter fields. For the positive cosmological constant case, we discuss conditions for hairy static black holes to exist in terms of the energy density of matter fields evaluated at the black hole horizon and the cosmological horizon. For the negative cosmological constant case, we study conditions for hairy black holes by presenting a no-hair theorem in which the asymptotic structure is assumed to be determined by the true cosmological constant.

On the dynamics of a dark sector coupling

Interacting dark energy models may play a crucial role in explaining several important observational issues in modern cosmology and also may provide a solution to current cosmological tensions. Since the phenomenology of the dark sector could be extremely rich, one should not restrict the interacting models to have a coupling parameter which is constant in cosmic time, rather allow for its dynamical behaviour, as it is common practice in the literature when dealing with other dark energy properties, as the dark energy equation of state. We present here a compendium of the current cosmological constraints on a large variety of interacting models, investigating scenarios where the coupling parameter of the interaction function and the dark energy equation of state can be either constant or dynamical. For the most general schemes, in which both the coupling parameter of the interaction function and the dark energy equation of state are dynamical, we find 95% CL evidence for a dark energy component at early times and slightly milder evidence for a dynamical dark coupling for the most complete observational data set exploited here, which includes CMB, BAO and Supernova Ia measurements. Interestingly, there are some cases where a dark energy component different from the cosmological constant case at early times together with a coupling different from zero today, can alleviate both the H0 and S8 tension for the full dataset combination considered here. Due to the energy exchange among the dark sectors, the current values of the matter energy density and of the clustering parameter σ8 are shifted from their ΛCDM-like values. This fact makes future surveys, especially those focused on weak lensing measurements, unique tools to test the nature and the couplings of the dark energy sector.

Newtonian cosmology from quantum corrected Newtonian potential

We study the Newtonian cosmology taking into account the leading classical and quantum corrections of order O(G2) in the Newtonian potential. We first derive the modified Friedmann equations starting from the non-relativistic conservation of kinetic energy and potential energy for an infinitesimal mass. We then consider the leading classical correction term and the quantum correction term in the Newtonian potential for deriving the Friedmann equation, however, the quantum correction term is too small and hence does not contribute in the physical results. We then investigate the difference in scale factor with the usual scale factor for various matters like radiation, dust and cosmological constant by considering the corrections in the Newtonian potential. We observe that the evolution of the universe is similar for radiation and dust cases at late times. The cosmological constant case shows a steep increase in the scale factor compared to the other cases. We also note that the universe may have a bounce in the case of radiation depending on the sign of the coefficient of the leading classical correction.

Hidden Spectral Symmetries and Mode Stability of Subextremal Kerr(-de Sitter) Black Holes

We uncover hidden spectral symmetries of the Teukolsky equation in Kerr(-de Sitter) black holes, recently conjectured by Aminov, Grassi and Hatsuda (Ann. Henri Poincaré 23, 1951-1977, 2022, and Gen. Relativ. Grav. 53(10):93, 2021) in the zero cosmological constant case. Using these symmetries, we provide a new, simpler proof of mode stability for subextremal Kerr black holes. We also present a partial mode stability result for Kerr–de Sitter black holes.

Swampland constraints on neutrino masses

Compactifying the Standard Model (SM) on a circle may lead to AdS 3D vacua, depending on the character (Majorana or Dirac) and the mass of the lightest neutrino. It has been shown that, imposing the Ooguri-Vafa conjecture that no stable non-SUSY AdS vacua are consistent with Quantum Gravity, one can obtain conditions on the mass of the lightest neutrino. This result has the shortcoming that it is in general sensitive to the UV structure of the theory. In the present paper we show that two other independent swampland conditions may yield constraints very similar to those. These other two conditions come from the AdS swampland distance conjecture and the dS conjecture as applied to AdS vacua by Lust, Palti and Vafa. Unlike the non-SUSY AdS constraints, for these conjectures the results require only local IR information of the radion potential. We consider both the case of an explicit cosmological 4D constant and the alternative of a simple quintessence 4D potential. Cosmological data in the next decade may falsify the results, giving us information on the constraints of particle physics from Quantum Gravity.

Phase profile of the wave function of canonical tensor model and emergence of large space—times

In this paper, to understand space–time dynamics in the canonical tensor model of quantum gravity for the positive cosmological constant case, we analytically and numerically study the phase profile of its exact wave function in a coordinate representation, instead of the momentum representation analyzed so far. A saddle point analysis shows that Lie group symmetric space–times are strongly favored due to abundance of continuously existing saddle points, giving an emergent fluid picture. The phase profile suggests that spatial sizes grow in “time,” where sizes are measured by the tensor-geometry correspondence previously introduced using tensor rank decomposition. Monte Carlo simulations are also performed for a few small [Formula: see text] cases by applying a re-weighting procedure to an oscillatory integral which expresses the wave function. The results agree well with the saddle point analysis, but the phase profile is subject to disturbances in a large space–time region, suggesting existence of light modes there and motivating future computations of primordial fluctuations from the perspective of canonical tensor model.

Wave function of simple universes analytically continued from negative to positive potentials

We elaborate on the correspondence between the canonical partition function in asymptotically AdS universes and the no-boundary proposal for positive vacuum energy. For the case of a pure cosmological constant, the analytic continuation of the AdS partition function is seen to define the no-boundary wave function (in dS) uniquely in the simplest minisuperspace model. A consideration of the AdS gravitational path integral implies that on the dS side, saddle points with Hawking-Moss/Coleman-De Luccia-type tunnelling geometries are irrelevant. This implies that simple topology changing geometries do not contribute to the nucleation of the universe. The analytic AdS/dS equivalence holds up once tensor fluctuations are added. It also works, at the level of the saddle point approximation, when a scalar field with a mass term is included, though in the latter case, it is the mass that must be analytically continued. Our results illustrate the emergence of time from space by means of a Stokes phenomenon, in the case of positive vacuum energy. Furthermore, we arrive at a new characterisation of the no-boundary condition, namely that there should be no momentum flux at the nucleation of the universe.

Induced equation of state for the universe epochs constrained by the hubble parameter

We present a five dimensional cosmological metric that reveals a four-dimensional energy-momentum tensor. We analyse three cases for the resulting field equations: null, positive and negative cosmological constant Λ. For the case with null cosmological constant, we obtain a solution able to describe the radiation-dominated era of the universe. The positive five-dimensional cosmological constant case yields a bounce cosmological model. In the negative Λ case, the scale factor for the line element is obtained as a(t)=c5sinh(23|Λ|t), where c5 is a constant. This solution can remarkably describe not only the late-time cosmic acceleration but also the non-accelerated stages of the cosmic expansion, namely the radiation and matter dominated epochs in a continuous form. We obtain an analytical equation of state capable of describing the different epochs of the universe and it reads as p=ω(z)ρ with ω(z)=13[1−41+c54(1+z)4], with p being the pressure of the universe, ρ its density and z is the redshift. In our model the constant c5 is related to the Hubble constant as H0=|Λ|6coth[arcsinh(1c5)2] and this satisfactorily fits the observational data for the low redshift sample of the experimental measurements of the Hubble parameter, which results in H0=72.2−5.5+5.3 km s−1 Mpc−1 and c5=0.600−0.058+0.061.

Symmetry enhancement in a two-logarithm matrix model and the canonical tensor model

Abstract We study a one-matrix model of a real symmetric matrix with a potential which is a sum of two logarithmic functions and a harmonic one. This two-logarithm matrix model is the absolute square norm of a toy wave function which is obtained by replacing the tensor argument of the wave function of the canonical tensor model (CTM) with a matrix. We discuss a symmetry enhancement phenomenon in this matrix model and show that symmetries and dimensions of emergent spaces are stable only in a phase which exists exclusively for the positive cosmological constant case in the sense of CTM. This would imply the importance of the positivity of the cosmological constant in the emergence phenomena in CTM.

$${\mathcal {H}}$$olographic $${\mathcal {N}}$$aturalness and $${\mathcal {C}}$$osmological $${\mathcal {R}}$$elaxation

We rediscuss the main Cosmological Problems as illusions originated from our ignorance of the hidden information holographically stored in vacuo. The Cosmological vacuum state is full of a large number of dynamical quantum hairs, dubbed hairons, which dominate the Cosmological Entropy. We elaborate on the Cosmological Constant (CC) problem, in both the dynamical and time-constant possibilities. We show that all dangerous quantum mixings between the CC and the Planck energy scales are exponentially suppressed as an entropic collective effect of the hairon environment. As a consequence, the dark energy scale is UV insensitive to any Planckian corrections. On the other hand, the inflation scale is similarly stabilized from any radiative effects. In the case of the Dark energy, we show the presence of a holographic entropic attractor, favoring a time variation of $$\Lambda \rightarrow 0$$ in future rather than a static CC case, i.e., the $$w>-1$$ Dynamical DE is favored over a CC or a $$w<-1$$ phantom cosmology. In both the inflation and dark energy sectors, we elaborate on the Trans-Planckian problem, in relation with the recently proposed Trans-Planckian Censorship Conjecture (TCC). We show that the probability for any sub-Planckian wavelength modes to survive after inflation is completely negligible as a holographic wash-out mechanism. In other words, the hairons provide for a holographic decoherence of the transplanckian modes in a holographic scrambling time. This avoids the TCC strong bounds on the Inflaton and DE potentials.

Bending of light from Reissner–Nordström–de Sitter-monopole black hole

We study light deflection from a Reissner-Nordstr\"om-de Sitter black hole in the gravitational monopole background. We first calculate the orbit equation and the contribution of the monopole and black hole parameters to the deflection angle up to second-order for the vanishing cosmological constant case using the Rindler-Ishak method. We also obtain the contribution of the cosmological constant to light deflection in this geometry in the weak field limit using the same method.

Measurements of H0 in modified gravity theories: The role of lensed quasars in the late-time Universe

In this work, we obtain measurements of the Hubble constant in the context of modified gravity theories. We set up our theoretical framework by considering viable cosmological $f(R)$ and $f(T)$ models, and we analyzed them through the use of geometrical data sets obtained in a model-independent way, namely, gravitationally lensed quasars with measured time delays, standard clocks from cosmic chronometers, and standard candles from the Pantheon Supernovae Ia sample. We find $H_0=(72.4\pm 1.4)$ km s$^{-1}$ Mpc$^{-1}$ and $H_0=(71.5\pm 1.3)$ km s$^{-1}$ Mpc$^{-1}$ for the $f(R)$ and $f(T)$ models, respectively. Our results represent 1.9\% and 1.8\% measurements of the Hubble constant, which are fully consistent with the local estimate of $H_0$ by the Hubble Space Telescope. We do not find significant departures from general relativity, as our study shows that the characteristic parameters of the extensions of gravity beyond general relativity are compatible with the $\Lambda$CDM cosmology. Moreover, within the standard cosmological framework, our full joint analysis suggests that it is possible to measure the dark energy equation of state parameter at 1.2\% accuracy, although we find no statistical evidence for deviations from the cosmological constant case.

The Effect of a Positive Cosmological Constant on the Bounce of Loop Quantum Cosmology

We provide an analytical solution to the quantum dynamics of a flat Friedmann-Lemaître- Robertson-Walker model with a massless scalar field in the presence of a small and positive cosmological constant, in the context of Loop Quantum Cosmology. We use a perturbative treatment with respect to the model without a cosmological constant, which is exactly solvable. Our solution is approximate, but it is precisely valid at the high curvature regime where quantum gravity corrections are important. We compute explicitly the evolution of the expectation value of the volume. For semiclassical states characterized by a Gaussian spectral profile, the introduction of a positive cosmological constant displaces the bounce of the solvable model to lower volumes and to higher values of the scalar field. These displacements are state dependent, and in particular, they depend on the peak of the Gaussian profile, which measures the momentum of the scalar field. Moreover, for those semiclassical states, the bounce remains symmetric, as in the vanishing cosmological constant case. However, we show that the behavior of the volume is more intricate for generic states, leading in general to a non-symmetric bounce.

The κ-(A)dS noncommutative spacetime

The (3+1)-dimensional κ-(A)dS noncommutative spacetime is explicitly constructed by quantizing its semiclassical counterpart, which is the κ-(A)dS Poisson homogeneous space. This turns out to be the only possible generalization of the well-known κ-Minkowski spacetime to the case of non-vanishing cosmological constant, under the condition that the time translation generator of the corresponding quantum (A)dS algebra is primitive. Moreover, the κ-(A)dS noncommutative spacetime is shown to have a quadratic subalgebra of local spatial coordinates whose first-order brackets in terms of the cosmological constant parameter define a quantum sphere, while the commutators between time and space coordinates preserve the same structure of the κ-Minkowski spacetime. When expressed in ambient coordinates, the quantum κ-(A)dS spacetime is shown to be defined as a noncommutative pseudosphere.

(A)dS4 in Bondi gauge

We obtain the general asymptotic solutions of Einstein gravity with or without cosmological constant in Bondi gauge. The Bondi gauge was originally introduced in the context of gravitational radiation in asymptotically flat gravity. In the original work, initial conditions were prescribed at a null hypersurface and the Einstein equations were shown to take a nested form, which may be used to explicitly integrate them asymptotically. We streamline the derivation of the general asymptotic solution in the asymptotically flat case, and derive the most general asymptotic solutions for the case of non-zero cosmological constant of either sign (asymptotically locally AdS and dS solutions). With non-zero cosmological constant, we present integration schemes which rely on either prescribing data on the conformal boundary or on a null hypersurface and part of the conformal boundary. We explicitly work out the transformation to Fefferman–Graham gauge and identity how to extract the holographic data directly in Bondi coordinates. We illustrate the discussion with a number of examples and show that for asymptotically AdS4 spacetimes the Bondi mass is constant.

Bonnor-Melvin universe with a cosmological constant

We generalize the well-known Bonnor-Melvin solution of the Einstein-Maxwell equations to the case of a non-vanishing cosmological constant. The spacetime is again cylindrically symmetric and static but, unlike the original solution, it truly represents a homogeneous magnetic field.

Local version of the no-hair theorem

Non-extremal isolated horizons embeddable in 4-dimensional spacetimes satisfying the vacuum Einstein equations with cosmological constant are studied. The horizons are assumed to be stationary to the second order. The Weyl tensor at the horizon is assumed to be of the Petrov type D. The corresponding equation on the intrinsic horizon geometry is solved in the axisymmetric case. The family of the solutions is $2$-dimensional, it is parametrized by the area and the angular momentum. The embeddability in the Kerr - de Sitter, the Kerr - anti de Sitter and the Near extremal Horizon spacetimes obtained by the Horowitz limit from the extremal Kerr - de Sitter and extremal Kerr - anti de Sitter is discussed. This uniqueness of the axisymmetric type D isolated horizons is a generalization of the similar earlier result valid in the cosmological constant free case.

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.

Parameter space for range of bare graviton mass in an FLRW universe based on dRGT massive gravity theory

We discuss the existence of graviton in a Friedmann–Lemaitre–Robertson–Walker (FLRW) metric of isotropic and homogeneous universe based on de Rham–Gabadadze–Tolley (dRGT) nonlinear massive gravity theory. We consider a similar FLRW fiducial metric in the formulation that lead to a Friedmann–Lemaitre equation similar to the case of cosmological constant based dark energy model. We show that these equations can be constructed by considering a constraint equation found from varying the corresponding action with respect to the fiducial metric. Under a specific choice of fiducial metric lapse function, we determine the range of present cosmological time bare graviton mass in a parameter space by considering the observed cosmological constant density parameter and the related Higuchi bound for the lower dressed graviton mass value. The existence of an indefinite condition in the corresponding parameter space is also discussed and analyzed, as well as the characteristics of the related bare graviton mass and the strong-coupling scale quantity.