Cosmological Constant Term Research Articles

A statistical representation of the cosmological constant from finite size effects at the apparent horizon

In this paper we present a statistical description of the cosmological constant in terms of massless bosons (gravitons). To this purpose, we use our recent results implying a non vanishing temperature ${T_{\Lambda}}$ for the cosmological constant. In particular, we found that a non vanishing $T_{\Lambda}$ allows us to depict the cosmological constant $\Lambda$ as composed of elementary oscillations of massless bosons of energy $\hbar\omega$ by means of the Bose-Einstein distribution. In this context, as happens for photons in a medium, the effective phase velocity $v_g$ of these massless excitations is not given by the speed of light $c$ but it is suppressed by a factor depending on the number of quanta present in the universe at the apparent horizon. We found interesting formulas relating the cosmological constant, the number of quanta $N$ and the mean value $\overline{\lambda}$ of the wavelength of the gravitons. In this context, we study the possibility to look to the gravitons system so obtained as being very near to be a Bose-Einstein condensate. Finally, an attempt is done to write down the Friedmann flat equations in terms of $N$ and $\overline{\lambda}$.

Surface term effects on mass estimators

Context. We propose a way of estimating the mass contained in the volume occupied by a sample of galaxies in a virialized system.Aims. We analyze the influence of surface effects and the contribution of the cosmological constant terms on our mass estimations of galaxy systems.Methods. We propose two equations that contain surface terms to estimate galaxy sample masses. When the surface terms are neglected, these equations provide the so-called virial and projected masses. Both equations lead to a single equation that allows sample masses to be estimated without the need for calculating surface terms. Sample masses for some nearest galaxy groups are estimated and compared with virialized masses determined from turn-around radii and results of a spherical infall model.Results. Surface effects have a considerable effect on the mass estimations of the studied galaxy groups. According to our results, they lead sample masses of some groups to being less than half the virial mass estimations and even less than 10% of projected mass estimations. However, the contributions of cosmological constant terms to mass estimations are smaller than 2% for the majority of the virialized groups studied. Our estimations are in agreement with virialized masses calculated from turn-around radii. Virialized masses for complexes were found to be: (8.9 ± 2.8) × 1011 M ⊙ for the Milky Way – M 31; (12.5 ± 2.5) × 1011 M ⊙ for M 81 – NGC 2403; (21.5 ± 7.7) × 1011 M ⊙ . for Cantaurs A – M 83; and (7.9 ± 2.6) × 1011 M ⊙ . for IC 324 – Maffei.Conclusions. The nearest galaxy groups located inside a sphere of 5 Mpc have been addressed to explore the performance of our mass estimator. We have seen that surface effects make mass estimations of galaxy groups rather smaller than both virial and projected masses. In mass calculations, cosmological constant terms can be neglected; nevertheless, the collapse of cold dark matter leading to virialized structures is strongly affected by the cosmological constant. We have also seen that, if mass density were proportional to luminosity density on different scales in the Universe, the 5 Mpc sphere would have a mean density close to that of the sphere region containing galaxies and systems of galaxies; thus, the rest of the sphere could contain regions of low-mass dark halos with similar mass density. This mass density would be about 4.5 times greater than that of the matter background of the Universe at present.

It is sufficient to set the cosmological constant to zero or to a small number at an initial time

I point out a simple but usually overlooked fact about the cosmological constant problem: to solve the cosmological constant problem it is sufficient to find a symmetry or mechanism that sets the cosmological constant to zero or to a tiny value at some time in the past, provided that general relativity is the relevant theory of gravity, and the energy-momentum tensor (excluding the part of the form of a cosmological constant) is conserved. The relevant symmetry or mechanism need not be applicable today. Any additional cosmological constant term induced by a phase transition in the energy-momentum tensor in this case is compensated by a shift in the cosmological constant term of gravitational origin.

A Deeper Analogy between Electromagnetism and Acoustics

Based on an assumption of that the cosmological constant term in Einstein field equation can be modeled as a material medium, we propose the concept of cosmological acoustic wave (CAW). In the process, we will see: 1) By the dual framework of electromagnet...

Traversable wormholes satisfying the weak energy condition in third-order Lovelock gravity

In this paper, we consider third order Lovelock gravity with a cosmological constant term in an n-dimensional spacetime $\mathcal{M}^{4}\times \mathcal{K}^{n-4}$, where $\mathcal{K}^{n-4} $ is a constant curvature space. We decompose the equations of motion to four and higher dimensional ones and find wormhole solutions by considering a vacuum $\mathcal{K}^{n-4} $ space. Applying the latter constraint, we determine the second and third order Lovelock coefficients and the cosmological constant in terms of specific parameters of the model, such as the size of the extra dimensions. Using the obtained Lovelock coefficients and $\Lambda$, we obtain the 4-dimensional matter distribution threading the wormhole. Furthermore, by considering the zero tidal force case and a specific equation of state, given by $\rho =(\gamma p-\tau )/[\omega (1+\gamma )]$, we find the exact solution for the shape function which represents both asymptotically flat and non-flat wormhole solutions. We show explicitly that these wormhole solutions in addition to traversibility satisfy the energy conditions for suitable choices of parameters and that the existence of a limited spherically symmetric traversable wormhole with normal matter in a 4-dimensional spacetime, implies a negative effective cosmological constant.

Nonminimal derivative coupling scalar-tensor theories: Odd-parity perturbations and black hole stability

We derive the odd parity perturbation equation in scalar-tensor theories with a non minimal kinetic coupling sector of the general Horndeski theory, where the kinetic term is coupled to the metric and the Einstein tensor. We derive the potential of the perturbation, by identifying a master function and switching to tortoise coordinates. We then prove the mode stability under linear odd- parity perturbations of hairy black holes in this sector of Horndeski theory, when a cosmological constant term in the action is included. Finally, we comment on the existence of slowly rotating black hole solutions in this setup and discuss their implications on the physics of compact objects configurations, such as neutron stars.

Non-minimal derivative coupling gravity in cosmology

We give a brief review of the non-minimal derivative coupling (NMDC) scalar field theory in which there is non-minimal coupling between the scalar field derivative term and the Einstein tensor. We assume that the expansion is of power-law type or super-acceleration type for small redshift. The Lagrangian includes the NMDC term, a free kinetic term, a cosmological constant term and a barotropic matter term. For a value of the coupling constant that is compatible with inflation, we use the combined WMAP9 (WMAP9+eCMB+BAO+ $H_0$) dataset, the PLANCK+WP dataset, and the PLANCK $TT,TE,EE$+lowP+Lensing+ext datasets to find the value of the cosmological constant in the model. Modeling the expansion with power-law gives a negative cosmological constants while the phantom power-law (super-acceleration) expansion gives positive cosmological constant with large error bar. The value obtained is of the same order as in the $\Lambda$CDM model, since at late times the NMDC effect is tiny due to small curvature.

Constraint algebra of general relativity from a formal continuum limit of canonical tensor model

Canonical tensor model (CTM for short below) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. In the classical case, the constraints form a first-class constraint Poisson algebra with structures similar to that of the ADM formalism of general relativity, qualifying CTM as a possible discrete formalism for quantum gravity. In this paper, we show that, in a formal continuum limit, the constraint Poisson algebra of CTM with no cosmological constant exactly reproduces that of the ADM formalism. To this end, we obtain the expression of the metric tensor field in general relativity in terms of one of the dynamical rank-three tensors in CTM, and determine the correspondence between the constraints of CTM and those of the ADM formalism. On the other hand, the cosmological constant term of CTM seems to induce non-local dynamics, and is inconsistent with an assumption about locality of the continuum limit.

Dynamics of charged shell with a cosmological constant

Using the Darmois–Israel formalism technique, charged thin shell in the presence of a cosmological constant is constructed. An equation governing the behavior of the radial pressure across the junction surface is deduced. The cosmological constant term and the charge term slows down the collapse of matter.The spherical N-shell model with an appropriate initial condition imitates quite well the FRW universe with Λ ≠ 0.

Effects of ghost dark energy perturbations on the evolution of spherical overdensities

While in the standard cosmological model the accelerated expansion of the Universe is explained by invoking the presence of the cosmological constant term, it is still unclear the true origin of this stunning observational fact. It is therefore interesting to explore alternatives to the simplest scenario, in particular by assuming a more general framework where the fluid responsible of the accelerated expansion is characterised by a time-dependant equation of state. Usually these models, dubbed dark energy models, are purely phenomenological, but in this work we concentrate on a theoretically justified model, the ghost dark energy model. Within the framework of the spherical collapse model, we evaluate effects of dark energy perturbations both at the linear and non-linear level and transfer these results into an observable quantity, the mass function, by speculatively taking into account contributions of dark energy to the mass of the halos. We showed that the growth rate is higher in ghost models and that perturbations enhance the number of structures with respect to the $\Lambda$CDM model, with stronger effects when the total mass takes into account dark energy clumps.

Modified gravity in three dimensional metric-affine scenarios

We consider metric-affine scenarios where a modified gravitational action is sourced by electrovacuum fields in a three dimensional space-time. Such scenarios are supported by the physics of crystalline structures with microscopic defects and, in particular, those that can be effectively treated as bi-dimensional (like graphene). We first study the case of $f(R)$ theories, finding deviations near the center as compared to the solutions of General Relativity. We then consider Born-Infeld gravity, which has raised a lot of interest in the last few years regarding its applications in astrophysics and cosmology, and show that new features always arise at a finite distance from the center. Several properties of the resulting space-times, in particular in presence of a cosmological constant term, are discussed.

Cosmological kinetic mixing

In this paper we generalize the kinetic mixing idea to time reparametrization invariant theories, namely, relativistic point particles and cosmology in order to obtain new insights for dark matter and energy. In the first example, two relativistic particles interact through an appropriately chosen coupling term. It is shown that the system can be diagonalized by means of a non-local field redefinition, and, as a result of this procedure, the mass of one the particles gets rescaled. In the second case, inspired by the previous example, two cosmological models (each with its own scale factor) are made to interact in a similar fashion. The equations of motion are solved numerically in different scenarios (dust, radiation or a cosmological constant coupled to each sector of the system). When a cosmological constant term is present, kinetic mixing rescales it to a lower value which may be more amenable to observations.

Casimir effect in the Hořava–Lifshitz gravity with a cosmological constant

We calculate the Casimir energy of a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed tangentially to the surface of a sphere with mass M and radius R. To this end, we take into account a static and spherically symmetric solution of Hořava–Lifshitz (HL) gravity, with a cosmological constant term, in lower orders of approximation, considering both weak-field and infrared limits. We show that the Casimir energy, just in the second order weak-field approximation, is modified due to the parameter of the HL gravity as well as to the cosmological constant.

New realizations of 𝒩 = 2l-conformal Newton–Hooke superalgebra

By applying Niederer-like transformation, we construct a representation of the 𝒩 = 2l-conformal Newton–Hooke (NH) superalgebra for the case of a negative cosmological constant in terms of linear differential operators as well as its dynamical realization. Another variant of 𝒩 = 2 supersymmetric Pais–Uhlenbeck oscillator for a particular choice of its frequencies is proposed. The advantages of such realizations as compared to their analogues introduced in [I. Masterov, J. Math. Phys.53, 072904 (2012)], are discussed.

The Einstein-Hilbert action with cosmological constant as a functional of generic form

The geometrical underpinnings of a specific class of Dirac operators are discussed. It is demonstrated how this class of Dirac operators allows to relate various geometrical functionals like the Yang-Mills action and the functional of non-linear σ − models (i.e., of (Dirac) harmonic maps). These functionals are shown to be similar to the Einstein-Hilbert action with cosmological constant (EHC). The EHC may thus be regarded as a “generic functional.” As a byproduct, the geometrical setup presented also allows to avoid the issue of “fermion doubling” as usually encountered, for instance, in the geometrical discussion of the Standard Model in terms of Dirac operators. Furthermore, it is demonstrated how the geometrical setup presented allows to derive the cosmological constant term of the EHC from the Einstein-Hilbert functional and the action of a purely gauge coupling Higgs field.

Cosmological dynamics and dark energy from nonlocal infrared modifications of gravity

We study the cosmological dynamics of a recently proposed infrared modification of the Einstein equations, based on the introduction of a nonlocal term constructed with m2gμν□-1R, where m is a mass parameter. The theory generates automatically a dynamical dark energy component, that can reproduce the observed value of the dark energy density without introducing a cosmological constant. Fixing m so to reproduce the observed value Ω DE ≃0.68, and writing w DE (a) = w0+(1-a)wa, the model provides a neat prediction for the equation of state parameters of dark energy, w0≃-1.042 and wa≃-0.020, and more generally provides a pure prediction for w DE as a function of redshift. We show that, because of some freedom in the definition of □-1, one can extend the construction so to define a more general family of nonlocal models. However, in a first approximation this turns out to be equivalent to adding an explicit cosmological constant term on top of the dynamical dark energy component. This leads to an extended model with two parameters, ΩΛ and m. Even in this extension the EOS parameter w0 is always on the phantom side, in the range -1.33 ≲w0≤-1, and there is a prediction for the relation between w0 and wa.

Thermodynamics of a BTZ black hole solution with a Horndeski source

In three dimensions, we consider a particular truncation of the Horndeski action that reduces to the Einstein-Hilbert Lagrangian with a cosmological constant $\mathrm{\ensuremath{\Lambda}}$ and a scalar field whose dynamics is governed by its usual kinetic term together with a nonminimal kinetic coupling. Requiring the radial component of the conserved current to vanish, the solution turns out to be the BTZ black hole geometry with a radial scalar field well defined at the horizon. This means in particular that the stress tensor associated to the matter source behaves on shell as an effective cosmological constant term. We construct a Euclidean action whose field equations are consistent with the original ones and such that the constraint on the radial component of the conserved current also appears as a field equation. With the help of this Euclidean action, we derive the mass and the entropy of the solution, and find that they are proportional to the thermodynamical quantities of the BTZ solution by an overall factor that depends on the cosmological constant. The reality condition and the positivity of the mass impose the cosmological constant to be bounded from above as $\mathrm{\ensuremath{\Lambda}}\ensuremath{\le}\ensuremath{-}\frac{1}{{l}^{2}}$ where the limiting case $\mathrm{\ensuremath{\Lambda}}=\ensuremath{-}\frac{1}{{l}^{2}}$ reduces to the BTZ solution with a vanishing scalar field. Exploiting a scaling symmetry of the reduced action, we also obtain the usual three-dimensional Smarr formula. In the last section, we extend all these results in higher dimensions where the metric turns out to be the Schwarzschild--anti--de Sitter spacetime with planar horizon.

NoncommutativeSO(2,3)gauge theory and noncommutative gravity

In this paper noncommutative gravity is constructed as a gauge theory of the noncommutative SO(2,3) group, while the noncommutativity is canonical (constant). The Seiberg-Witten map is used to express noncommutative fields in terms of the corresponding commutative fields. The commutative limit of the model is the Einstein-Hilbert action with the cosmological constant term and the topological Gauss-Bonnet term. We calculate the second order correction to this model and obtain terms that are of zeroth to fourth power in the curvature tensor and torsion. Trying to relate our results with $f(R)$ and $f(T)$ models, we analyze different limits of our model. In the limit of big cosmological constant and vanishing torsion we obtain a $x$-dependent correction to the cosmological constant, i.e. noncommutativity leads to a $x$-dependent cosmological constant. We also discuss the limit of small cosmological constant and vanishing torsion and the teleparallel limit.

Quantum Gravity and Cosmological Density Perturbations

We explore the possible cosmological consequences of a running Newton’s constant, G(⎕), as suggested by the non-trivial ultraviolet fixed point scenario for Einstein gravity with a cosmological constant term. Here, we examine what possible effects a scale-dependent coupling might have on large-scale cosmological density perturbations. Starting from a set of manifestly covariant effective field equations, we develop the linear theory of density perturbations for a non-relativistic perfect fluid. The result is a modified equation for the matter density contrast, which can be solved and thus provides an estimate for the corrections to the growth index parameter, ɤ.

Renormalisation group, trace anomaly and Feynman–Hellmann theorem

We show that the logarithmic derivative of the gauge coupling on the hadronic mass and the cosmological constant term of a gauge theory are related to the gluon condensate of the hadron and the vacuum respectively. These relations are akin to Feynman–Hellmann relations whose derivation for the case at hand is complicated by the construction of the gauge theory Hamiltonian. We bypass this problem by using a renormalisation group equation for composite operators and the trace anomaly. The relations serve as possible definitions of the gluon condensates themselves which are plagued in direct approaches by power divergences. In turn these results might help to determine the contribution of the QCD phase transition to the cosmological constant and test speculative ideas.