Cosmological constant: a lesson from the effective gravity of topological weyl media

Topological matter with Weyl points, such as superfluid ³He-A, provide an explicit example where there is a direct connection between the properly determined vacuum energy and the cosmological constant of the effective gravity emerging in condensed matter. This is in contrast to the acoustic gravity emerging in Bose-Einstein condensates (S. Finazzi, S. Liberati, and L. Sindoni, Phys. Rev. Lett. 108, 071101 (2012); arXiv:1103.4841). The advantage of topological matter is that the relativistic fermions and gauge bosons emerging near the Weyl point obey the same effective metric and thus the effective gravity is more closely related to real gravity. We study this connection in the bi-metric gravity emerging in ³He-A, and its relation to the graviton masses, by comparison with a fully relativistic bi-metric theory of gravity. This shows that the parameter ??, which in ³He-A is the bi-metric generalization of the cosmological constant, coincides with the difference in the proper energy of the vacuum in two states (the nonequilibrium state without gravity and the equilibrium state in which gravity emerges) and is on the order of the characteristic Planck energy scale of the system. Although the cosmological constant ?? is huge, the cosmological term T _??? ^?? itself is naturally non-constant and vanishes in the equilibrium vacuum, as dictated by thermodynamics. This suggests that the equilibrium state of any system including the final state of the Universe is not gravitating.     

Einstein–Maxwell gravity with additional corrections

Motivated by the E ₈×E ₈ heterotic string theory, we obtain topological black hole solutions of Einstein–Maxwell gravity with additional corrections. We consider the Gauss–Bonnet (GB) and (F _μν F ^μν )² terms as an effective quartic order Lagrangian of gauge–gravity coupling and investigate geometric and thermodynamic properties of the black hole solutions. We also analyze the effects of the GB term as well as the correction of Maxwell field on the properties of the solutions.     

Perturbation theory in terms of electron density

When an inhomogeneous electron gas is subjected to a perturbation, its energy and density both change by small amounts. We calculate the changes in the energy explicitly in terms of the density changes within the density-functional theory of many-electron systems. We also derive the equations for the induced densities, and using these show that a density correct up to order n in terms of the perturbation parameter is sufficient to give energy changes up to order (2n + 1). As a corollary, the even-order energy changes E⁽²ⁿ⁾ are variational with respect to the density changes ?⁽ⁿ⁾. The equations for the induced densities also follow from this corollary. The even-order corollary also gives a variational method of calculating the induced densities. The theory is demonstrated by applying it to calculate the polarizability and hyperpolarizability of the hydrogen, helium and neon atoms.     

Quantization of conformal gravity: Another approach to the renormalization of gravity

The non-renormalizability of quantum gravity poses a great problem to the construction of any unified field theory of all known interactions. Normally, we start with a unitary theory of gravity and investigate its renormalization properties. This is the first of a series of papers where we start with the opposite approach, beginning with a renormalizable theory and investigating its unitarity structure. In particular, we study non-perturbative approaches to the quantization of conformal gravity. Using ADM coordinates, we perform the canonical quantization of the Weyl action C_μναβ², which is renormalizable and is also local scale invariant. Although this theory is certainly not unitary in perturbation theory, we speculate that unitarity may be restored when we approach this theory non-perturbatively, by examining the possibility of different phase transitions.     

Dual models for non-hadrons

The possibility of describing particles other than hadrons (leptons, photons, gauge bosons, gravitons, etc.) by a dual model is explored. The Virasoro-Shapiro model is studied first, interpreting the massless spin-two state of the model as a graviton. We prove that in the limit of zero slope (with g_vs²α′ held fixed) one obtains the Einstein theory of gravitation accompanied by a massless scalar field. Next, the Veneziano model is studied for small slope as an expansion in powers of α′. It is known from previous work that the zeroth order term is precisely the Yang-Mills theory of a multiplet of massless vector bosons. We show that there are order α′ terms arising both from the dual tree and loop graphs. The former constitutes a relatively unimportant modification of the Yang-Mills theory, whereas the latter involves the coupling of the massless scalar and graviton states of the Virasoro-Shapiro model. Thus one may take the point of view that gravity arises as a unitarization effect in a dual unified theory of electromagnetism and weak interactions. In order to obtain the correct values for the electric charge and Newton's constant it is necessary that α′ ? 10^?34 GeV^?2 The coupling of massless scalar states is also studied.     

Diffeomorphism symmetry in simplicial quantum gravity

A construction of simplicial quantum gravity with an extremely strong form of diffeomorphism symmetry of the functional integral measure (Π d ℓ e^−S_pg) is proposed using the method of mathematical induction. By means of the formalism of introducing a continuous four-space approximating a lattice model in our previous paper this symmetry results in a “free gas” behavior of the vertices of the lattice on a C^∞ manifold. Furthermore, we argue that this kind of a simplicial quantum gravity model leads to a gravitational theory described by a local action in the long wavelength (continuum) limit.     

The Vilkovisky-DeWitt effective action for quantum gravity

The Vilkovisky-DeWitt effective action for gauge theories is reviewed and then discussed in the context of N-dimensional quantum gravity and quantum Kaluza-Klein theory. The formalism gives an effective action which is gauge-independent and gauge and field-parametrization invariant. These features are illustrated for the vacuum energy of N-dimensional gravity. The Bunch-Parker local momentum space approach is used to calculate also the induced Ricci scalar term in the expansion of the effective action in powers of the curvature. The effective field equations are applied to the self-consistent dimensional reduction of five-dimensional Kaluza-Klein theory. A solution exists, but is found to be physically unacceptable.     

Effective field theory for massive gravitons and gravity in theory space

We introduce a technique for restoring general coordinate invariance into theories where it is explicitly broken. This is the analog for gravity of the Callan-Coleman-Wess-Zumino formalism for gauge theories. We use this to elucidate the properties of interacting massless and massive gravitons. For a single graviton with a Planck scale M_Pl and a mass m_g, we find that there is a sensible effective field theory which is valid up to a high-energy cutoff Λ parametrically above m_g. Our methods allow for a transparent understanding of the many peculiarities associated with massive gravitons, among them the need for the Fierz-Pauli form of the Lagrangian, the presence or absence of the van Dam-Veltman-Zakharov discontinuity in general backgrounds, and the onset of non-linear effects and the breakdown of the effective theory at large distances from heavy sources. The natural sizes of all non-linear corrections beyond the Fierz-Pauli term are easily determined. The cutoff scales as Λ∼(m_g⁴M_Pl)^1/5 for the Fierz-Pauli theory, but can be raised to Λ∼(m_g²M_Pl)^1/3 in certain non-linear extensions. Having established that these models make sense as effective theories, there are a number of new avenues for exploration, including model building with gravity in theory space and constructing gravitational dimensions.     

Dark energy,induced gravity and broken scale invariance

We study the cosmological evolution of an induced gravity model with a self-interacting scalar field σ and in the presence of matter and radiation. Such model leads to Einstein gravity plus a cosmological constant as a stable attractor among homogeneous cosmologies and is therefore a viable dark-energy (DE) model for a wide range of scalar field initial conditions and values for its positive γ   coupling to the Ricci curvature γσ²R$\gamma {\sigma }^{2}R$.     

Weak equivalence principle from a spontaneously broken gauge theory of gravity

Further consequences of a finite topological field theory for gravity based on the SL(5,R) gauge group are reported. After symmetry breaking, it induces four-dimensional Einstein spaces with a cosmological constant related to the tiny scale of the symmetry breaking. It is shown that not only a ‘background’ metric emerges from a Higgs-like mechanism, but also consistently the geodesic equation central to Einstein?s equivalence principle. In next order of the symmetry breaking scale, the induced torsion could even provoke a tiny Lorentz violation.     

Covariant chronogeometry and extreme distances. III. Macro-micro relations

A theory is proposed that provides a coherent, concise, and nonparametric analysis of major features of the fundamental physical structure of the universe, from micro- to macroscopic. In particular it indicates that gravity is essentially the transform of the aggregate of the basic microscopic forces under conformal inversion, and not a specific force in irself. The theory also suggests a natural form for elementary particle structure that implies a nonparametric cosmological effect and indicates an intrinsic hierarchy among the microscopic forces. The theory replaces Minkowski spaceM ₀ by a larger space-time M that osculates at the point of observation, and in which it is canonically imbedded by a causality-preserving transformation that is a relativistic variant of stereographic projection. The natural energy in M exceeds that inM ₀ by an amount that becomes observationally significant in large-scale contexts; an earlier proposal that this energy difference represents the extragalactic redshift has resolved a variety of anomalies and provided a greatly improved nonparametric fit to statistical data in cosmology. The energetic contents of the universe appear to distinguish a global inertial frame in which M takes the metric formR ¹×S ³ proposed by Einstein. It is argued that in the case of massive particles the energy excess in M in this frame over that inM ₀ is observed as gravity. Implications include more explicit forms of the Mach and Einstein Equivalence principles.     

On wormhole throats in f (R) gravity theory

We study the existence and properties of wormhole throats in modified f (R) gravity theory. Specifically, we concentrate on the cases where the lapse is not necessarily constant, and hence are not limited to the zero tidal force scenarios. In the class of theories whose actions are generated by Lagrangians of the form f (R)?=?∑ α _n ?R ⁿ we find parameters which allow for the existence of energy condition respecting throats, which do not exist in Einstein gravity. We also consider the effect of the modified action on the anisotropy of the models, and find that modified gravity can minimize the amount of anisotropy required to support the existence of a throat. In both these respects, the sector containing theories with positive n is more promising than the negative n sector in comparison to Einstein gravity alone, with large n being most favorable.     

Low-energy gluon to the vacuum polarization of heavy quarks

We calculate a correction to the effective electromagnetic current at low energies, induced by a heavy-quark loop, and determine the analytic structure of the vacuum polarization function at small q ², for which an explicit expression is given to the O(α _s ³ ) order of perturbation theory. Implications to the high-precision analysis of experimental data on heavy-quark production in e ⁺ e ^? annihilation are discussed.     

Renormalizability and asymptotic freedom in quantum gravity

We discuss a previously proposed renormalizable theory of gravity involving R²_μν, and N massless fermion (vector boson) fields in which the unitarity problem is resolved within a $\text{1}\text{N}$ expansion. The infrared limit is precisely Einstein's theory, but the high-energy behavior is determined by the dimensionless, asymptotically free coupling of the R²_μν. Various attractive possible consequences of the theory are pointed out.     

Gauge theory of gravity

General relativity is formulated in the framework of Yang-Mills theory whose gauge group isO(3, 2). This theory allows the global topological charge of spin without breaking Bianchi identity. β function in the renormalization group equation is negative and the confinement of gravity is expected. The confinement radius is, however, actually infinite and we can read off the relation that the average mass density of the present universe is exactly equal to the critical value ρ _c (t)=6H ²(t)/K ².     

On torsion-free vacuum solutions of the model of de Sitter gauge theory of gravity (II)

It is shown that all torsion-free vacuum solutions of the model of de Sitter (dS) gauge theory of gravity are the vacuum solutions of Einstein field equations with the same positive cosmological constant. Furthermore, for the gravitational theories with more general quadratic gravitational Lagrangian (F ² + T ²), the torsion-free vacuum solutions are also the vacuum solutions of Einstein field equations.     

On the cosmological viability of the Hu-Sawicki type modified induced gravity

It has been shown recently that the normal branch of a DGP braneworld scenario self-accelerates if the induced gravity on the brane is modified in the spirit of f(R) modified gravity. Within this viewpoint, we investigate cosmological viability of the Hu-Sawicki type modified induced gravity. Firstly, we present a dynamical system analysis of a general f(R)-DGP model. We show that in the phase space of the model, there exist three standard critical points; one of which is a de Sitter point corresponding to accelerating phase of the universe expansion. The stability of this point depends on the effective equation of state parameter of the curvature fluid. If we consider the curvature fluid to be a canonical scalar field in the equivalent scalar-tensor theory, the mentioned de Sitter phase is unstable, otherwise it is an attractor, stable phase. We show that the effective equation of state parameter of the model realizes an effective phantom-like behavior. A cosmographic analysis shows that this model, which admits a stable de Sitter phase in its expansion history, is a cosmologically viable scenario.     

On the pure rotational spectrum of BF3 in its vibronic ground state

The centrifugally induced pure rotational absorption spectrum of BF₃ in its vibronic ground state has been computed using the theory of Watson. Maximum absorption of order 10^?5 (mol/liter)^?1 cm^?1 is found to occur in a frequency region around ～30 cm^?1. Due to the coincidence of the Q and R branches the full spectrum exhibits an intensity alternation of the individual lines which is not present in the case of T_d molecules studied previously; it could facilitate the experimental detection of the spectrum.     

Modified gravity in contemporary universe

Astronomical data in favor of cosmological acceleration and possible explanations of accelerated expansion of the universe are discussed. Main attention is paid to gravity modifications at small curvature which could induce accelerated cosmological expansion. It is shown that gravitating systems with mass density rising with time evolve to a singular state with infinite curvature scalar. The universe evolution during the radiation-dominated epoch is studied in the R ²-extended gravity theory. Particle production rate by the oscillating curvature and the back reaction of particle production on the evolution of R are calculated in one-loop approximation. Possible implications of the model for cosmological creation of non-thermal dark matter are discussed.