Unimodular quantum gravity and the cosmological constant

It is shown that the one-loop effective action of unimodular gravity is the same as that of ordinary gravity, restricted to unimodular metrics. The only difference is in the treatment of the global scale degree of freedom and of the cosmological term. A constant vacuum energy does not gravitate, addressing one aspect of the cosmological constant problem.     

New solution of the cosmological constant problems

We extend the usual gravitational action principle by promoting the bare cosmological constant (CC) to a field which can take many possible values. Variation gives a new integral constraint equation for the classical value of the effective CC that dominates the wave function of the Universe. The expected value of the effective CC, is calculated from measurable quantities to be O(t(U)(-2)) as observed, where t(U) is the present age of the Universe in Planck units. This also leads to a falsifiable prediction for the observed spatial curvature parameter of Ω(k0) = -0.0055. Our proposal requires no fine-tunings or extra dark-energy fields but suggests a new view of time evolution.     

TCP, quantum gravity,the cosmological constant and all that...

We study cosmology from the point of view of quantum gravity. Some light is thrown on the nature of time, and it is suggested that the cosmological arrow of time is generated by a spontaneous breakdown of TCP. Conventional cosmological models in which quantum fields interact with a time-dependent gravitational field are shown to describe an approximation to the quantum gravitational wave function which is valid in the long-wavelength limit. Two problems with initial conditions are resolved in models in which a negative bare cosmological constant is cancelled by the classical excitation of a Bose field η with a very flat potential. These models can also give a natural explanation for the observed value of the cosmological constant.     

Taming the cosmological constant in 2D causal quantum gravity with topology change

As shown in previous work, there is a well-defined nonperturbative gravitational path integral including an explicit sum over topologies in the setting of causal dynamical triangulations in two dimensions. In this paper we derive a complete analytical solution of the quantum continuum dynamics of this model, obtained uniquely by means of a double-scaling limit. We show that the presence of infinitesimal wormholes leads to a decrease in the effective cosmological constant, reminiscent of the suppression mechanism considered by Coleman and others in the four-dimensional Euclidean path integral. Remarkably, in the continuum limit we obtain a finite spacetime density of microscopic wormholes without assuming fundamental discreteness. This shows that one can in principle make sense of a gravitational path integral which includes a sum over topologies, provided suitable causality restrictions are imposed on the path integral histories.     

Positive cosmological constant,non-local gravity and horizon entropy

We discuss a class of (local and non-local) theories of gravity that share same properties: (i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; (ii) the on-shell action of such a theory vanishes and (iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positive cosmological constant does not have a non-trivial entropy. The main focus is made on a recently proposed non-local model. This model has two phases: with a positive cosmological constant Λ>0$\Lambda >0$ and with zero Λ. The effective gravitational coupling differs essentially in these two phases. Generalizing the previous result of Barvinsky we show that the non-local theory in question is free of ghosts on the background of any Einstein spacetime and that it propagates a standard spin-2 particle. Contrary to the phase with a positive Λ, where the entropy vanishes for any type of horizon, in an Einstein spacetime with zero cosmological constant the horizons have the ordinary entropy proportional to the area. We conclude that, somewhat surprisingly, the presence of any, even extremely tiny, positive cosmological constant should be important for the proper resolution of the entropy problem and, possibly, the information puzzle.     

Quantizing gravity with a cosmological constant

We argue that the quantization of gravity with a cosmological constant, Λ, is both necessary and feasible (in the sense that the evaluation of the functional integral is no more difficult than when Λ= 0). We illustrate this point by evaluating the one-loop counterterms and anomalous scaling behavior for pure gravity with a Λ term and for matter fieldsin an external gravitational field. Previous attempts at these calculations are found to be in error. The new results have implications for Hawking's “spacetime foam”.     

Brane world solution to the cosmological constant problem

We consider a model with two parallel (positive tension) 3-branes separated by a distance L in five-dimensional spacetime. If the interbrane space is anti--de Sitter, or is not precisely anti--de Sitter but contains no event horizons, the effective four-dimensional cosmological constant seen by observers on one of the branes (chosen to be the visible brane) becomes exponentially small as L grows large.     

Evolution of the cosmological constant in effective gravity

In contrast to the phenomenon of nullification of the cosmological constant in equilibrium vacuum, which is the general property of any quantum vacuum, there are many options in modifying the Einstein equation to allow the cosmological constant to evolve in a nonequilibrium vacuum. An attempt is made to extend the Einstein equation in the direction suggested by the condensed matter analogy of the quantum vacuum. Different scenarios are found depending on the behavior of and the relation between the relaxation parameters involved, some of these scenarios having been discussed in the literature. One of them reproduces the scenario in which the effective cosmological constant emerges as a constant of integration. The second one describes the situation when, after the cosmological phase transition, the cosmological constant drops from zero to a negative value; this scenario describes the relaxation from this big negative value back to zero and then to a small positive value. In the third example, the relaxation time is not a constant but depends on matter; this scenario demonstrates that vacuum energy (or its fraction) can play the role of cold dark matter.     

On the Casimir energy for a massive quantum scalar field and the cosmological constant

We present a rigorous, regularization-independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass μ≠0 which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field in which the expectation value of the renormalized energy–momentum tensor is, for any fixed time, independent of the space coordinate and of the perfect fluid form g_μ,νρ with ρ>0, thus providing a concrete quantum field theoretic model of the cosmological constant. This ρ represents the energy density associated to a state consisting of the vacuum and a certain number of excitations of zero momentum, i.e., the constituents correspond to lowest energy and pressure p0.     

Stability of gravity with a cosmological constant

The stability properties of Einstein theory with a cosmological constant Λ are investigated. For Λ > 0, stability is established for small fluctuations, about the de Sitter background, occurring inside the event horizon and semiclassical stability is analyzed. For Λ < 0, stability is demonstrated for all asymptotically anti-de Sitter metrics. The analysis is based on the general construction of conserved flux-integral expressions associated with the symmetries of a chosen background. The effects of an event horizon, which lead to Hawking radiation, are expressedfor general field hamiltonians. Stability for Λ < 0 is proved, using supergravity techniques, in terms of the graded anti-de Sitter algebra with spinorial charges also expressed as flux integrals.     

Screening of cosmological constant in non-local gravity

We discuss a possible mechanism to screen a cosmological constant in non-local gravity. We find that in a simple model of non-local gravity with the Lagrangian of the form, R+f(^□−1R)−2Λ$R+f({\square }^{-1}R)-2\Lambda$ where f(X)$f(X)$ is a quadratic function of X, there is a flat spacetime solution despite the presence of the cosmological constant Λ. Unfortunately, however, we also find that this solution contains a ghost in general. Then we discuss the condition to avoid a ghost and find that one can avoid it only for a finite range of ‘time’. Nevertheless our result suggests the possibility of solving the cosmological constant problem in the context of non-local gravity.     

Holographic cosmological constant and dark energy

A general holographic relation between UV and IR cutoff of an effective field theory is proposed. Taking the IR cutoff relevant to the dark energy as the Hubble scale, we find that the cosmological constant is highly suppressed by a numerical factor and the fine tuning problem seems alleviative. We also use different IR cutoffs to study the case in which the universe is composed of matter and dark energy.     

Vacuum energy,cosmological constant and Standard Model physics

The conditions for the cancellation of one loop contributions to vacuum energy (both U.V. divergent and finite) coming from the Standard Model (SM) fields are examined. It is proven that this is not possible unless one introduces besides several bosons, at least one massive fermion having mass within specific ranges. On examining one of the simplest SM extensions satisfying the constraints one finds that the mass range of the lightest massive boson is compatible with the present Higgs mass bounds. We briefly address the possible treatment of the presence of interactions. The article is published in the original.     

On the induced cosmological term in quantum gravity

Tadpole diagrams where zero-momentum gravitons couple to massive matter loops lead to divergences which are not a consequence of infinite momentum integrals, but of the masslessness of the gravitons. It is shown that there exists no definition of these diagrams consistent with the Ward identities. They can be eliminated by an appropriate gauge choice, but then the BRS symmetry is spontaneously broken. Also in the scalar-tensor, conformally invariant formulation of quantum gravity, the tadpole problem does survive. The tadpole diagrams can, however, be cancelled by a cosmological counter-term. In that case, the Ward identities are satisfied.     

A possible solution to the main cosmological problems

A model of the universe with an additional term Λ(x)g_μν in the energy-momentum tensor is motivated and presented. The model is completely determined by the assumption that the energy density ofthe universe equals its critical value. It has k = 1 geometry, is free of the initial singularity and does not possess a horizon, entropy or monopole problem.     

Higher-dimensional Florides-like solution with cosmological constant

N-dimensional generalization of Florides' interior solution with cosmological constant and Kotller's exterior solution are presented here. The case of uniform density configuration is also considered. One can get back the solutions in four-dimensional space-time by puttingN=4 in the solutions presented here.     

Loop quantum modified gravity and its cosmological application

A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously constructed. Both the Hamiltonian and master constraint operators are well defined and proposed to represent quantum dynamics of scalar-tensor theories. As an application to models, we set up the basic structure of loop quantum Brans-Dicke cosmology. The effective dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology.     

Instabilities in thermal gravity with a cosmological constant

It is shown that in quantum gravity at finite temperature, the effective potential evaluated in the tadpole approximation can have a local minimum below a certain critical temperature. However, when the leading higher order thermal loop corrections are included, one finds that no static solution exists at high temperature.