The standard model of elementary particle physics and the theory of general relativity can be extended by the introduction of a vacuum variable which is responsible for the near vanishing of the present cosmological constant (vacuum energy density). The explicit realization of this vacuum variable can be via a three-form gauge field, an aether-type velocity field, or any other field appropriate for the description of the equilibrium state corresponding to the Lorentz-invariant quantum vacuum. The extended theory has, without fine-tuning, a Minkowski-type solution of the field equations with spacetime-independent fields and provides, therefore, a possible solution of the main cosmological constant problem.
A modification of general relativity is presented in which Newton's constant and the cosmological constant become a conjugate pair of dynamical variables.
The possibility of extending the quantum mechanical superposition principle to free parameters such as the cosmological constant appearing in the Lagrangian of physical theories is examined. If the cosmological constant is subject to a quantum mechanical superposition principle, its observed value is a weighted average of its two natural values, one at the Planck scale and the other at zero. As zero and nonzero values of the cosmological constant leads to topologically distinct spacetimes, the amplitude for the cosmological constant to take a Planck scale value is weighted over a topological E…
One hope to solve the cosmological constant problem is to identify a symmetry principle, based on which the cosmological constant can be reduced either to zero, or to a tiny value. Here, we note that requiring that the vacuum state is Lorentz invariant significantly reduces the theoretical value of the vacuum energy density. Hence, this also reduces the discrepancy between the observed value of the cosmological constant and its theoretical expectation, down from 123 orders of magnitude to 56 orders of magnitude. We find that, at one loop level, massless particles do not yield any contribution …
Graviton fluctuations induce strong non-perturbative infrared renormalization effects for the cosmological constant. The functional renormalization flow drives a positive cosmological constant towards zero, solving the cosmological constant problem without the need to tune parameters. We propose a simple computation of the graviton contribution to the flow of the effective potential for scalar fields. Within variable gravity we find that the potential increases asymptotically at most quadratically with the scalar field. With effective Planck mass proportional to the scalar field, the solutions…
We use the ideas of entropic gravity to derive the FRW cosmological model and show that for late time evolution we have an effective cosmological constant. By using the first law of thermodynamics and the modified entropy area relationship derived from the supersymmetric Wheeler-DeWitt equation of the Schwarzschild black hole, we obtain modifications to the Friedmann equations that in the late time regime gives an effective positive cosmological constant. Therefore, this simple model can account for the dark energy component of the universe by providing an entropic origin to the cosmological c…
The one-loop effective action for non-minimal scalar modified gravity on de Sitter background with a constant scalar field is found. The corresponding induced cosmological constant is evaluated. It is shown that quantum effects in non-minimal modified gravity may induce an early-time de Sitter universe even in the situation when such solution does not occur on the classical level. Classical reconstruction of the theory is presented in such a way that the resulting theory has a cosmological solution unifying early-time inflation with late-time acceleration.
Varying physical constant cosmologies were claimed to solve standard cosmological problems such as the horizon, the flatness and the $Λ$-problem. In this paper, we suggest yet another possible application of these theories: solving the singularity problem. By specifying some examples we show that various cosmological singularities may be regularized provided the physical constants evolve in time in an appropriate way.
In this paper we suppose that the cosmological constant will change when the universe expends. For a general consideration, the cosmological constant is assumed to be a function of scale factor and Hubble constant. According to the ADM formulation, to the FRW metric, the extrinsic curvature $I$ equals $-6H^{2}$ and spatial curvature $R$ equals $6k/a^{2}$. Therefore we suppose cosmological constant is a function of extrinsic curvature and spatial curvature. We investigate the cosmological evolution of FRW universe in these models. At last we investigate two particular models which could fit the…
In a recent paper we discovered that a fermionic condensate is formed from gravitational interactions due to the covariant coupling of fermions in the presence of a torsion-fermion contact interaction. The condensate gap gives a negative contribution to the bare cosmological constant. In this letter, we show that the cosmological constant problem can be solved without fine tuning of the bare cosmological constant. We demonstrate how a universe with a large initial cosmological constant undergoes inflation, during which time the energy gap grows as the volume of the universe. Eventually the gap…
We describe a link between the cosmological constant problem and the problem of time in quantum gravity. This arises by examining the relationship between the cosmological constant and vacuum energy in light of non-perturbative formulations of quantum gravity.
It is known that Gauss-Bonnet terms in higher dimensional gravity can produce an effective cosmological constant. We add extra examples to this picture by presenting explicitly two branches of accelerating vacuum solutions to the Einstein-Gauss-Bonnet gravities with a bare cosmological constant in 5 and 6 dimensions. Both branches of solutions are of constant curvature and the effective cosmological constants are independent of the acceleration parameter. One branch (the "-" branch) of the solutions is well defined in the limit when the Gauss-Bonnet parameter approaches zero, in which case the…
We have recently presented a manifestly local and general coordinate invariant formulation of a nonlocal approach to the cosmological constant problem which has been proposed by Carroll and Remmen. In this article, based on our formulation, we investigate some quantum aspects of this approach to the cosmological constant problem. In particular, we explicitly evaluate quantum effects to the effective cosmological constant from matter fields at one-loop level, and show that the effective cosmological constant receives radiative corrections and is not stable against quantum corrections so that it…
We exhibit a mechanism which dynamically adjusts cosmological constant toward $0^+$. The adjustment is quantum-mechanical, discharging cosmological constant in random discrete steps. It renders de Sitter space unstable, and triggers its decay toward Minkowski. Since the instability dynamically stops at $Λ= 0$, the evolution favors the terminal Minkowski space without a need for anthropics. The mechanism works for any QFT coupled to gravity.
We present a simple model where the effective cosmological constant appears from chameleon scalar fields. For a Kachru-Kallosh-Linde-Trivedi (KKLT)-inspired form of the potential and a particular chameleon coupling to the local density, patches of approximately constant scalar field potential cluster around regions of matter with density above a certain value, generating the effect of a cosmological constant on large scales. This construction addresses both the cosmological constant problem (why $Λ$ is so small, yet nonzero) and the coincidence problem (why $Λ$ is comparable to the matter dens…
The static, cylindrically symmetric vacuum solutions with a cosmological constant in the framework of the Brans-Dicke theory are investigated. Some of these solutions admitting Lorentz boost invariance along the symmetry axis correspond to local, straight cosmic strings with a cosmological constant. Some physical properties of such solutions are studied. These strings apply attractive or repulsive forces on the test particles. A smooth matching is also performed with a recently introduced interior thick string solution with a cosmological constant.
Naive calculations in quantum field theory suggest that vacuum fluctuations should induce an enormous cosmological constant. What if these estimates are right? I argue that even a huge cosmological constant might be hidden in Planck scale fluctuations of geometry and topology---what Wheeler called `spacetime foam'---while remaining virtually invisible macroscopically.
It is known that there is a quantum mechanical tunneling process which, through nucleation of a membrane, induces a transition between two de Sitter spaces, lowering the cosmological constant. It is shown in this paper that a different, new, membrane nucleation process exists, which, in addition to lowering the cosmological constant, leaves a black hole behind. Once a black hole is present, the relaxation of the cosmological constant may proceed via an analog of the old process, which decreases the black hole horizon area, or via the new process, which increases it.
It is argued in a recent letter Phys. Rev. Lett. 123, 131302(2019) that the effect of a large cosmological constant can be naturally hidden in Planck scale curvature fluctuations. We point out that there are problems with the author's arguments. The hiding of the cosmological constant proposed in the letter by choosing a suitable lapse function is just an illusion maintained by external forces. In particular, it can not be achieved if the cosmological constant is positive. Fortunately, it works for a negative cosmological constant in a different way, and, interestingly, the sign of the cosmolo…
We compute the cosmological constant in a scale invariant scalar field theory. The gravitational action is also suitably modified to respect scale invariance. Due to scale invariance the theory does not admit a cosmological constant term. The scale invariance is broken by a recently introduced mechanism called cosmological symmetry breaking. This leads to a nonzero cosmological constant. We compute the one loop corrections to the cosmological constant and show that it is finite.
Considering the Barrett-Crane spin foam model for quantum gravity with (positive) cosmological constant, we show that speeds must be quantized and we investigate the physical implications of this effect such as the emergence of an effective deformed Poincare symmetry.
I consider a simple model where the graviton mass and the cosmological constant depend on a scalar field with appropriate couplings and I calculate the graviton propagator and the resulting effective potential for the scalar field in order to examine issues of stability and symmetry breaking.
A modified-gravity-type model of two hypothetical massless vector fields is presented. These vector fields are gravitationally coupled to standard matter and an effective cosmological constant. Considered in a cosmological context, the vector fields dynamically cancel an arbitrary cosmological constant, and flat Minkowski spacetime appears as the limit of attractor-type solutions of the field equations. Asymptotically, the field equations give rise to a standard Friedmann-Robertson-Walker universe and standard Newtonian gravitational dynamics of small systems.
It was recently suggested that the cosmological constant problem as viewed in a non-perturbative framework is intimately connected to the choice of time and a physical Hamiltonian. We develop this idea further by calculating the non-perturbative vacuum energy density as a function of the cosmological constant with multiple choices of time. We also include a spatial curvature of the universe and generalize this calculation beyond cosmology at a classical level. We show that vacuum energy density depends on the choice of time, and in almost all time gauges, is a non-linear function of the cosmol…
We complete the proof of Weinberg's no-go theorem on the cosmological constant problem in classical gravity when the theory has a (global) scale symmetry. Stimulated with this proof, we explore a solution to the cosmological constant problem by the help of renormalization group equations. We find that the manifestly scale invariant regularization method provides a physically plausible solution to the cosmological constant problem, in particular, to the issue of radiative instability of the cosmological constant.
It is shown that in the model [3,4] of quantum mechanics besides probability amplitudes, the Planck constant and the Fock space, the cosmological constant also appear in the natural way. The Poisson brackets are generalized for the case of kinetics.
The cosmological constant is inherently determined by the scale of breaking down supersymmetry in the mechanism of seesaw fluctuations of two vacuum-states.
In the light of the proposal of hep-th/0207195, we discuss in detail the issue of the cosmological constant, explaining how can string theory naturally predict the value which is experimentally observed, without low-energy supersymmetry.
In the Kaluza-Klein model with a cosmological constant and a flux, the external spacetime and its dimension of the created universe from a $S^s \times S^{n-s}$ seed instanton can be identified in quantum cosmology. One can also show that in the internal space the effective cosmological constant is most probably zero.
In the framework of a model of minimal of dilatonic gravity (MDG) with cosmological potential we consider: the relations of MDG with nonlinear gravity and string theory; natural cosmological units, defined by cosmological constant; the properties of cosmological factor, derived from solar system and Earth-surface gravitational experiments; universal anty-gravitational interactions, induced by positive cosmological constant and by Nordtved effect; a new formulation of cosmological constant problem using the ratio of introduced cosmological action and Planck constant $\sim 10 ^{122}$;qualitative…
The cosmological constant problem is studied in a two component cosmological model. The universe contains a cosmological constant of an arbitrary size and sign and an additional component with an inhomogeneous equation of state. It is shown that, in a proper parameter regime, the expansion of the universe with a large absolute value of the cosmological constant may asymptotically tend to de Sitter space corresponding to a small effective positive cosmological constant. It is argued that such a behavior can be regarded as a solution of the cosmological constant problem in this model. The mechan…
The observed small value of cosmological constant can be naturally related with the scale of breaking down supersymmetry in agreement with other evaluations in particle physics.
We show that in the framework of the classical general relativity the presence of a positive cosmological constant implies the existence of a minimal mass and of a minimal density in nature. These results rigorously follow from the generalized Buchdahl inequality in the presence of a cosmological constant.
Recent cosmological observations suggest the existence of a positive cosmological constant $Λ$ with the magnitude $Λ(G\hbar/c^3) \approx 10^{-123}$. This review discusses several aspects of the cosmological constant both from the cosmological (sections 1-6) and field theoretical (sections 7-11) perspectives. The first section introduces the key issues related to cosmological constant and provides a brief historical overview. This is followed by a summary of the kinematics and dynamics of the standard Friedmann model of the universe paying special attention to features involving the cosmologica…
The fluctuations of the vacuum energy are treated as a non-equilibrium process and a stochastic model for the cosmological constant is presented, which yields a natural explanation for the smallness or zero value of the constant in the present epoch and its large value in an era of inflation in the early universe.
We address issues on the origin of gravity and the cosmological constant problem based on a recent understanding about the correspondence between noncommutative field theory and gravity. We suggest that the cosmological constant problem can be resolved in a natural way if gravity emerges from a gauge theory in noncommutative spacetime. Especially, we elucidate why the emergent gravity implies that vacuum energy does not gravitate but only fluctuations around the vacuum generate gravity. That is, a flat spacetime emerges from uniform condensation of energy, previously identified with the cosmol…
We present a model that naturally tunes a large positive cosmological constant to a small cosmological constant. A slowly rolling scalar field decreases the cosmological constant to a small negative value, causing the universe to contract, thus reheating it. An expanding universe with a small positive cosmological constant can be obtained, respectively, by coupling this solution to any model of a cosmological bounce and coupling the scalar field to a sector that undergoes a technically natural phase transition at the meV scale. A robust prediction of this model is a rolling scalar field today …
Treating the metric as a classical background field, we show that the cosmological constant does not run with the renormalization scale -- contrary to some claims in the literature.
The cosmological constant problem and brane universes are reviewed briefly. We discuss how the cosmological constant problem manifests itself in various scenarios for brane universes. We review attempts - and their difficulties - that aim at a solution of the cosmological constant problem.
We review arguments that the cosmological constant (c.c.) should not be thought of as a local contribution to the energy density, but rather as an infrared boundary condition specifying particular models of quantum gravity.
Hawking proposed that the cosmological constant is probably zero in quantum cosmology. Duff claimed that Hawking's proof is invalidated. Using the right configuration for the wave function of the universe, we provide a complete proof.
We study a mechanism, inspired from the mechanism for generating the gauge hierarchy in Randall-Sundrum model, to investigate the cosmological constant problem. First we analyze the bulk cosmological constant and brane vacuum energies in RS model. We show that the five-dimensional bulk cosmological constant and the vacuum energies of the two branes all obtain their natural values. Finally we argue how we can generate a small four-dimensional effective cosmological constant on the branes through modifying the original RS model.
This is a review of the physics and cosmology of the cosmological constant. Focusing on recent developments, I present a pedagogical overview of cosmology in the presence of a cosmological constant, observational constraints on its magnitude, and the physics of a small (and potentially nonzero) vacuum energy.
In the quantum adelic field (string) theory models, vacuum energy -- cosmological constant vanish. The other (alternative ?) mechanism is given by supersymmetric theories. Some observations on prime numbers, zeta -- function and fine structure constant are also considered.
Spacetime geometry is treated as a fluctuating, stochastic quantum system allowing an effective quantum gravity solution to the cosmological constant problem. A Focker-Planck equation for the probability density of spacetime metric fluctuations is solved for an FRW universe and the most probable value for the metric scale factor R is for a very small cosmological constant.
We show that the theory of gravity constructed from the non-linear realisation of the semi-direct product of the Kac-Moody algebra A1+++ with its vector representation does not allow a cosmological constant. The existence of a cosmological constant in this theory is related to the breaking of the gravitational duality symmetry.
We advance the viewpoint that only relevant modes of the vacuum fluctuations, namely, with wavelengths conditioned by the size, homogeneity, geometry and topology of the Universe, do contribute into the cosmological constant. A formula is derived which relates the cosmological constant with the size of the Universe and the three fundamental constants: the velocity of light, Planck and Newton gravitational constants. Then the current value of the cosmological constant remarkably agrees with the value indicated by distant supernovae observations, i.e. is of the order of the critical density. Thu…
The quantum gravitational contribution to the renormalization group behavior of the electric charge in Einstein-Maxwell theory with a cosmological constant is considered. Quantum gravity is shown to lead to a contribution to the running charge not present when the cosmological constant vanishes. This re-opens the possibility, suggested by Robinson and Wilczek, of altering the scaling behaviour of gauge theories at high energies although our result differs. We show the possibility of an ultraviolet fixed point that is linked directly to the cosmological constant.
We re-examine claims that anthropic arguments provide an explanation for the observed smallness of the cosmological constant, and argue that correlations between the cosmological constant value and the existence of life can be demonstrated only under restrictive assumptions. Causal effects are more subtle to uncover.
In this talk we provide arguments on possible relation between the cosmological constant in our space and the non-commutativity parameter of the internal space of compactified string theory. The arguments are valid in the context of D3/D7 brane cosmological model of inflation/acceleration.
In this manuscript we study the cosmological constant of a $(p+1)$-dimensional world, which lives in the higher dimensional bulk space. We assume the extra dimensions are compact on tori. We consider two cases: positive and negative bulk cosmological constant. It is pointed out that the tiny cosmological constant of our world can be obtained by the dynamics of a scalar field and adjusting the parameters of the model. The cosmological constant of the dual world also will be discussed. We obtain the Dirac quantization of these cosmological constants.
After a brief outlook of the dynamic quantization method and application of the method to gravity the idea of natural solution of cosmological constant problem in inflating Universe is presented.
We discuss a Randall-Sundrum-type two D-braneworld model in which D-branes possess different values of the tensions from those of the charges, and derive an effective gravitational equation on the branes. As a consequence, the Einstein-Maxwell theory is realized together with the non-zero cosmological constant. Here an interesting point is that the effective gravitational constant is proportional to the cosmological constant. If the distance between two D-branes is appropriately tuned, the cosmological constant can have a consistent value with the current observations. From this result we see …
