Cosmological Constant Problem Research Articles

The dynamics of vacuum, gravity and matter: Implications on the fundamental constants

The possibility that the vacuum energy density (VED) [Formula: see text] could be time dependent in the expanding Universe is intuitively more reasonable than just a rigid cosmological constant for the entire cosmic history. The dynamics of [Formula: see text] as a function of the Hubble rate, [Formula: see text], most likely contributes to alleviate cosmological problems and tensions, having also implications on the so-called fundamental ‘constants’ of Nature, which should be slowly drifting with the cosmic expansion owing to the fluctuations of the quantum vacuum. This includes the gravitational ‘constant’ G, but also the gauge and Yukawa couplings as well as the particle masses themselves (both of dark matter and baryonic matter). The subtle exchange of energy involved is the basis for the “micro and macro connection”. Herein, I discuss not only this connection as a possibility but also show that it is in fact a generic prediction of QFT in cosmological spacetime which is fully compatible with general covariance. This fact has not been pointed out until recently when an appropriate renormalization framework for the VED has been found which is free from the usual conundrums associated with the cosmological constant problem.

Generalized K-essence inflation in Jordan and Einstein frames

We here explore a generalized K-essence model which exhibits characteristics akin to ordinary matter. The inflationary framework proposed aims to unify old with chaotic inflation into a single scheme and it considers minimally and non-minimally coupled scenarios, adopting three classes of potentials, in both Jordan and Einstein frames. We show that, to obtain a suitable amount of particles obtained from vacuum energy conversion during inflation, mitigating the classical cosmological constant problem, large-field inflation and, particularly, the Starobinsky-like class of solutions appears the most suitable one.

The cosmological constant problem and the extra dimensions of [formula omitted]=2 [formula omitted]=5 supergravity

We propose an interpretation for the cosmological constant problem based on modeling the universe as a 3-brane embedded in the bulk of 5-dimensional supergravity with hypermultiplets. When solving the modified Friedmann equations the complex structure moduli of the Calabi-Yau manifold cancel the large value of the vacuum energy density on the brane, wherein this value transfers to an Anti-de Sitter fifth dimensional bulk compactified on a scale (∼10−26m). An effective dark energy density is produced on the brane which equals the observed value responsible for the late-time acceleration of the universe. The bulk undergoes a decelerated contraction while we show that cosmic expansion of the brane-universe consists with the recent observed data of the ΛCDM model. On the other hand, through this model, the hierarchy between the electroweak scale (MEW=100GeV) and the Planck scale (Mpl∼1018GeV) is interpreted by compactifying the 6-extra dimensions of D=5 supergravity on a sub-millimeters scale, where the fundamental scale of gravity within these extra dimensions is MEW.

On the Apparent Discretization of Spacetime and Its Connection with the Cosmological Constant

The emergence of a minimal observable length of order of the Planck scale is a prediction of many quantum theories of gravity. However, the question arises as to whether this is a real fundamental length affecting nature in all of its facets, including spacetime. In this work, we show that the quantum measurement process implies the existence of a minimal measurable length and consequently the apparent discretization of spacetime. The obtained result is used to infer the value of zero-point energy in the universe, which is found to be in good agreement with the observed cosmological constant. This potentially offers some hints towards the resolution of the cosmological constant problem.

Spontaneous collapse models lead to the emergence of classicality of the Universe

Assuming that Quantum Mechanics is universal and that it can be applied over all scales, then the Universe is allowed to be in a quantum superposition of states, where each of them can correspond to a different space-time geometry. How can one then describe the emergence of the classical, well-defined geometry that we observe? Considering that the decoherence-driven quantum-to-classical transition relies on external physical entities, this process cannot account for the emergence of the classical behaviour of the Universe. Here, we show how models of spontaneous collapse of the wavefunction can offer a viable mechanism for explaining such an emergence. We apply it to a simple General Relativity dynamical model for gravity and a perfect fluid. We show that, by starting from a general quantum superposition of different geometries, the collapse dynamics leads to a single geometry, thus providing a possible mechanism for the quantum-to-classical transition of the Universe. Similarly, when applying our dynamics to the physically-equivalent Parametrised Unimodular gravity model, we obtain a collapse on the basis of the cosmological constant, where eventually one precise value is selected, thus providing also a viable explanation for the cosmological constant problem. Our formalism can be easily applied to other quantum cosmological models where we can choose a well-defined clock variable.

Solving Particle–Antiparticle and Cosmological Constant Problems

We solve the particle-antiparticle and cosmological constant problems proceeding from quantum theory, which postulates that: various states of the system under consideration are elements of a Hilbert space H with a positive definite metric; each physical quantity is defined by a self-adjoint operator in H; symmetry at the quantum level is defined by a representation of a real Lie algebra A in H such that the representation operator of any basis element of A is self-adjoint. These conditions guarantee the probabilistic interpretation of quantum theory. We explain that in the approaches to solving these problems that are described in the literature, not all of these conditions have been met. We argue that fundamental objects in particle theory are not elementary particles and antiparticles but objects described by irreducible representations (IRs) of the de Sitter (dS) algebra. One might ask why, then, experimental data give the impression that particles and antiparticles are fundamental and there are conserved additive quantum numbers (electric charge, baryon quantum number and others). The reason is that, at the present stage of the universe, the contraction parameter R from the dS to the Poincare algebra is very large and, in the formal limit R→∞, one IR of the dS algebra splits into two IRs of the Poincare algebra corresponding to a particle and its antiparticle with the same masses. The problem of why the quantities (c,ℏ,R) are as are does not arise because they are contraction parameters for transitions from more general Lie algebras to less general ones. Then the baryon asymmetry of the universe problem does not arise. At the present stage of the universe, the phenomenon of cosmological acceleration (PCA) is described without uncertainties as an inevitable kinematical consequence of quantum theory in semiclassical approximation. In particular, it is not necessary to involve dark energy the physical meaning of which is a mystery. In our approach, background space and its geometry are not used and R has nothing to do with the radius of dS space. In semiclassical approximation, the results for the PCA are the same as in General Relativity if Λ=3/R2, i.e., Λ>0 and there is no freedom for choosing the value of Λ.

Foundations of time-symmetric physics. 2. Quantum field theory

Time symmetric theory (TST), described in the first article and based on the equivalence principle of particle physics, is applied to quantum fields and time-symmetric quantum field theory is formulated. This principle is based on the Zisman-Stückelberg-Feynman interpretation, where antiparticles are described as negative energy particles moving backward in time, and generalizes it to the rest frames of such particles also moving backward in time. In TST, relativistic fields are described by complex field operators, and observables are automatically normally ordered. For this reason, at time-symmetric quantization (TSQ) of fields, the vacuum energy and charge disappear and there is no cosmological constant problem. In TST, the probabilities of states are positive, and the probability currents can have two signs depending on the direction of evolution along the time axis. The operator of interaction current is defined as the product of the probability current and the matrix of interaction constants. Applications of TST to the Standard Model fields and graviton field are considered. In TSQ correctly describes the observable effects, since in terms of ordinary time it leads to a standard diagram technique, transforming mathematical recipes of the latter into logical consequences of physical principles.

A mass scale law connecting cosmophysics to microphysics

We introduce different mass scales corresponding to the Universe, fermion stars, mini boson stars, Planck black holes, the electron, the neutrino, and the cosmon. These mass scales are obtained by combining the maximum mass of fermion stars, boson stars and soliton stars set by quantum mechanics and general relativity with the Eddington relation connecting the mass me of the electron to the cosmological constant Λ. In this manner, we can express the mass of these objects in terms of the fundamental constants of physics G, c, ħ and Λ. By normalizing the mass Ma of these objects by the Planck mass MP, we find that Ma/MP∼χa/6, where χ∼ρP/ρΛ∼10120 is the “largest large number” in Nature (the ratio of the Planck density on the Einstein cosmological density) and a=3,2,1,0,−1,−2,−3 for the Universe, fermion stars, mini boson stars, Planck black holes, the electron, the neutrino, and the cosmon respectively. This formula suggests an interesting symmetrical mass scale law connecting cosmophysics (Universe, fermion stars, mini boson stars) to microphysics (electron, neutrino, cosmon). A generalization of this law including the earth mass and another neutrino mass scale is proposed. We highlight an accurate form of Eddington relation me≃α(Λħ4/G2)1/6 or Λ≃G2me6/α6ħ4=α−6(me/MP)6lP−2, where α=e2/ħc≃1/137 is the fine structure constant, and provide different heuristic derivations of this relation. We consider another relation Λ=Gc(mΛ∗)4/ħ3=(mΛ∗/MP)4lP−2, where mΛ∗=(Λħ3/Gc)1/4 is the neutrino mass. We relate these relations to the two expressions of the vacuum energy density given by Zeldovich in 1968. We suggest that the dark energy particle (cosmon) of mass mΛ=ħΛ/c could be a quantum of mass and entropy so that Λ=mΛ2c2/ħ2=(mΛ/MP)2lP−2. We relate the large number 10120 to the total number of degrees of freedom (or number of cosmons) in the universe. Finally, we give hints how to possibly solve the cosmological constant problem, the cosmic coincidence problem, and the large number coincidence problem.

Clifford algebra Cl(0,6) approach to beyond the standard model and naturalness problems

Is there more to Dirac’s gamma matrices than meets the eye? It turns out that gamma zero can be factorized into a product of three operators. This revelation facilitates the expansion of Dirac’s space-time algebra to Clifford algebra [Formula: see text]. The resultant rich geometric structure can be leveraged to establish a combined framework of the standard model and gravity, wherein a gravi-weak interaction between the vierbein field and the extended weak gauge field is allowed. Inspired by the composite Higgs model, we examine the vierbein field as an effective description of the fermion–antifermion condensation. The compositeness of space-time manifests itself at an energy scale which is different from the Planck scale. We propose that all the regular classical Lagrangian terms are of quantum condensation origin, thus possibly addressing the cosmological constant problem provided that we exercise extreme caution in the renormalization procedure that entails multiplications of divergent integrals. The Clifford algebra approach also permits a weaker form of charge conjugation without particle–antiparticle interchange, which leads to a Majorana-type mass that conserves lepton number. Additionally, in the context of spontaneous breaking of two global [Formula: see text] symmetries, we explore a three-Higgs-doublet model which could explain the fermion mass hierarchies.

Informational Nature of Dark Matter and Dark Energy and the Cosmological Constant

In this article, realistic quantitative estimation of dark matter and dark energy considered as informational phenomena have been computed, thereby explaining certain anomalies and effects within the universe. Moreover, by the same conceptual approach, the cosmological constant problem has been reduced by almost 120 orders of magnitude in the prediction of the vacuum energy from a quantum point of view. We argue that dark matter is an informational field with finite and quantifiable negative mass, distinct from the conventional fields of matter of quantum field theory and associated with the number of bits of information in the observable universe, while dark energy is negative energy, calculated as the energy associated with dark matter. Since dark energy is vacuum energy, it emerges from dark matter as a collective potential of all particles with their individual zero-point energy via Landauer's principle.

Revising the cosmological constant problem through a fluid different from the quintessence

Revising the cosmological constant problem through a fluid different from the quintessence

Vacuum Energy, the Casimir Effect, and Newton’s Non-Constant

The idea of quantum mechanical vacuum energy contributing to the cosmological vacuum energy density is not new. However, despite the persisting cosmological constant problem, few investigations have focused on this subject. We explore the possibility that the quantum vacuum energy density contributes to the (local) gravitational energy density in the framework of a scale-dependent cosmological constant Λ and Newton’s constant G. This hypothesis has several important consequences, ranging from quantum scale-dependence to the hypothetical prospect of novel experimental insight concerning the quantum origin of cosmological energy density.

The cosmological constant is probably still zero

We consider a wide class of four-dimensional effective field theories in which gravity is coupled to multiple four-forms and their dual scalar fields, with membrane sources charged under the corresponding three-form potentials. Four-form flux, quantised in units of the membrane charges, generically generates a landscape of vacua with a range of values for the cosmological constant that is scanned through membrane nucleation. We list various ways in which the landscape can be made sufficiently dense to be compatible with observations of the current vacuum without running into the empty universe problem. Further, we establish the general criteria required to ensure the absolute stability of the Minkowski vacuum under membrane nucleation and the longevity of those vacua that are parametrically close by. This selects the current vacuum on probabilistic grounds and can even be applied in the classic model of Bousso and Polchinski, albeit with some mild violation of the membrane weak gravity conjecture. We present other models where the membrane weak gravity conjecture is not violated but where the same probabilistic methods can be used to tackle the cosmological constant problem.

Perils of towers in the swamp: dark dimensions and the robustness of EFTs

Recently there has been an interesting revival of the idea to use large extra dimensions to address the dark energy problem, exploiting the (true) observation that towers of states with masses split, by MN2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {M}_N^2 $$\\end{document} = f(N)m2, with f an unbounded function of the integer N, sometimes contribute to the vacuum energy only an amount of order mD in D dimensions. It has been argued that this fact is a consequence of swampland conjectures and may require a departure from Effective Field Theory (EFT) reasoning. We test this claim with calculations for Casimir energies in extra dimensions. We show why the domain of validity for EFTs ensures that the tower spacing scale m is always an upper bound on the UV scale for the lower-energy effective theory; use of an EFT with a cutoff part way up a tower is not a controlled approximation. We highlight the role played by the sometimes-suppressed contributions from towers in extra-dimensional approaches to the cosmological constant problem, old and new, and point out difficulties encountered in exploiting it. We compare recent swampland realizations of these arguments with earlier approaches using standard EFT examples, discussing successes and limitations of both.

Unraveling the mystery of the cosmological constant: Does spacetime uncertainty hold the key?(a)

In addressing the cosmological constant problem, we propose that the discrepancy between the theoretical and observed values can be ascribed to the inherent uncertainty in the spacetime metric. Mach's principle, which posits that mass shapes spacetime, intersects with quantum mechanics’ description of a particle as a quantum cloud, rendering the precise location of a particle's mass unknowable. Consequently, understanding spacetime structure at the quantum level becomes elusive. This connection between quantum and spacetime uncertainty could hold the key to resolving the cosmological constant problem. Intriguingly, the length scale of spacetime uncertainty, aligns with the macroscopic quantum weirdness observed in recent experiments. The spacetime uncertainty can be quantified by the scale factor in the Friedmann-Lemaître-Robertson-Walker (FLRW) universe.

Constraints on f (Q) logarithmic model using gravitational wave standard sirens

ABSTRACT In this paper, we revise the constraints on the f (Q) = Q/(8πG) – αln (Q/Q0), symmetric teleparallel model using local measurements and gravitational waves mock standard sirens. Using observational local SNIa and BAO data and energy conditions, the logarithmic f (Q) model is capable of explaining the cosmic late-time acceleration by geometrical means. This result suggests that the logarithmic symmetric teleparallel model could be a candidate to solve the cosmological constant problem. In the case of the simulated standard siren data, by using the performance of the future Einstein Telescope (ET) and Laser Interferometer Space Antenna (LISA) detectors, we expect to be able to measure the current Hubble constant H0, and the matter content Ωm, with a precision better than 1 and 6 per cent, respectively. Furthermore, we explore the predicted f (Q) logarithmic model deviation from the standard General Relativity (GR) using ET and LISA mock standard sirens. The ratio $\mathrm{ \mathit{ d}}_\mathrm{ L}^{\text{gw}}(z)/\mathrm{ \mathit{ d}}_\mathrm{ L}^{\text{em}}(z)$, which quantifies the deviation from GR gives us a significant deviation higher than 13 per cent at z = 1, and it continues growing to reach a deviation higher than 18 per cent in its median value. Future standard siren data will be able to quantify the strength of the deviation from GR, and hence whether a cosmology like the one implied by this f (Q) model is feasible.

On the inevitable lightness of vacuum

In this essay, we present a new understanding of the cosmological constant problem, built upon the realization that the vacuum energy density can be expressed in terms of a phase space volume. We introduce a UV-IR regularization which implies a relationship between the vacuum energy and entropy. Combining this insight with the holographic bound on entropy then yields a bound on the cosmological constant consistent with observations. It follows that the universe is large, and the cosmological constant is naturally small, because the universe is filled with a large number of degrees of freedom.

Cosmology in Minkowski space

Theoretical and observational challenges to standard cosmology such as the cosmological constant problem and tensions between cosmological model parameters inferred from different observations motivate the development and search of new physics. A less radical approach to venturing beyond the standard model is the simple mathematical reformulation of our theoretical frameworks underlying it. While leaving physical measurements unaffected, this can offer a reinterpretation and even solutions of these problems. In this spirit, metric transformations are performed here that cast our Universe into different geometries. Of particular interest thereby is the formulation of cosmology in Minkowski space. Rather than an expansion of space, spatial curvature, and small-scale inhomogeneities and anisotropies, this frame exhibits a variation of mass, length and time scales across spacetime. Alternatively, this may be interpreted as an evolution of fundamental constants. As applications of this reframed cosmological picture, the naturalness of the cosmological constant is reinspected and promising candidates of geometric origin are explored for dark matter, dark energy, inflation and baryogenesis. An immediate observation thereby is the apparent absence of the cosmological constant problem in the Minkowski frame. The formalism is also applied to identify new observable signatures of conformal inhomogeneities, which have been proposed as simultaneous solution of the observational tensions in the Hubble constant, the amplitude of matter fluctuations, and the gravitational lensing amplitude of cosmic microwave background anisotropies. These are found to enhance redshifts to distant galaxy clusters and introduce a mass bias with cluster masses inferred from gravitational lensing exceeding those inferred kinematically or dynamically.

On de Sitter spacetime and string theory

We review various aspects of de Sitter spacetime in string theory: its status as an Effective Field Theory spacetime solution, its relation to the vacuum energy problem in string theory, its (global) holographic definition in terms of two entangled and noncanonical conformal field theories as well as a realization of a realistic de Sitter universe endowed with the observed visible matter and the necessary dark sector in order to reproduce the realistic cosmological structure. In particular, based on the new insight regarding the cosmological constant problem in string theory, we argue that in a doubled, [Formula: see text]-duality-symmetric, phase-space-like and noncommutative generalized-geometric formulation, string theory can naturally lead to a small and positive cosmological constant that is radiatively stable and technically natural. Such a formulation is fundamentally based on a quantum spacetime, but in an effective spacetime description of this general formulation of string theory, the curvature of the dual spacetime is the cosmological constant of the observed spacetime, while the size of the dual spacetime is the gravitational constant of the same observed spacetime. Also, the three scales associated with intrinsic noncommutativity of string theory, the cosmological constant scale, the Planck scale as well as the Higgs scale, can be arranged to satisfy various seesaw-like formulae. Along the way, we show that these new features of string theory can be implemented in a particular deformation of cosmic-string-like models.

Emergent Diffeomorphism Invariance in Toy Models

AbstractConceptual difficulties in semiclassical and quantum gravity arise from diffeomorphism invariance of classical general relativity. With a motivation to shed some light on these difficulties, a class of toy models for which one‐dimensional diffeomorphism invariance, namely time‐reparametrization invariance, emerges at the classical level from energy conservation are studied. An attempt to quantize the models while taking the invariance seriously leads to toy versions of the problem of time in quantum gravity, of the cosmological constant problem, and of the black hole firewall problem. Nevertheless, all these problems are easily resolved by taking into account that the invariance emerges only at the classical level, while the fundamental theory that needs to be quantized is not diffeomorphism invariant.