Cosmological Constant Problem Research Articles

The Variation of G and Λ in Cosmology

The idea of varying constants of nature is very old, and has commanded a lot of attention since first mooted. The variation in the gravitational parameter G and cosmological parameter Λ is still an active area of research. Since the idea of a varying G was introduced by Dirac almost a century ago, there are even theories that have variable G such as the Brans–Dicke theory and the scale covariant theory. Both these theories also have a varying Λ in their full generalisations. A varying Λ was also introduced around the same time as that of varying G. It is interesting to note that a possible solution to the cosmological constant problem can be realised from a dynamic Λ. In this work, we focus on a varying Λ and G framework. In almost all studies in the simplest framework of variables Λ and G, it is found that one of them has to increase with time. However, observations and theoretical considerations indicate that both Λ and G should decrease with time. In this paper, we propose a solution to this problem, finding theories in which both Λ and G decrease with time.

The cosmological constant problem and the effective potential of a gravity-coupled scalar

We consider a quantum scalar field in a classical (Euclidean) De Sitter background, whose radius is fixed dynamically by Einstein’s equations. In the case of a free scalar, it has been shown by Becker and Reuter that if one regulates the quantum effective action by putting a cutoff N on the modes of the quantum field, the radius is driven dynamically to infinity when N tends to infinity. We show that this result holds also in the case of a self-interacting scalar, both in the symmetric and broken-symmetry phase. Furthermore, when the gravitational background is put on shell, the quantum corrections to the mass and quartic self-coupling are found to be finite.

Incorporating the cosmological constant in a modified uncertainty principle

This study explores the cosmological constant problem and modified uncertainty principle within a unified framework inspired by a void-dominated scenario for cosmology. In a recent paper [E. Yusofi, M. Khanpour, B. Khanpour, M. A. Ramzanpour and M. Mohsenzadeh, Mon. Not. R. Astron. Soc. 511, L82 (2022)], voids were modeled as spherical bubbles of similar average sizes, and the surface energy on the voids’ borders was calculated across various scales in a heuristic manner. We show that these result in a significant discrepancy of approximately [Formula: see text] between the cosmological constant values from the minimum to the maximum radii of bubbles. Furthermore, when considering the generalized form of the uncertainty principle with both minimum and maximum lengths, i.e. [Formula: see text], a similar order of discrepancy is observed between [Formula: see text] and [Formula: see text], indicating that [Formula: see text]. As a primary outcome of this finding, we offer a novel uncertainty principle that incorporates a nonzero cosmological constant.

A phenomenological approach to the dark energy models in the Finsler–Randers framework

This study extends two phenomenological models of dark energy within the framework of Finsler–Randers space–time, accommodating anisotropies. The models consider the cosmological constant Λ in two scenarios: one where Λ is proportional to the second time derivative of the scale factor ä, and another where it varies with the matter-energy density ρ. Earlier, such Λ-decaying cosmologies were proposed to address long-standing cosmological constant problems. However, following the discovery of late-time cosmic acceleration, the focus shifted to modeling dark energy. Since Λ is widely viewed as the most significant and suitable candidate for driving cosmic acceleration, it is worthwhile to revisit the phenomenological approach in this context. This work uses this approach to find solutions for the scale factor a(t) and other geometrical and physical parameters. Additionally, we analyze the evolution of density parameters Ωm, ΩΛ, and Ωκ, representing matter, dark energy, and curvature, from early to late times. The phenomenological approach is employed to solve the field equations, with model parameters constrained using recent observational data, yielding ranges consistent with observations. The solutions converge to the ΛCDM cosmology at early and late times. The added complexity introduced by Finsler–Randers geometry enhances accuracy compared to analogous solutions in Riemannian space–time.

The cosmological constant and the weak gravity conjecture

We examine the descent via membrane nucleation through a landscape of vacua where the cosmological constant is given by a combination of four-form fluxes. It has been shown that this descent can be slowed exponentially for very low curvature vacua close to Minkowski space in a wide class of models satisfying certain parametric conditions, providing a possible solution to the cosmological constant problem. We explore in detail whether or not those parametric conditions are compatible with the membrane weak gravity conjecture. Whilst it is true that there is often tension, we show that this is not always the case and present an explicit model where Minkowski space is absolutely stable and the weak gravity conjecture is satisfied. This corresponds to an extension of the Bousso-Polchinski model into a generalised DBI action for four-forms. We also clarify how the landscape should be populated in a consistent model.

Thermodynamic formulation of vacuum energy density in flat spacetime and potential implications for the cosmological constant

We propose a thermodynamical definition of the vacuum energy density ρvac, defined as 〈vac|Tμν|vac〉 = − ρvacgμν, in quantum field theory in flat Minkowski space in D spacetime dimensions, which can be computed in the limit of high temperature, namely in the limit β = 1/T → 0. It takes the form ρvac = const ∙ mD where m is a fundamental mass scale and “const” is a computable constant which can be positive or negative depending on interaction couplings. Due to modular invariance ρvac can also be computed in a different non-thermodynamic channel where one spatial dimension is compactifed on a circle of circumference β and we confirm this modularity for free massive theories for both bosons and fermions for D = 2, 3, 4. We list various properties of ρvac that are generally required, for instance ρvac = 0 for conformal field theories, and others, such as the constraint that ρvac has opposite signs for free bosons verses fermions of the same mass, which is related to constraints from supersymmetry. Using the Thermodynamic Bethe Ansatz we compute ρvac exactly for 2 classes of integrable QFT’s in 2D and interpreting some previously known results. We apply our definition of ρvac to Lattice QCD data with two light quarks (up and down) and one additional massive flavor (the strange quark), and find it is negative, ρvac ≈ − (200 MeV)4. Finally we make some remarks on the Cosmological Constant Problem since ρvac is central to any discussion of it.

Unimodular quadratic gravity and the cosmological constant

Unimodular gravity addresses the old cosmological constant (CC) problem, explaining why such constant is not at least as large as the largest particle mass scale, but classically it is indistinguishable from ordinary gravity. Conversely, quantum physics may give us a way to distinguish the two theories. Thus, here the unimodular constraint is imposed on a non-perturbative and background-independent quantum version of quadratic gravity, which was recently formulated. It is shown that unimodularity does lead to different predictions for some inflationary quantum observables. Unimodular gravity per se does not solve the new CC problem (why the CC has the observed value?) even in this realization. To address this issue a multiverse made by different eras in a single big bang is considered and the observed scale of dark energy is explained anthropically.

Theoretical and observational implications of Planck’s constant as a running fine structure constant

This paper explores how a reinterpretation of the generalized uncertainty principle as an effective variation of Planck’s constant provides a physical explanation for a number of fundamental quantities and couplings. In this context, a running fine structure constant is naturally emergent and the cosmological constant problem is solved, yielding a novel connection between gravitation and quantum field theories. The model could potentially clarify the recent experimental observations by the DESI Collaboration that could imply a fading of dark energy over time. When applied to quantum systems and their characteristic length scales, a simple geometric relationship between energy and entropy is disclosed. Lastly, a mass–radius relation for both quantum and classical systems reveals a phase transition-like behavior similar to thermodynamical systems, which we speculate to be a consequence of topological defects in the universe.

Cosmic clues: DESI, dark energy, and the cosmological constant problem

Several attempts to solve the cosmological constant problem, which concerns the value of the cosmological constant being extremely smaller than the Standard Model mass scales, have introduced a scalar field with a very flat potential that can be approximated as linear around any given position. The scalar field scans the cosmological constant in such a way that the current small value is explained. Recently, Dark Energy Spectroscopic Instrument (DESI) reported the results of the first year. Combining the data with CMB, Pantheon, Union3, and/or DES-SN5YR, there is a preference or anomaly, indicating that the dark energy in the current Universe slightly deviates from that in the ΛCDM model and varies over time. In this paper, I show that the simple linear potential of a scalar field that may explain the small cosmological constant, can explain the DESI anomaly. The conclusions do not change by including or not including a thermal friction effect. In particular, the model proposed by the present author in [1], which relaxes the cosmological constant by the condition that inflation ends, predicts a time-dependence of the dark energy close to the one favored by the data.

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.

N -cutoff regularization for fields on hyperbolic space

We apply a novel background independent regularization scheme, the N-cutoffs, to self-consistently quantize scalar and metric fluctuations on the maximally symmetric but noncompact hyperbolic space. For quantum matter fields on a classical background or full quantum Einstein gravity (regarded here as an effective field theory) treated in the background field formalism, the N-cutoff is an ultraviolet regularization of the fields’ mode content that is independent of the background hyperbolic space metric. For each N>0, the regularized system backreacts on the geometry to dynamically determine the self-consistent background metric. The limit in which the regularization is removed then automatically yields the “physically correct” spacetime on which the resulting quantum field theory lives. When self-consistently quantized with the N-cutoff, we find that without any fine-tuning of parameters, the vacuum fluctuations of scalar and (linearized) graviton fields do not lead to the usual cosmological constant problem of a curvature singularity. Instead, the presence of increasingly many field modes tends to reduce the negative curvature of hyperbolic space, leading to vanishing values in the limit of removing the cutoff. Published by the American Physical Society 2024

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.