Mysterious dark energy causes the universe to expand at an accelerated rate which, in the standard model of cosmology, is described by a nonzero cosmological constant having experimental value of Ω_Λ =0.686±0.02. Einstein’s theory of gravity, derived from the postulate that spacetime geometry is gravitational field, does not predict Ω_Λ.

Assumption that universe has a fixed Euclidean background geometry and gravity is a vector field in the four-dimensional Euclidean space, yields an alternative vector theory of gravity proposed in 2017 [1]. Vector gravity predicts no spacetime singularities such as black holes and, despite being fundamentally different from general relativity, passes all gravitational tests, including gravitational wave detection by LIGO and Virgo [1]. In contrast to general relativity, vector gravity explains dark energy as the energy of gravitational field induced by the universe expansion (Fig. 1a). In vector gravity, the energy density of the induced gravitational field is negative, which produces apparent acceleration of the universe expansion. With no free parameters, vector gravity predicts the value of Ω_Λ =2/3, in agreement with observations. In addition, vector gravity predicts vector polarization of gravitational waves, which is supported by LIGO/Virgo gravitational wave detection [2].

 Recent paper [3] studies elementary particles in the framework of vector gravity and shows that charged elementary particles are nonsingular bound states of fundamental fields held together by gravity (Fig. 1b). For example, electron is the lowest-energy bound state of electromagnetic, weak and gravitational fields. Energy of the bound-state solutions yields particle masses (e.g., electron and muon) in perfect agreement with experiment without free parameters [3]. The striking agreement with experiment indicates that vector gravity gives correct microscopic description of elementary particles and that particle masses are not generated by the Higgs mechanism. Instead, particle mass is simply the total energy of the fields forming the bound state.

 Vector gravity yields small value of particle’s mass on the Planck scale, because in vector gravity, the spinning gravitational field can have negative energy density, which screens the large positive contribution to the mass from the electromagnetic field.  Thus, dark energy in the universe and lightness of elementary particles have the same physical origin. In both cases, the negative energy of gravitational field causes the effect.

 Vector gravity also predicts existence of nonsingular bound state formed solely from the gravitational field. The corresponding particle does not carry electroweak or color charges and couples only to the mass through gravity. Thus, such a particle very weakly interacts with ordinary matter, and is a natural candidate for the dark matter in the universe.

Figure 1: (a) Universe expansion generates matter current directed away from an observer O. Such current induces longitudinal gravitational field which has negative energy density and produces apparent acceleration of the universe expansion. (b) Structure of charged leptons from vector gravity perspective. The particle center contains a quantum core of Planck size and Planck mass, which is the lowest energy bound state of electromagnetic, weak (Z), and gravitational (G) fields. At distance greater than Planck length the core behaves as a point electroweak charge. In vector gravity, similarly to dark energy, the spinning gravitational field can have negative energy. To decrease the particle energy (mass), the field around the core spins, which reduces the mass from the Planck scale to the orders of magnitude smaller value of elementary particle masses we observe in experiment. In the presence of the electric field, the spinning gravitational field induces a magnetic moment due to field dragging. For the given electroweak charge and spin, a spinning gravitational field can be attached to the core in different bound state configurations, yielding electron, muon, tau lepton, W boson, and much heavier particles not yet discovered [3].

Agreement between predictions of vector gravity and observations suggests the following:

1. Einstein's general relativity is ruled out together with black holes. The latter are replaced with nonsingular dark point-like objects described by the exponential metric which mimic black holes (see Sect. 3.1 in Ref. [3]).
2. Higgs mechanism of mass generation is ruled out. Higgs boson naturally appears in vector gravity as the scalar field restoring the gauge symmetry of gravity at low energy, and the emerging scalar particle has properties of the Higgs boson discovered in LHC. Namely, vector gravity predicts that the Higgs boson does exist and is coupled to the rest mass (see Sect. 8 in Ref. [3]). However, there is no Higgs condensate.
3. String theory, as a physical theory describing elementary particles, is ruled out. According to our findings, charged elementary particles are bound states of fundamental fields held together by gravity, and they are not strings or branes.

References:

[1] A.A. Svidzinsky, Vector theory of gravity: Universe without black holes and solution of dark energy problem. Physica Scripta 92, 125001, (2017). https://iopscience.iop.org/article/10.1088/1402-4896/aa93a8

[2] A.A. Svidzinsky, R.C. Hilborn, GW170817 event rules out general relativity in favor of vector gravity. Eur. Phys. J. Spec. Top. 230, 1149 (2021). https://link.springer.com/article/10.1140/epjs/s11734-021-00080-6

[3] A.A. Svidzinsky, Inner structure of leptons, nature of dark matter, and non-Higgs origin of elementary particle masses. Quantum Stud.: Math. Found. 13, 17 (2026). https://link.springer.com/article/10.1007/s40509-026-00387-w