We present a model of the gravitational field based on two symmetric tensors. Gravity is affected by the new field, but if Tμν = 0, the predictions of the model coincide exactly with general relativity, so all classical tests are satisfied. We find that massive particles do not follow a geodesic, while massless particles trajectories are null geodesics of an effective metric. We study the cosmological case, where we obtain an accelerated expansion of the Universe without dark energy.
We discuss the quantization of Delta gravity, a two symmetric tensors model of gravity. This model , in Cosmology, shows accelerated expansion without a cosmological constant. We present theδ transformation which defines the geometry of the model. Then we show that all delta type models live at one loop only. We apply this to General Relativity and we calculate the one loop divergent part of the Effective Action showing its null contribution in vacuum, implying a finite model. Then we proceed to study the existence of ghosts in the model. Finally, we study the form of the finite quantum corrections to the classical action of the model.
A gravitational field model based on two symmetric tensors, g µν andg µν , is presented. In this model, new matter fields are added to the original matter fields, motivated by an additional symmetry (δ symmetry). We call them δ matter fields. We find that massive particles do not follow geodesics, while trajectories of massless particles are null geodesics of an effective metric. Then we study the Cosmological case, where we get an accelerated expansion of the Universe without dark energy. Introduction.Recent discoveries in cosmology have revealed that most part of matter is in the form of unknown matter, dark matter [1]- [9], and that the dynamics of the expansion of the Universe is governed by a mysterious component that accelerates its expansion, the so called dark energy [10]- [12]. That is the Dark Sector. Although GR is able to accommodate the Dark Sector, its interpretation in terms of fundamental theories of elementary particles is problematic [13]. Although some candidates exist that could play the role of dark matter, none have been detected yet. Also, an alternative explanation based on the modification of the dynamics for small accelerations cannot be ruled out [14,15]. Dark energy can be explained if a small cosmological constant (Λ) is present. At early times, this constant is irrelevant, but at the later stages of the evolution of the Universe Λ will dominate the expansion, explaining the observed acceleration. However Λ is too small to be generated in quantum field theory (QFT) models, because Λ is the vacuum energy, which is usually predicted to be very large [16].One of the most important mysteries in cosmology and cosmic structure formation is to understand the nature of dark energy in the context of a fundamental physical theory [17,18]. In recent years there has been various proposals to explain the observed acceleration of the Universe. They include some additional fields in approaches like quintessence, chameleon, vector dark energy or massive gravity; The addition of higher order terms in the Einstein-Hilbert action, like f (R) theories and Gauss-Bonnet terms and finally the introduction of extra dimensions for a modification of gravity on large scales (See [19]).Recently, in [20], a model of gravitation that is very similar to GR is presented, but works different at the quantum level. In that paper, we considered two different points. The first is that GR is finite on shell at one loop in vacuum [21], so renormalization is not necessary at this level. The second is theδ gauge theories (DGT) originally presented in [22,23], where the main properties are: (a) A new kind of fieldφ I is introduced, different from the original set φ I . (b) The classical equations of motion of φ I are satisfied even in the full quantum theory. (c) The model lives at one loop. (d) The action is obtained through the extension of the original gauge symmetry of the model, introducing an extra symmetry that we callδ symmetry, since it is formally obtained as the variation
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