Bulg. J. Phys. vol.48 no.2 (2021), pp. 117-137

Running Dark Energy and Dark Matter from Dynamical Spacetime

S. Banerjee1,2, D. Benisty2,3,4, E.I. Guendelman2,3,5
1Inst. for Quantum Gravity, FAU Erlangen-Nuremberg, Staudtstr. 7, 91058 Erlangen, Germany
2Physics Department, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
3Frankfurt Institute for Advanced Studies (FIAS), Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main, Germany
4DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
5Bahamas Advanced Study Institute and Conferences, 4A Ocean Heights, Hill View Circle, Stella Maris, Long Island, The Bahamas
Abstract. Running Dark Energy and Dark Matter models are candidates to resolve the Hubble constant tension. However the model does not consider a Lagrangian formulation directly. In this paper we formulate an action principle where the Running Vacuum Model (RVM) is obtained from an action principle, with a scalar field model for the whole dark components. The Dynamical Spacetime vector field χμ is a Lagrange multiplier that forces the kinetic term of the scalar field to behave as the modified dark matter. When we replace the vector field by a derivative of a scalar the model predicts diffusion interactions between the dark components with a different correspondence to the RVM. We test the models with the Cosmic Chronometers, Type Ia Supernova, Quasars, Gamma ray Bursts and the Baryon Acoustic Oscillations data sets. We find that ΛCDM is still the best model. However this formulation suggests an action principle for the RVM model and other extensions.

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