Extending Λ(t)-CDM to the inflationary epoch using dynamical foliations and a pre-inflationary vacuum energy from 5D geometrical vacuum as a unifying mechanism

• Published in: European physical journal plus 2022-01, Vol.137 (1), p.135, Article 135
• Main Authors: Aguilar, José Edgar Madriz, Zamarripa, J., Montes, M., Licea, J. A., Loza, C. De, Peraza, A.
• Format: Article
• Language: English
• Subjects: Acceleration; Applied and Technical Physics; Atomic; Complex Systems; Condensed Matter Physics; Cosmological constant; Cosmology; Dark energy; Deceleration; Energy; Geometry; Gravitational waves; Manifolds (mathematics); Mathematical and Computational Physics; Mathematical models; Molecular; Optical and Plasma Physics; Parameters; Physics; Physics and Astronomy; Quantum field theory; Regular Article; Spacetime; Tensors; Theoretical; Universe
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-021-02143-y

In this paper assuming a 5D quantum pre-inflationary vacuum energy, we propose a manner to extend some Λ ( t ) -CDM models to the inflationary period by using dynamical foliations of the five-dimensional (5D) Ricci-flat space-time manifold, regarding a non-compact extra space-like coordinate. In this formalism, we achieve also a geometrical unification of inflation and the present accelerating epoch. In this approach, inflation is generated by a pre-inflationary quantum vacuum energy that maintains the 5D classical vacuum on cosmological scales. We obtain from geometrical conditions that we can model the presence of the pre-inflationary vacuum energy in 4D as a dynamical cosmological constant. In this model, the 4D inflationary period is governed by a power law expansion and for certain values of some parameters of the model, we obtain an spectral index satisfying 0.9607 ≤ n s ≤ 0.9691 and a scalar-to-tensor ratio r = 0.098 , values that fit well according to Planck 2018 results. The 4D inflationary potential is induced for the 5D geometry and the 4D pre-inflationary potential is determined by the model and its contribution is necessary so that n s and r can fit the observational data. We also show that in this theoretical framework, the present acceleration in the expansion of the universe can be explained due to a remanent of this pre-inflationary vacuum energy scaled to the present epoch and that its description can be done with the same Λ ( t ) . In this period, we obtain a deceleration parameter in agreement with Planck 2018 data under certain restrictions of the parameters of the model. From the geometrical point of view, Λ ( t ) is depending on the dynamical foliation of the 5D space-time manifold.