Hamilton’s approach in cosmological inflation with an exponential potential and its observational constraints

• Published in: Astrophysics and space science Vol. 364; no. 4; pp. 1 - 10
• Main Authors: Núñez, Omar E., Socorro, J., Hernández-Jiménez, Rafael
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-04-2019; Springer Nature B.V
• Subjects: Astrobiology; Astronomy; Astrophysics; Astrophysics and Astroparticles; Cosmology; Equations of motion; Inflation (cosmology); Kinetic energy; Observations and Techniques; Original Article; Physics; Physics and Astronomy; Space Exploration and Astronautics; Space Sciences (including Extraterrestrial Physics; Tensors; Inflation; Observational parameters; Quantum and classical cosmology; Exact solutions
• ISSN: 0004-640X; 1572-946X
• DOI: 10.1007/s10509-019-3558-4

The Friedmann-Robertson-Walker (FRW) cosmology is analyzed with a general potential
V
(
ϕ
)
in the scalar field inflation scenario. The Bohmian approach (a WKB-like formalism) was employed in order to constraint a generic form of potential to the most suited to drive inflation, from here a family of potentials emerges; in particular we select an exponential potential as the first non trivial case and remains the object of interest of this work. The solution to the Wheeler-DeWitt (WDW) equation is also obtained for the selected potential in this scheme. Using Hamilton’s approach and equations of motion for a scalar field
ϕ
with standard kinetic energy, we find the exact solutions to the complete set of Einstein-Klein-Gordon (EKG) equations without the need of the slow-roll approximation (SR). In order to contrast this model with observational data (Akrami et al.
2018
,
arXiv:1807.06211
, (Planck Collaboration) results), the inflationary observables: the tensor-to-scalar ratio and the scalar spectral index are derived in our proper time, and then evaluated under the proper condition such as the number of e-folding corresponds exactly at 50–60 before inflation ends. The employed method exhibits a remarkable simplicity with rather interesting applications in the near future.