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

Abstract

The Friedmann-Robertson-Walker (FRW) cosmology is analyzed with a general potential $\mathrm{V}(\varphi )$ 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 $\varphi$ 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 (Planck 2018 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.

14 pages, 1 figure and 1 table. Part of a conference talk at "Alfredo Macías 60th Birthday Conference" imparted by Dr. J. Socorro at México City, México, April 27th 2018

References in corpus (16)

• Exponential potentials and cosmological scaling solutions
• Inflation Dynamics and Reheating
• Cosmology with a Primordial Scaling Field
• Quintessence arising from exponential potentials
• A classification of scalar field potentials with cosmological scaling solutions
• Exact solution of scalar field cosmology with exponential potentials and transient acceleration
• Integrable Scalar Cosmologies I. Foundations and links with String Theory
• General solution of scalar field cosmology with a (piecewise) exponential potential
• On exact solutions for quintessential (inflationary) cosmological models with exponential potentials
• Universality for quintessence
• Stability of multi-field cosmological solutions
• Scalar potentials out of canonical quantum cosmology
• Inflation from Supersymmetric Quantum Cosmology
• Slow rolling, inflation and quintessence
• Scalar-Tensor theories and current Cosmology
• Scalar potentials with Multi-scalar fields from quantum cosmology and supersymmetric quantum mechanics

Cited by in corpus (74)

• Search for the isotropic stochastic background using data from Advanced LIGO's second observing run
• Did NANOGrav see a signal from primordial black hole formation?
• Unifying Holographic Inflation with Holographic Dark Energy: a Covariant Approach
• Unifying of Inflation with Early and Late Dark Energy Epochs in Axion $F(R)$ Gravity
• Gravitational perturbations from oscillons and transients after inflation
• When Primordial Black Holes from Sound Speed Resonance Meet a Stochastic Background of Gravitational Waves
• Primordial Gravitational Waves in Nonstandard Cosmologies
• Signals of a Quantum Universe
• XENON1T excess from anomaly-free ALP dark matter and its implications for stellar cooling anomaly
• Gravitational waves and proton decay: complementary windows into GUTs
• GUT Baryogenesis With Primordial Black Holes
• Primordial Extremal Black Holes as Dark Matter
• Observational Constraints on the Regularized 4D Einstein-Gauss-Bonnet Theory of Gravity
• Primordial Black Holes from Cosmic Domain Walls
• Unification of a Bounce with a Viable Dark Energy Era in Gauss-Bonnet Gravity
• Swampland, Axions and Minimal Warm Inflation
• Lighting the Dark: The Evolution of the Post-Inflationary Universe
• Early Cosmological Evolution of Primordial Electromagnetic Fields
• Parameters Estimation for the Cosmic Microwave Background with Bayesian Neural Networks
• Imprints of the Early Universe on Axion Dark Matter Substructure
• Scale independent $R^2$ inflation
• Bayesian inflationary reconstructions from Planck 2018 data
• Primordial Black Holes from No-Scale Supergravity
• Shift-Symmetric Orbital Inflation: single field or multi-field?
• Swampland conjecture in $f(R)$ gravity by the Noether Symmetry Approach
• Accounting for the time evolution of the equation of state parameter during reheating
• Non-singular Bounce Cosmology from Lagrange Multiplier $F(R)$ Gravity
• First Results on Dark Matter Substructure from Astrometric Weak Lensing
• The Inflaton Portal to a Highly decoupled EeV Dark Matter Particle
• Dynamical analysis of cosmological models with non-Abelian gauge vector fields
• Two phase reheating: CMB constraints on inflaton and dark matter phenomenology
• Generality of Starobinsky and Higgs inflation in the Jordan frame
• Constraining galactic structures of mirror dark matter
• Disformal Dark Matter
• A novel exact magnetic black hole solution in four-dimensional extended scalar-tensor-Gauss-Bonnet theory
• Reheating Constraints on Inflaton, Dark Matter: Swampland Conjecture
• Dark matter as Planck relics without too exotic hypotheses
• Stochastic Effects in Anisotropic Inflation
• Gravitational wave generation in a viable scenario of inflationary magnetogenesis
• Fermion Dark Matter with Scalar Triplet at Direct and Collider Searches
• Probing primordial non-Gaussianity with Fast Radio Bursts
• Analytical approximations for curved primordial power spectra
• Freeze-in Production of Dark Matter Prior to Early Matter Domination
• A simple, exact, model of quasi-single field inflation
• Stochastic evolution of scalar fields with continuous symmetries during inflation
• Classical and quantum exact solutions for a FRW in chiral like cosmology
• On the origin of entropy of gravitationally produced dark matter: the entanglement entropy
• A Unified No-Scale Model of Modulus Fixing, Inflation, Supersymmetry Breaking and Dark Energy
• Primordial gravitational wave phenomenology with polarized Sunyaev Zel'dovich tomography
• Quantum initial conditions for inflation and canonical invariance
• Reheating constraints to WIMPflation
• Induced Gravity and Quantum Cosmology
• Gravitational production of superheavy baryonic and dark matter in quintessential inflation: nonconformally coupled case
• Spectator dark matter in non-standard cosmologies
• Anisotropic chiral cosmology: exact solutions
• Dark Energy and Cosmological Horizon Thermal Effects
• Resonant Reconciliation of Convex Models and the Planck
• Tachyon Mimetic Inflation as an Instabilities-Free Model
• Constraining graviton non-Gaussianity through the CMB bispectra
• A Dynamical Solution to the Axion Domain Wall Problem
• Exploring Early and Late Cosmology with Next Generation Surveys
• Flattened Axion Monodromy Beyond Two Derivatives
• G-Warm inflation: Intermediate model
• Potential-driven Inflation with Disformal Coupling to Gravity
• QCD Axion From a Spontaneously Broken B-L Gauge Symmetry
• Natural inflation, strong dynamics, and the role of generalized anomalies
• Cosmic perturbations, baryon asymmetry and dark matter from the minimal supersymmetric standard model
• Aspects of gauged R-symmetry in SU(1,1)/U(1) supergravity
• A simple supergravity model of inflation constrained with Planck 2018 data
• Lowering tensor-to-scalar ratio by pre-inflationary dynamics
• Towards degeneracy breaking of early universe models
• Higgs-Squark-Slepton Inflation from the MSSM
• Chaotic Inflation from the MSSM Along Flat $D$-Term Trajectory
• Inflationary spectral tilts as a result of the dilatation symmetry breaking