Viable Inflationary Evolution from Loop Quantum Cosmology Scalar-Tensor Theory

Abstract

In this work we construct a bottom-up reconstruction technique for Loop Quantum Cosmology scalar-tensor theories, from the observational indices. Particularly, the reconstruction technique is based on fixing the functional form of the scalar-to-tensor ratio as a function of the $e$-foldings number. The aim of the technique is to realize viable inflationary scenarios, and the only assumption that must hold true in order for the reconstruction technique to work is that the dynamical evolution of the scalar field obeys the slow-roll conditions. We shall use two functional forms for the scalar-to-tensor ratio, one of which corresponds to a popular inflationary class of models, the $\alpha$-attractors. For the latter, we shall calculate the leading order behavior of the spectral index and we shall demonstrate that the resulting inflationary theory is viable and compatible with the latest Planck and BICEP2/Keck-Array data. In addition, we shall find the classical limit of the theory, and as we demonstrate, the Loop Quantum Cosmology corrected theory and the classical theory are identical at leading order in the perturbative expansion quantified by the parameter ${\rho }_c$, which is the critical density of the quantum theory. Finally, by using the formalism of slow-roll scalar-tensor Loop Quantum Cosmology, we shall investigate how several inflationary potentials can be realized by the quantum theory, and we shall calculate directly the slow-roll indices and the corresponding observational indices. In addition, the $f(R)$ gravity frame picture is presented.

arXiv commentPRD Accepted

References in corpus (68)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Extended Theories of Gravity
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• The Standard Model Higgs boson as the inflaton
• Particle Physics Models of Inflation and the Cosmological Density Perturbation
• f(T) teleparallel gravity and cosmology
• Loop Quantum Cosmology: A Status Report
• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Universality Class in Conformal Inflation
• Superconformal Inflationary $\alpha$-Attractors
• BICEP2 / Keck Array VI: Improved Constraints On Cosmology and Foregrounds When Adding 95 GHz Data From Keck Array
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Loop Quantum Cosmology
• Matter Bounce Cosmology with the f(T) Gravity
• Minimal Supergravity Models of Inflation
• Towards a Nonsingular Bouncing Cosmology
• The Unity of Cosmological Attractors
• Bouncing Cosmologies: Progress and Problems
• Black holes, cosmological solutions, future singularities, and their thermodynamical properties in modified gravity theories
• A universal attractor for inflation at strong coupling
• The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations
• A Quantum Gravity Extension of the Inflationary Scenario
• Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology
• An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era
• Suppressing CMB Quadrupole with a Bounce from Contracting Phase to Inflation
• Large Field Inflation and Double $\alpha$-Attractors
• Singular Bouncing Cosmology from Gauss-Bonnet Modified Gravity
• Planck, LHC, and $\alpha$-attractors
• Bouncing cosmology with future singularity from modified gravity
• Two Field Matter Bounce Cosmology
• Obtaining the CMB anomalies with a bounce from the contracting phase to inflation
• Quintessential Inflation with $\alpha$-attractors
• Single-field $\alpha$-attractors
• Consistency of holonomy-corrected scalar, vector and tensor perturbations in Loop Quantum Cosmology
• Cosmological Attractors from $\alpha$-Scale Supergravity
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Perturbation, Non-Gaussianity and Reheating in a GB-$\alpha$-Attractor Model
• Non-singular bounce scenarios in loop quantum cosmology and the effective field description
• Cosmological Attractor Models and Higher Curvature Supergravity
• Inflationary $\alpha$-attractors from $F(R)$ Gravity
• Cosmic Bounces and Cyclic Universes
• Non-Singular Bouncing Cosmology: Consistency of the Effective Description
• Consistent Loop Quantum Cosmology
• On the geometrical interpretation of scale-invariant models of inflation
• The Reconstruction of $f(\varphi )R$ and Mimetic Gravity from Viable Slow-roll Inflation
• On $R+\alpha R^2$ Loop Quantum Cosmology
• Viability of the matter bounce scenario in Loop Quantum Cosmology from BICEP2 last data
• Turning Big Bang into Big Bounce: I. Classical Dynamics
• Dark Energy from $\alpha$-Attractors
• The reconstruction of inflationary potentials
• Reconstruction of Slow-roll $F(R)$ Gravity Inflation from the Observational Indices
• Reconstructing a $f(R)$ theory from the $\alpha$-Attractors
• Detailed investigation of the duration of inflation in loop quantum cosmology for a Bianchi-I universe with different inflaton potentials and initial conditions
• Nonminimal coupling and inflationary attractors
• Running of the scalar spectral index in bouncing cosmologies
• Cyclic Universe with Quintom matter in Loop Quantum Cosmology
• The reconstruction of tachyon inflationary potentials
• Transcending Big Bang in Loop Quantum Cosmology: Recent Advances
• Future singularity avoidance in phantom dark energy models
• Effective Actions from Loop Quantum Cosmology: Correspondence with Higher Curvature Gravity
• Inverse Symmetric Inflationary Attractors
• Endlessly flat scalar potentials and $\alpha$-attractors
• Bouncing cosmologies via modified gravity in the ADM formalism: Application to Loop Quantum Cosmology
• On the Renormalization Group perspective of $\alpha$-attractors
• Qualitative study in Loop Quantum Cosmology

Cited by in corpus (7)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Primordial regular black holes as all the dark matter. II. Non-time-radial-symmetric and loop quantum gravity-inspired metrics
• Implication of GW170817 for cosmological bounces
• The effective dynamics of loop quantum $R^2$ cosmology
• Loop quantum cosmological dynamics of scalar-tensor theory in the Jordan frame
• Nonclassical cosmological dynamics in the low-energy limit of loop quantum scalar-tensor theory
• Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmology