Slow-roll inflation in loop quantum cosmology of scalar–tensor theories of gravity

2015 ◽  
Vol 30 (26) ◽  
pp. 1550127
Author(s):  
Yu Han
Keyword(s):  
Quantum Cosmology ◽  
Field Model ◽  
Equations Of Motion ◽  
Index Formula ◽  
Jordan Frame ◽  
Loop Quantum Cosmology ◽  
Slow Roll ◽  
Scalar Spectral Index ◽  
Theories Of Gravity ◽  
Slow Roll Inflation

The slow-roll inflation of scalar–tensor theories (STTs) of gravity in the context of loop quantum cosmology (LQC) is investigated in this paper. After deriving the effective Hamiltonian, we obtain the semiclassical equations of motion for the background variables in both Jordan frame and Einstein frame of STTs. Then we apply these equations in the slow-roll limit and derive the LQC corrections to the scalar spectral index [Formula: see text] and the tensor-to-scalar ratio [Formula: see text] in the two frames of STTs. Finally, we take two special sectors of STTs as specific examples, namely the Starobinsky model and the non-minimally coupled scalar field model (with the coupling function [Formula: see text] and the potential [Formula: see text]). We derive the detailed expressions of the LQC corrections to [Formula: see text] and [Formula: see text] in terms of the [Formula: see text]-folding number for these two models in both frames.

scholarly journals Measuring the effects of loop quantum cosmology in the CMB data

2017 ◽  
Vol 26 (12) ◽  
pp. 1743023 ◽  
Author(s):  
Spyros Basilakos ◽  
Vahid Kamali ◽  
Ahmad Mehrabi
Keyword(s):  
Power Spectrum ◽  
Spectral Index ◽  
Excellent Agreement ◽  
Quantum Cosmology ◽  
Loop Quantum Cosmology ◽  
Alternative Scenario ◽  
Slow Roll ◽  
Scalar Spectral Index ◽  
Robust Prediction ◽  
Scalar Fluctuation

In this paper we investigate the observational signatures of Loop Quantum Cosmology (LQC) in the CMB data. First, we concentrate on the dynamics of LQC and we provide the basic cosmological functions. We then obtain the power spectrum of scalar and tensor perturbations in order to study the performance of LQC against the latest CMB data. We find that LQC provides a robust prediction for the main slow-roll parameters, like the scalar spectral index and the tensor-to-scalar fluctuation ratio, which are in excellent agreement within [Formula: see text] with the values recently measured by the Planck collaboration. This result indicates that LQC can be seen as an alternative scenario with respect to that of standard inflation.

The evolutionary pictures for phantom field in loop quantum cosmology

2019 ◽  
Vol 28 (15) ◽  
pp. 1950170
Author(s):  
Kui Xiao
Keyword(s):  
Dark Matter ◽  
Quantum Cosmology ◽  
Scalar Fields ◽  
Chaplygin Gas ◽  
Loop Quantum Cosmology ◽  
Phantom Field ◽  
Dynamical Behaviors ◽  
Slow Roll ◽  
The Universe ◽  
Slow Roll Inflation

The evolutionary pictures for phantom field in loop quantum cosmology are discussed in this paper. Comparing the dynamical behaviors of the phantom field with one of the canonical scalar fields in loop quantum cosmology scenario, we found that the [Formula: see text] phase trajectories are the same, but the [Formula: see text] phase-spaces are very different, and the phantom field with considering potentials can drive neither super inflation nor slow-roll inflation in loop quantum cosmology (LQC) scenario. While the universe is filled with multiple dark fluids, to ensure that the condition [Formula: see text] does not violate, the energy density of dark matter [Formula: see text] and the equation-of-state of phantom field [Formula: see text] should satisfy the condition [Formula: see text] at the bounce point. If this constraint condition holds, the universe can enter an inflationary stage, and it is possible to unify the description of phantom field, dark matter and inflation. We introduced a toy model which has the same form of the general Chaplygin gas to unify the dark energy, dark matter and slow-roll inflation, and the slow-roll inflation of the toy model has also been discussed.

scholarly journals Pre-inflation dynamical behavior of warm inflation in loop quantum cosmology

2020 ◽  
Vol 35 (35) ◽  
pp. 2050293
Author(s):  
Kui Xiao ◽  
Sheng-Qin Wang
Keyword(s):  
Quantum Cosmology ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Loop Quantum Cosmology ◽  
Warm Inflation ◽  
Dynamical Behaviors ◽  
Slow Roll ◽  
Dissipative Coefficient ◽  
Slow Roll Inflation ◽  
Three Phases

Considering a constant dissipative coefficient [Formula: see text], the pre-inflation dynamical behaviors of warm inflation in the loop quantum cosmology scenario are discussed. We consider three sets of initial conditions. The evolution of the background can always be divided into three phases, namely super-inflation, damping, and slow-roll inflation phases, with the duration of each phase depending on the initial conditions. As an example, we compare the background evolution between [Formula: see text] and [Formula: see text] under special initial conditions and find that there is no slow-roll inflation phase for [Formula: see text] while the number of e-folds is about 60.209 for [Formula: see text].

scholarly journals Tachyonic inflation in loop quantum cosmology

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Kui Xiao
Keyword(s):  
Quantum Cosmology ◽  
Early Time ◽  
Field Energy ◽  
Loop Quantum Cosmology ◽  
Initial Condition ◽  
Tachyon Field ◽  
Slow Roll ◽  
Cosmological Inflation ◽  
Very High ◽  
Slow Roll Inflation

AbstractA tachyon field might be responsible for cosmological inflation at an early time and contribute to cosmological dark matter at a later time. We investigate tachyonic inflation by analyzing a tachyon field with different potentials in the framework of loop quantum cosmology. No matter which tachyon field energy dominates at the bounce, the evolution of the background can be divided into three phases: super-inflation, damping, and slow-roll inflation. The duration of each phase depends on the initial condition. During the slow-roll inflation, when the initial condition is $$V(T_\mathrm{B})/\rho _\mathrm{c}\ge 10^{-6}$$V(TB)/ρc≥10-6, the number of e-folds is very high ($$N\gg 60$$N≫60) for $$V\propto T^{-n}$$V∝T-n with $$n=1$$n=1 and 1 / 2. For an exponential potential, to get enough e-folds, $$V(T_\mathrm{B})/\rho _\mathrm{c}$$V(TB)/ρc should be greater than $$7.802\times 10^{-4}$$7.802×10-4. Furthermore, the probability of slow-roll inflation is obtained. We find that the probability of obtaining slow-roll inflation with 60 or more e-folds is very close to 1.

scholarly journals INFLATIONARY COSMOLOGY AND OSCILLATING UNIVERSES IN LOOP QUANTUM COSMOLOGY

2005 ◽  
Vol 20 (11) ◽  
pp. 2347-2357 ◽  
Author(s):  
DAVID J. MULRYNE ◽  
N. J. NUNES ◽  
REZA TAVAKOL ◽  
JAMES E. LIDSEY
Keyword(s):  
Comparative Study ◽  
Quantum Cosmology ◽  
Initial Conditions ◽  
Scalar Fields ◽  
Inflationary Cosmology ◽  
Loop Quantum Cosmology ◽  
Oscillatory Dynamics ◽  
Slow Roll ◽  
Positively Curved ◽  
Slow Roll Inflation

We study oscillatory universes within the context of Loop Quantum Cosmology. We make a comparative study of flat and positively curved universes sourced by scalar fields with either positive or negative potentials. We investigate how oscillating universes can set the initial conditions for successful slow-roll inflation, while ensuring that the semi-classical bounds are satisfied. We observe rich oscillatory dynamics with negative potentials, although it is difficult to respect the semi-classical bounds in models of this type.

scholarly journals Loop quantum cosmology and slow roll inflation

2010 ◽  
Vol 694 (2) ◽  
pp. 108-112 ◽  
Author(s):  
Abhay Ashtekar ◽  
David Sloan
Keyword(s):  
Quantum Cosmology ◽  
Loop Quantum Cosmology ◽  
Slow Roll ◽  
Slow Roll Inflation

scholarly journals CHAPLYGIN INFLATION IN LOOP QUANTUM COSMOLOGY

2009 ◽  
Vol 24 (22) ◽  
pp. 1763-1773 ◽  
Author(s):  
XIN ZHANG ◽  
JINGFEI ZHANG ◽  
JINGLEI CUI ◽  
LI ZHANG
Keyword(s):  
Equation Of State ◽  
Quantum Cosmology ◽  
Chaplygin Gas ◽  
Effective Theory ◽  
Loop Quantum Cosmology ◽  
Inflationary Universe ◽  
Quadratic Potential ◽  
Inflation Model ◽  
Slow Roll ◽  
Scalar Spectral Index

In this paper we discuss the inflationary universe in the context of a Chaplygin gas equation of state within the framework of the effective theory of loop quantum cosmology. Under the slow-roll approximation, we calculate the primordial perturbations for this model. We give the general expressions of the scalar spectral index, its running, and the tensor-to-scalar ratio, etc. For the chaotic inflation with a quadratic potential, using the WMAP 5-year results, we determine the parameters of the Chaplygin inflation model in loop quantum cosmology. The results are consistent with the WMAP observations.

scholarly journals Noncommutative Friedmann equations in effective LQC

2020 ◽  
Vol 29 (06) ◽  
pp. 2050039
Author(s):  
Luis Rey Díaz-Barrón ◽  
Abraham Espinoza-García ◽  
S. Pérez-Payán ◽  
J. Socorro
Keyword(s):  
Scalar Field ◽  
Effective Potential ◽  
Quantum Cosmology ◽  
Equations Of Motion ◽  
Loop Quantum Cosmology ◽  
Friedmann Equations ◽  
Noncommutative Version ◽  
Previous Proposal ◽  
Free Scalar ◽  
Raychaudhuri Equations

In this work, we construct a noncommutative version of the Friedmann equations in the framework of effective loop quantum cosmology, extending and applying the ideas presented in a previous proposal by some of the authors. The model under consideration is a flat FRW spacetime with a free scalar field. First, noncommutativity in the momentum sector is introduced. We establish the noncommutative equations of motion and obtain the corresponding exact solutions. Such solutions indicate that the bounce is preserved, in particular, the energy density is the same as in the standard LQC. We also construct an extension of the modified Friedmann equations arising in effective LQC which incorporates corrections due to noncommutativity, and argue that an effective potential is induced. This, in turn, leads us to investigate the possibility of an inflationary era. Finally, we obtain the Friedmann and the Raychaudhuri equations when implementing noncommutativity in the configuration sector. In this case, no effective potential is induced.

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