$${f(\mathcal R)}$$ quantum cosmology

Shojai, Ali; Shojai, Fatimah

doi:10.1007/s10714-008-0617-5

Cited by 23 publications

(39 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[12] The quantum cosmology of the f (R)-type gravity has been already studied. [13] However, it is well known that, in general, the Wheeler-DeWitt equation has the problem that the probabilistic interpretation is difficult as in the case of the KleinGordon equation. One of the proposed ideas to solve this problem is the third quantization in analogy with the quantum field theory.…”

Section: Introductionmentioning

confidence: 99%

Third quantization of f ( R )-type gravity

Ohkuwa¹,

Ezawa²

2012

Class. Quantum Grav.

View full text Add to dashboard Cite

We examine the third quantization of f (R)-type gravity, based on its effective Lagrangian in the case of a flat Friedmann-Lemaitre-Robertson-Walker metric. Starting from the effective Lagrangian, we execute a suitable change of variable and the second quantization, and we obtain the Wheeler-DeWitt equation. The third quantization of this theory is considered. And the uncertainty relation of the universe is investigated in the example of f (R)-type gravity, where f (R) = R 2 . It is shown, when the time is late namely the scale factor of the universe is large, the spacetime does not contradict to become classical, and, when the time is early namely the scale factor of the universe is small, the quantum effects are dominating.

show abstract

Section: Introductionmentioning

confidence: 99%

Third quantization of f ( R )-type gravity

Ohkuwa¹,

Ezawa²

2012

Class. Quantum Grav.

View full text Add to dashboard Cite

show abstract

“…3There are some other works about theoretical constructions of f ( R ) models based on quantum gravity, super-gravity and extra dimensional theories [341, 345, 537, 406, 163, 287, 288, 518, 519]. …”

mentioning

confidence: 99%

f(R) Theories

Felice

Tsujikawa

2010

Living Rev. Relativ.

3,670

3,400

View full text Add to dashboard Cite

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity — such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

show abstract

“…The Weyl space is construct so as to incorporate the gauge transformation of a vector field (w μ → w μ + Λ, μ ) analogous to the electromagnetic gauge transformation [34][35][36][37][38]. This new vector field is associated with the non-zero covariant derivative of the metric tensor.…”

Section: Appendix: Weyl Geometrymentioning

confidence: 99%

Geometrizing Relativistic Quantum Mechanics

2010

View full text Add to dashboard Cite

We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation that recover both of them in the non-relativistic limit.

show abstract

$${f(\mathcal R)}$$ quantum cosmology

Abstract: We have quantized a flat cosmological model in the context of the metric f (R) models, using the causal Bohmian quantum theory. The equations are solved and then we have obtained how the quantum corrections influence the classical equations.

Cited by 23 publications

References 30 publications

Third quantization of f ( R )-type gravity

Third quantization of f ( R )-type gravity

f(R) Theories

Geometrizing Relativistic Quantum Mechanics

Contact Info

Product

Resources

About