scholarly journals Primordial perturbations in kinetically dominated regimes of general relativity and hybrid quantum cosmology

2021 ◽  
Vol 104 (10) ◽  
Author(s):  
Beatriz Elizaga Navascués ◽  
Rafael Jiménez-Llamas ◽  
Guillermo A. Mena Marugán
Keyword(s):  
General Relativity ◽  
Quantum Cosmology

scholarly journals Beyond General Relativity: Models for Quantum Gravity, Loop Quantum Cosmology and Black Holes

Universe ◽  
2020 ◽  
Vol 6 (12) ◽  
pp. 232
Author(s):  
Nick E. Mavromatos
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Precision Measurements ◽  
Loop Quantum Cosmology ◽  
The Past

In the past two decades, we have witnessed extraordinary progress in precision measurements in cosmology [...]

THE GEOMETRY OF CLASSICAL CHANGE OF SIGNATURE

1995 ◽  
Vol 04 (02) ◽  
pp. 175-187 ◽  
Author(s):  
MAURO CARFORA ◽  
GEORGE ELLIS
Keyword(s):  
General Relativity ◽  
Fundamental Form ◽  
Initial Value Problem ◽  
Quantum Cosmology ◽  
Second Fundamental Form ◽  
Classical General Relativity ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Initial Value ◽  
The Second Fundamental Form

The proposal of the possibility of change of signature in quantum cosmology has led to the study of this phenomenon in classical general relativity theory, where there has been some controversy about what is and is not possible. Here we present a new analysis of such a change of signature, based on previous studies of the initial value problem in general relativity. We emphasize that there are various continuity suppositions one can make at a classical change of signature, and consider more general assumptions than have been made up to now. We confirm that in general such a change can take place even when the second fundamental form of the surface of change does not vanish.

Stability analysis of Einstein’s universe in loop quantum cosmology

2020 ◽  
Vol 35 (28) ◽  
pp. 2050166
Author(s):  
Eamon Mc Caughey
Keyword(s):  
General Relativity ◽  
Stability Analysis ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Hamiltonian Structure ◽  
Loop Quantum Cosmology ◽  
Universe Model ◽  
Integrals Of Motion ◽  
Cyclic Universe ◽  
The Stability

A stability analysis of Einstein’s universe in both classical general relativity and semiclassical loop quantum cosmology regimes is presented. The stability properties of the general relativity model are significantly altered due to loop quantum gravity corrections. Comparisons between both dynamical systems are considered on the basis of these modifications. The loop quantum cosmology solutions are restricted to an open universe model [Formula: see text] and represent a cyclic universe. The integrals of motion for both systems are found and their Hamiltonian structure determined.

scholarly journals The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology

Universe ◽  
2018 ◽  
Vol 4 (10) ◽  
pp. 98 ◽  
Author(s):  
Beatriz Elizaga Navascués ◽  
Daniel Martín de Blas ◽  
Guillermo Mena Marugán
Keyword(s):  
General Relativity ◽  
Kinetic Energy ◽  
Quantum Cosmology ◽  
Power Spectra ◽  
Mass Term ◽  
Vacuum State ◽  
Initial Time ◽  
Loop Quantum Cosmology ◽  
Quantum Geometry ◽  
Effective Dynamics

We investigate the role played by the vacuum of the primordial fluctuations in hybrid Loop Quantum Cosmology. We consider scenarios where the inflaton potential is a mass term and the unperturbed quantum geometry is governed by the effective dynamics of Loop Quantum Cosmology. In this situation, the phenomenologically interesting solutions have a preinflationary regime where the kinetic energy of the inflaton dominates over the potential. For these kind of solutions, we show that the primordial power spectra depend strongly on the choice of vacuum. We study in detail the case of adiabatic states of low order and the non-oscillating vacuum introduced by Martín de Blas and Olmedo, all imposed at the bounce. The adiabatic spectra are typically suppressed at large scales, and display rapid oscillations with an increase of power at intermediate scales. In the non-oscillating vacuum, there is power suppression for large scales, but the rapid oscillations are absent. We argue that the oscillations are due to the imposition of initial adiabatic conditions in the region of kinetic dominance, and that they would also be present in General Relativity. Finally, we discuss the sensitivity of our results to changes of the initial time and other data of the model.

scholarly journals $$f(\mathcal {G})$$ Noether cosmology

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Francesco Bajardi ◽  
Salvatore Capozziello
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Scalar Field ◽  
Power Law ◽  
Quantum Cosmology ◽  
Hamiltonian Formalism ◽  
Topological Invariant ◽  
De Sitter ◽  
Einstein Theory ◽  
Symmetry Approach

Abstract We develop the n-dimensional cosmology for $$f(\mathcal {G})$$f(G) gravity, where $$\mathcal {G}$$G is the Gauss–Bonnet topological invariant. Specifically, by the so-called Noether Symmetry Approach, we select $$f(\mathcal {G})\simeq \mathcal {G}^k$$f(G)≃Gk power-law models where k is a real number. In particular, the case $$k = 1/2$$k=1/2 for $$n=4$$n=4 results equivalent to General Relativity showing that we do not need to impose the action $$R+f(\mathcal {G})$$R+f(G) to reproduce the Einstein theory. As a further result, de Sitter solutions are recovered in the case where $$f(\mathcal {G})$$f(G) is non-minimally coupled to a scalar field. This means that issues like inflation and dark energy can be addressed in this framework. Finally, we develop the Hamiltonian formalism for the related minisuperspace and discuss the quantum cosmology for this model.

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