Towards the quantization of Eddington-inspired-Born-Infeld theory
TLDR
In this article, the Wheeler-DeWitt (WDW) equation is obtained and solved based on an alternative action proposed in ref. [1], under two different factor ordering choices.Abstract:
The quantum effects close to the classical big rip singularity within the Eddington-inspired-Born-Infeld theory (EiBI) are investigated through quantum geometrodynamics. It is the first time that this approach is applied to a modified theory constructed upon Palatini formalism. The Wheeler-DeWitt (WDW) equation is obtained and solved based on an alternative action proposed in ref. [1], under two different factor ordering choices. This action is dynamically equivalent to the original EiBI action while it is free of square root of the spacetime curvature. We consider a homogeneous, isotropic and spatially flat universe, which is assumed to be dominated by a phantom perfect fluid whose equation of state is a constant. We obtain exact solutions of the WDW equation based on some specific conditions. In more general cases, we propose a qualitative argument with the help of a Wentzel-Kramers-Brillouin (WKB) approximation to get further solutions. Besides, we also construct an effective WDW equation by simply promoting the classical Friedmann equations. We find that for all the approaches considered, the DeWitt condition hinting singularity avoidance is satisfied. Therefore the big rip singularity is expected to be avoided through the quantum approach within the EiBI theory.read more
Citations
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Born–Infeld inspired modifications of gravity
Jose Beltrán Jiménez,Jose Beltrán Jiménez,Lavinia Heisenberg,Gonzalo J. Olmo,Gonzalo J. Olmo,Diego Rubiera-Garcia +5 more
TL;DR: In particular, the breakdown of unitarity near the Planck scale strongly suggests that General Relativity needs to be modified at high energies and quantum gravity effects are expected to be important.
Journal ArticleDOI
Born-Infeld inspired modifications of gravity
Jose Beltrán Jiménez,Jose Beltrán Jiménez,Lavinia Heisenberg,Gonzalo J. Olmo,Gonzalo J. Olmo,Diego Rubiera-Garcia +5 more
TL;DR: In particular, the breakdown of unitarity near the Planck scale strongly suggests that General Relativity needs to be modified at high energies and quantum gravity effects are expected to be important as mentioned in this paper.
Journal ArticleDOI
Black hole solutions in mimetic Born-Infeld gravity.
TL;DR: In this article, the authors studied the vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity model and showed that the spacelike singularity inside a Schwarzschild black hole could be altered to a light-like singularity, even though the curvature invariants still diverge at the singularity.
Journal ArticleDOI
Primordial cosmology in mimetic born-infeld gravity
TL;DR: In this article, the Eddington-inspired Born-Infeld (EiBI) model is reformulated within the mimetic approach and the existence of regular solutions, such as primordial inflationary solutions of de Sitter type or bouncing solutions, is proved.
Journal ArticleDOI
f(R) quantum cosmology: avoiding the Big Rip
TL;DR: In this paper, the authors analyze the big rip singularity in the framework of metric $f(R)$ quantum geometrodynamics and prove that the wave function vanishes at the classical singularity.
References
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Measurements of Omega and Lambda from 42 High-Redshift Supernovae
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TL;DR: In this article, the authors used spectral and photometric observations of 10 Type Ia supernovae (SNe Ia) in the redshift range 0.16 " z " 0.62.
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Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
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TL;DR: In this paper, the authors present observations of 10 type Ia supernovae (SNe Ia) between 0.16 0 and 4.0 sigma confidence levels, for two fitting methods respectively.
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Measurements of Omega and Lambda from 42 High-Redshift Supernovae
Saul Perlmutter,Greg Aldering,G. Goldhaber,R. A. Knop,Peter Nugent,P. G. Castro,Susana E. Deustua,Sebastien Fabbro,A. Goobar,D. E. Groom,I. M. Hook,A. G. Kim,M. Y. Kim,Julia C. Lee,Nelson J. Nunes,Reynald Pain,C. R. Pennypacker,R. M. Quimby,C. Lidman,Richard S. Ellis,Michael G. Irwin,Richard G. McMahon,P. Ruiz-Lapuente,Nicholas A. Walton,Bradley E. Schaefer,B. J. Boyle,Alexei V. Filippenko,Thomas Matheson,A. S. Fruchter,Nino Panagia,Heidi Jo Newberg,W. J. Couch +31 more
TL;DR: In this paper, the mass density, Omega_M, and cosmological-constant energy density of the universe were measured by the analysis of 42 Type Ia supernovae discovered by the Supernova Cosmology Project.
Book
A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.