Fetching the paper…

Reading the bibliography…

Polynomial $f(R)$ Palatini cosmology -- dynamical system approach · Around

2017

Polynomial $f(R)$ Palatini cosmology -- dynamical system approach

Szydlowski, Marek, Stachowski, Aleksander

Original
PDF
Post on X

Understand

We investigate cosmological dynamics based on $f(R)$ gravity in the Palatini formulation.

In this study we use the dynamical system methods.
We show that the evolution of the Friedmann equation reduces to the form of the piece-wise smooth dynamical system.
This system is is reduced to a 2D dynamical system of the Newtonian type.

Built on

V. F. Mukhanov and G. V. Chibisov, Quantum Fluctuations and a Nonsingular Universe
1981
Earlier work this paper cites.
A. A. Starobinsky, The Perturbation Spectrum Evolving from a Nonsingular Initially De-Sitter Cosmology and the Microwave Background Anisotropy
1983
Earlier work this paper cites.
L. A. Kofman, A. D. Linde, and A. A. Starobinsky, Inflationary Universe Generated by the Combined Action of a Scalar Field and Gravitational Vacuum Polarization
1985
Earlier work this paper cites.
A. Królak, Towards the proof of the cosmic censorship hypothesis
1986
Earlier work this paper cites.
L. Perko, Differential Equations and Dynamical Systems , 3rd edn. (Springer, New York, 2001)
2001
Earlier work this paper cites.
E. E. Flanagan, Palatini form of 1 / R 1/R gravity
2004
Earlier work this paper cites.
E. E. Flanagan, The conformal frame freedom in theories of gravitation
2004
Earlier work this paper cites.
G. Allemandi, A. Borowiec, M. Francaviglia, Accelerated cosmological models in Ricci squared gravity
2004
Earlier work this paper cites.
J. D. Barrow, Sudden future singularities
2004
Earlier work this paper cites.
S. M. Carroll, A. De Felice, V. Duvvuri, D. A. Easson, M. Trodden, and M. S. Turner, The Cosmology of generalized modified gravity models
2005
Earlier work this paper cites.
G. J. Olmo, Post-Newtonian constraints on f(R) cosmologies in metric and Palatini formalism
2005
Earlier work this paper cites.
G. J. Olmo, The gravity Lagrangian according to solar system experiments
2005
Earlier work this paper cites.
S. Nojiri, S. D. Odintsov, and S. Tsujikawa, Properties of singularities in (phantom) dark energy universe
2005
Earlier work this paper cites.
T. Koivisto, Covariant conservation of energy momentum in modified gravities
2006
Earlier work this paper cites.
V. Faraoni, Solar System experiments do not yet veto modified gravity models
2006
Earlier work this paper cites.

Similar

G. J. Olmo, Limit to general relativity in f(R) theories of gravity
2007
Cited alongside, same era.
M. Bouhmadi-Lopez, P. F. Gonzalez-Diaz, and P. Martin-Moruno, Worse than a big rip?
2008
Cited alongside, same era.
S. Capozziello, M. De Laurentis, S. Nojiri, and S. D. Odintsov, Classifying and avoiding singularities in the alternative gravity dark energy models
Original
2009
Cited alongside, same era.
C. Barragan, G. J. Olmo and H. Sanchis-Alepuz Bouncing cosmologies in Palatini f ⁡ ( R ) f(R) gravity
Original
2009
Cited alongside, same era.
O. Hrycyna, and M. Szydlowski, Non-minimally coupled scalar field cosmology on the phase plane
Original
2009
Cited alongside, same era.

Then

C. Cheng, Q.-G. Huang, and Y.-Z. Ma, Constraints on single-field inflation with WMAP, SPT and ACT data — a last-minute stand before Planck
Original
2013
Later among the works it cites.
Q.-G. Huang, A polynomial f(R) inflation model
Original
2014
Later among the works it cites.
G. J. Olmo and D. Rubiera-Garcia, Nonsingular Black Holes in f ⁡ ( R ) f(R) Theories
Original
2015
Later among the works it cites.
A. Alho, S. Carloni, and C. Uggla, On dynamical systems approaches and methods in f ⁡ ( R ) f(R) cosmology
Original
2016
Later among the works it cites.
S. Capozziello, M. F. De Laurentis, L. Fatibene, M. Ferraris, and S. Garruto, Extended Cosmologies
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

M. P. Dabrowski, J. Garecki, D. B. Blaschke, Conformal transformations and conformal invariance in gravitation

2009

Cited alongside, same era.

T. P. Sotiriou and V. Faraoni, f(R) Theories of Gravity

2010

Cited alongside, same era.

S. A. Appleby, R. A. Battye, and A. A. Starobinsky, Curing singularities in cosmological evolution of F(R) gravity

2010

Cited alongside, same era.

S. Capozziello, P. Martin-Moruno, and C. Rubano, Physical non-equivalence of the Jordan and Einstein frames

2010

Cited alongside, same era.

C. Barragan and G. J. Olmo, Isotropic and Anisotropic Bouncing Cosmologies in Palatini Gravity

2010

Cited alongside, same era.

A. De Felice and S. Tsujikawa, f(R) theories

2010

Cited alongside, same era.

S. V. Ketov and A. A. Starobinsky, Embedding ( R + R 2 R+R^{2} )-Inflation into Supergravity

2011

Cited alongside, same era.

2016

Later among the works it cites.

C. Bambi, A. Cardenas-Avendano, G. J. Olmo and D. Rubiera-Garcia, Wormholes and nonsingular spacetimes in Palatini f ⁡ ( R ) f(R) gravity

2016

Later among the works it cites.

A. Stachowski, M. Szydlowski, Dynamical system approach to running Λ \Lambda cosmological models

2016

Later among the works it cites.

M. Szydlowski, A. Stachowski, A. Borowiec, A. Wojnar, Do sewn up singularities falsify the Palatini cosmology?

2016

Later among the works it cites.

G. F. R. Ellis, E. Platts, D. Sloan, and A. Weltman, Current observations with a decaying cosmological constant allow for chaotic cyclic cosmology

2016

Later among the works it cites.

C. Bejarano, G. J. Olmo and D. Rubiera-Garcia, What is a singular black hole beyond General Relativity?

2017

Closest in time.

T. Pannia et al. Structure of Compact Stars in R-squared Palatini Gravity

2017

Closest in time.

M. Szydlowski, A. Stachowski, A. Borowiec, Emergence of running dark energy from polynomial f(R) theory in Palatini formalism

2017

Closest in time.

G. J. Galloway, E. Ling Some remarks on the C 0 C^{0} -(in)extendibility of spacetimes

2017

Closest in time.

G. J. Olmo and D. Rubiera-Garcia, Nonsingular black holes in quadratic Palatini gravity

2098

Closest in time.