Cosmological singularity theorems for $f(R)$ gravity theories - INSPIRE

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Cosmological singularity theorems for $f(R)$ gravity theories

Ivo Alani
(
- Buenos Aires U.
)
,
Osvaldo Santillan
(
- Buenos Aires, CONICET
)

Feb 13, 2016

24 pages

Published in:

JCAP 05 (2016) 023

Published: May 10, 2016

e-Print:

1602.04397 [gr-qc]

DOI:

10.1088/1475-7516/2016/05/023

View in:

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Abstract: (IOP)

In the present work some generalizations of the Hawking singularity theorems in the context of f(R) theories are presented. The main assumptions are: the matter fields stress energy tensor satisfies the condition (Tij−(gij/2)T)kikj ≥ 0 for any generic unit time like field ki, the scalaron takes bounded positive values during its evolution and the resulting space time is globally hyperbolic. Then, if there exist a Cauchy hyper-surface Σ for which the expansion parameter θ of the geodesic congruence emanating orthogonally from Σ satisfies some specific bounds, then the resulting space time is geodesically incomplete. Some mathematical results of reference [92] are very important for proving this. The generalized theorems presented here apply directly for some specific models such as the Hu-Sawicki or Starobinsky ones [27,38]. For other scenarios, some extra assumptions should be implemented in order to have a geodesically incomplete space time. The hypothesis considered in this text are sufficient, but not necessary. In other words, their negation does not imply that a singularity is absent.

Note:

An improved version is published in JCAP 05 (2016) 023

singularity
cosmological model
space-time
geodesic
gravitation: model
gravitation: f(R)
scalaron

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[1]

Discovery of a supernova explosion at half the age of the Universe and its cosmological implications

Supernova Cosmology Project

Collaboration

•

S. Perlmutter
(
- LBL, Berkeley and
- UC, Berkeley, CfPA
)

et al.

- Nature 391 (1998) 51-54
•
e-Print:
- astro-ph/9712212
•
DOI:
- 10.1038/34124

[1]

Observational evidence from supernovae for an accelerating universe and a cosmological constant

et al.

- Astron.J. 116 (1998) 1009-1038
•
e-Print:
- astro-ph/9805201
•
DOI:
- 10.1086/300499

[2]

Cosmological Consequences of a Rolling Homogeneous Scalar Field

Bharat Ratra
(
- Princeton U.
)
,
P.J.E. Peebles
(
- Princeton U.
)

- Phys.Rev.D 37 (1988) 3406
•
DOI:
- 10.1103/PhysRevD.37.3406

[2]

Cosmology with a Time Variable Cosmological Constant

P.J.E. Peebles
(
- Princeton U.
)
,
Bharat Ratra
(
- Princeton U.
)

- Astrophys.J.Lett. 325 (1988) L17
•
DOI:
- 10.1086/185100

[2]

Dynamical Lambda models of structure formation

Kimberly Coble
(
- Chicago U., Astron. Astrophys. Ctr. and
- Fermilab
)
,
Scott Dodelson
(
- Fermilab
)
,
Joshua A. Frieman
(
- Chicago U., Astron. Astrophys. Ctr. and
- Fermilab
)

- Phys.Rev.D 55 (1997) 1851-1859
•
e-Print:
- astro-ph/9608122
•
DOI:
- 10.1103/PhysRevD.55.1851

[3]

CDM models with a smooth component

Michael S. Turner
(
- Chicago U. and
- Fermilab and
- Chicago U., EFI
)
,
Martin J. White
(
- Fermilab and
- Chicago U., EFI
)

- Phys.Rev.D 56 (1997) 8, R4439
•
e-Print:
- astro-ph/9701138
•
DOI:
- 10.1103/PhysRevD.56.R4439

[3]

Cosmological imprint of an energy component with general equation of state

R.R. Caldwell
(
- Pennsylvania U.
)
,
Rahul Dave
(
- Pennsylvania U.
)
,
Paul J. Steinhardt
(
- Pennsylvania U.
)

- Phys.Rev.Lett. 80 (1998) 1582-1585
•
e-Print:
- astro-ph/9708069
•
DOI:
- 10.1103/PhysRevLett.80.1582

[4]

Cosmological Structure Formation from Soft Topological Defects

Christopher T. Hill
(
- Fermilab
)
,
David N. Schramm
(
- Fermilab and
- Chicago U.
)
,
James N. Fry
(
- Florida U.
)

- Comments Nucl.Part.Phys. 19 (1989) 1, 25-39,

[4]

Late time cosmological phase transitions. 1. Particle physics models and cosmic evolution

- Phys.Rev.D 46 (1992) 1226-1238
•
DOI:
- 10.1103/PhysRevD.46.1226

[4]

Cosmology with ultralight pseudo Nambu-Goldstone bosons

Joshua A. Frieman
(
- Fermilab and
- Chicago U., Astron. Astrophys. Ctr.
)
,
Christopher T. Hill
(
- Fermilab
)
,
Albert Stebbins
(
- Fermilab
)
,
Ioav Waga
(
- Fermilab and
- Rio de Janeiro Federal U.
)

- Phys.Rev.Lett. 75 (1995) 2077-2080
•
e-Print:
- astro-ph/9505060
•
DOI:
- 10.1103/PhysRevLett.75.2077

[5]

The Cosmological constant

- Ann.Rev.Astron.Astrophys. 30 (1992) 499-542
•
DOI:
- 10.1146/annurev.aa.30.090192.002435

[6]

Galactic dynamics, Princeton, Princeton University Press

J. Binney
,
S. Tremaine

[6]

The Universal rotation curve of spiral galaxies: 1. The Dark matter connection

Massimo Persic
(
- Trieste Observ. and
- SISSA, Trieste
)
,
Paolo Salucci
(
- SISSA, Trieste
)
,
Fulvio Stel
(
- Trieste U., Astron. Dept.
)

- Mon.Not.Roy.Astron.Soc. 281 (1996) 27
•
e-Print:
- astro-ph/9506004
•
DOI:
- 10.1093/mnras/278.1.27

[6]

The Dark matter distribution in disk galaxies

Annamaria Borriello
(
- SISSA, Trieste
)
,
Paolo Salucci
(
- SISSA, Trieste
)

- Mon.Not.Roy.Astron.Soc. 323 (2001) 285
•
e-Print:
- astro-ph/0001082
•
DOI:
- 10.1046/j.1365-8711.2001.04077.x

[7]

Dark matter and background light

James M. Overduin
(
- Stanford U., HEPL
)
,
P.S. Wesson
(
- Waterloo U.
)

- Phys.Rept. 402 (2004) 267-406
•
e-Print:
- astro-ph/0407207
•
DOI:
- 10.1016/j.physrep.2004.07.006

[8]

On Einstein clusters as galactic dark matter halos

C.G. Boehmer
(
- Portsmouth U., ICG
)
,
T. Harko
(
- Hong Kong U.
)

- Mon.Not.Roy.Astron.Soc. 379 (2007) 393-398
•
e-Print:
- 0705.1756
•
DOI:
- 10.1111/j.1365-2966.2007.11977.x

[8]

Late time cosmological phase transition and galactic halo as Bose liquid

Sang-Jin Sin
(
- Florida U.
)

- Phys.Rev.D 50 (1994) 3650-3654
•
e-Print:
- hep-ph/9205208
•
DOI:
- 10.1103/PhysRevD.50.3650

[8]

Dark matter as a cosmic Bose-Einstein condensate and possible superfluid

- Gen.Rel.Grav. 34 (2002) 633-649
•
DOI:
- 10.1023/A:1015934027224

[9]

Bose Einstein condensation as dark energy and dark matter

e-Print:
- astro-ph/0403571

[9]

Bose-Einstein condensation, dark matter and acoustic peaks

F. Ferrer
(
- Oxford U.
)
,
J.A. Grifols
(
- Barcelona, IFAE
)

- JCAP 12 (2004) 012
•
e-Print:
- astro-ph/0407532
•
DOI:
- 10.1088/1475-7516/2004/12/012

[9]

Can dark matter be a Bose-Einstein condensate?

C.G. Boehmer
(
- Portsmouth U., ICG
)
,
T. Harko
(
- Hong Kong U.
)

- JCAP 06 (2007) 025
•
e-Print:
- 0705.4158
•
DOI:
- 10.1088/1475-7516/2007/06/025

[10]

Direct detection constraints on superheavy dark matter

- Phys.Rev.Lett. 90 (2003) 221301,
- Phys.Rev.Lett. 91 (2003) 229903 (erratum)
•
e-Print:
- astro-ph/0301188
•
DOI:
- 10.1103/PhysRevLett.90.221301

[11]

The Confrontation between general relativity and experiment

Clifford M. Will
(
- Washington U., St. Louis
)

- Living Rev.Rel. 9 (2006) 3
•
e-Print:
- gr-qc/0510072
•
DOI:
- 10.12942/lrr-2006-3

[12]

Is Cosmic Speed-Up Due to New Gravitational Physics?

Sean M. Carroll
(
- Chicago U., EFI and
- Chicago U. and
- Chicago U., KICP
)
,
Vikram Duvvuri
(
- Chicago U., EFI and
- Chicago U. and
- Chicago U., KICP
)
,
Mark Trodden
(
- Syracuse U.
)
,
Michael S. Turner
(
- Chicago U., EFI and
- Chicago U. and
- Chicago U., KICP and
- Chicago U., Astron. Astrophys. Ctr. and
- Fermilab
)

- Phys.Rev.D 70 (2004) 043528
•
e-Print:
- astro-ph/0306438
•
DOI:
- 10.1103/PhysRevD.70.043528

[13]

A New Type of Isotropic Cosmological Models Without Singularity

Alexei A. Starobinsky
(
- Cambridge U. and
- Landau Inst.
)

- Phys.Lett.B 91 (1980) 99-102,
- Adv.Ser.Astrophys.Cosmol. 3 (1987) 130-133,
•
DOI:
- 10.1016/0370-2693(80)90670-X

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