We approach the cosmological inflation thought symmetries of differential equations. We consider the general inflaton field in a homogeneous Friedmann–Lemaître–Robertson–Walker spacetime and with the use of conformal transformations we are able to write the generic algebraic solution for the field equations. We put emphasis on the inflationary models and we show how we can construct new inflationary models from already known models by using symmetry transformations.
REFERENCES
1.
2.
3.
4.
L. V.
Ovsiannikov
, Group Analysis of Differential Equations
(Academic Press
, New York
, 1982
).5.
N. H.
Ibragimov
, CRC Handbook of Lie Group Analysis of Differential Equations, Volume I: Symmetries, Exact Solutions, and Conservation Laws
(CRC Press
, Florida
, 2000
).6.
P. J.
Olver
, Applications of Lie Groups to Differential Equations
(Springer-Verlag
, New York
, 1993
).7.
M.
Crampin
, Rep. Math. Phys.
20
, 31
(1984
).8.
P. G. L.
Leach
, J. Math. Phys.
18
, 1902
(1977
).9.
E.
Noether
, Nachr. d. König. Gesellsch. d. Wiss. zu Göttingen, Math-phys. Klasse
, 235
, (1918
) (translated by M.A. Tavel, arXiv:physics/0503066).10.
11.
G.
Costa
and G.
Fogli
, Symmetry and Group Theory in Particle Physics, Lecture Notes in Physics
(Springer-Verlag
, Berlin
, 2012
).12.
G. S.
Hall
, Symmetries and Curvature Structure in General Relativity, World Scientific Lecture Notes in Physics
46
(World Scientific
, Singapore
, 2004
).13.
D. P.
Mason
and M.
Tsamparlsi
, J. Math. Phys.
26
, 2881
(1985
).14.
H.
Stephani
, D.
Kramer
, M.
MacCallum
, C.
Hoenselsers
, and E.
Herlt
, Exact Solutions of Einstein’s Field Equations
(Cambridge University Press
, New York
, 2009
).15.
G. W.
Bluman
and S.
Kumei
, Symmetries of Differential Equations
(Springer-Verlag
, New York
, 1989
).16.
S. D.
Maharaj
, P. G. L.
Leach
, and R.
Maartens
, Gen. Relativ. Grav.
28
, 35
(1996
).17.
C. Wafo
Soh
and F. M.
Mahomed
, Class. Quantum Grav.
16
, 3553
(1999
).18.
P. A. R.
Ade
, et al. (Planck Collaboration
), A & A
571
, A22
(2014
).19.
P. A. R.
Ade
, et al. (Planck 2015 Collaboration
), A & A
594
, A20
(2016
).20.
A.
Guth
, Phys. Rev. D
23
, 347
(1981
).21.
A. A.
Starobinsky
, Phys. Lett. B
91
, 99
(1980
).22.
A. D.
Linde
, Phys. Lett. B
129
, 177
(1983
).23.
J. D.
Barrow
, Phys. Lett. B
235
, 40
(1990
).24.
G. F. R.
Ellis
and M. S.
Madsen
, Class. Quant. Grav.
8
, 667
(1991
).25.
J. G.
Russo
, Phys. Lett. B
600
, 185
(2004
).26.
S.
Basilakos
, M.
Tsamparlis
and A.
Paliathanasis
, Phys. Rev. D
83
, 103512
(2011
).27.
A.
Paliathanasis
, M.
Tsamplis
, S.
Basilakos
, and J. D.
Barrow
, Phys. Rev. D
91
, 123535
(2015
).28.
A. Yu
Kamenshchik
, E. O.
Pozdeeva
, A.
Tronconi
, G.
Venturi
, and S.Yu
Vernov
, Phys. Part. Nucl.
49
, 1
(2018
).29.
R.
de Ritis
, G.
Marmo
, G.
Platania
, C.
Rubano
, P.
Scudellaro
, and C.
Stornaiolo
, Phys. Rev. D
42
, 1091
(1990
).30.
T.
Christodoulakis
, N.
Dimakis
and P. A.
Terzis
, J. Phys. A: Math. Theor.
47
, 095202
(2014
).31.
S.
Capozziello
and K. F.
Dialektopoulos
, EPJC
78
, 447
(2018
).32.
N.
Dimakis
, A.
Giacomini
, S.
Jamal
, G.
Leon
, and A.
Paliathanasis
, Phys. Rev. D
95
, 064031
(2017
).33.
M.
Tsamparlis
and A.
Paliathanasis
, Symmetry (MDPI)
10
, 233
(2018
).34.
T.
Christodoulakis
, A.
Karagiorgos
and A.
Zampeli
, Symmetry
10
, 70
(2018
).35.
A.
Paliathanasis
, A.
Zampeli
, T.
Christodoulakis
, and M. T.
Mustafa
, Class. Quantum Grav.
35
, 125005
(2018
).36.
37.
M.
Tsamparlis
and A.
Paliathanasis
, Gen. Rel. Gravit.
43
, 1861
(2011
).38.
P. A.
Terzis
, N.
Dimakis
, T.
Christodoulakis
, A.
Paliathanasis
, and M.
Tsamparlis
, J. Geom. Phys.
101
, 52
(2016
).39.
N.
Dimakis
, A.
Karagiorgos
, A.
Zampeli
, A.
Paliathanasis
, T.
Christodoulakis
, and P. A.
Terzis
, Phys. Rev. D
93
, 123518
(2016
).40.
J. D.
Barrow
and A.
Paliathanasis
, Phys. Rev. D
94
, 083518
(2016
).41.
A. R.
Liddle
and D. H.
Lyth
, Phys. Lett. B
291
, 391
(1992
).42.
E. J.
Copeland
, E. W.
Kolb
, A. R.
Liddle
, and J.E.
Lidsey
, Phys. Rev. D
49
, 1840
(1994
).43.
J. D.
Barrow
and A.
Paliathanasis
, Gen. Rel. Grav.
50
, 82
(2018
).
This content is only available via PDF.
© 2019 Author(s).
2019
Author(s)
