General scalar–tensor cosmology: analytical solutions via noether symmetry
Eur. Phys. J. C
General scalar-tensor cosmology: analytical solutions via noether symmetry
Erfan Massaeli 0
Meysam Motaharfar 0
Hamid Reza Sepangi 0
0 Department of Physics, Shahid Beheshti University , G. C., Evin, Tehran 19839 , Iran
We analyze the cosmology of a general scalartensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galilean gravity and also the general kessence type models. Instead of taking into account phenomenological considerations we adopt a Noether symmetry approach, as a physical criterion, to single out the form of undetermined functions in the action. These specified functions symmetrize equations of motion in the simplest possible form which result in exact solutions. Demanding de Sitter, power-law and bouncing universe solutions in the absence and presence of matter density leads to exploring new as well as well-investigated models. We show that there are models for which the dynamics of the system allows a transition from a decelerating phase (matter dominated era) to an accelerating phase (dark energy epoch) and could also lead to general Brans-Dicke with string correction without a self-interaction potential. Furthermore, we classify the models based on a phantom or quintessence dark energy point of view. Finally, we obtain the condition for stability of a de Sitter solution for which the solution is an attractor of the system.
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of ultraviolet scales are concerned. The consequences of
these shortcomings and most importantly the absence of
an ultimate quantum theory of gravity provides an
incentive to consider modifications to GR in order to construct
a semi-classical description toward quantization. These
theories are aimed at addressing gravitational interactions by
adding physically motivated, non-minimally coupled scalar
fields or higher-order curvature invariants, like the inclusion
of Gauss–Bonnet term in the Einstein–Hilbert action.
Therefore, to obtain the low-energy effective action of quantum
gravity on scales closer to Planck scale, one needs the
inclusion of such corrective terms [1–4].
The enthusiasm in considering such an approach in the
cosmology of early universe stems from the fact that extended
theories of gravity (ETG) can “naturally” reproduce
inflationary behavior due to the existence of a non-minimal coupled
scalar field to curvature, its higher orders and the kinetic term.
Therefore, such models are able to overcome the
aforementioned shortcomings of the standard model of cosmology [4]
and seem also capable of justifying several observational data
coming from various sources. In addition, the Mach principle,
which states that a local inertial frame is determined by the
average motion of remote astronomical objects, has brought
about further incentives to modify GR [5]. Consequently, the
gravitational coupling can be scale-dependent whereby the
concept of inertia and the equivalence principle have to be
revised, since there is no a priori reason to constrain the
gravitational Lagrangian to a linear function of the Ricci scalar
R, minimally coupled to matter fields [6–13].
In recent years, ETGs have been playing an absorbing role
in depicting today’s observable universe. In fact, the
spectacular amount of high quality data produced over the past few
decades seem to shed new light on the effective picture of
the universe. Type Ia Supernovae (SNeIa) [14–16],
largescale structure (LSS) [17,18], baryon acoustic oscillations
(BAO) [19,20], anisotropies in the cosmic microwave
background radiation (CMBR) [21–23], and matter power
spectrum extracted from the wide and deep galaxy surveys
provide incontrovertible evidence whereby the standard model
of cosmology should radically be revised at cosmological
scales. Specifically, the ubiquitous CDM model indicates
that the baryon contribution to the total matter-energy
budget is roughly around (∼4%), while cold dark matter (CDM)
represents the bulk of the clustered large-scale structure by
(∼25%) and the so-called cosmological constant plays the
role of dark energy (DE) contributing (∼75%) [24,25] to the
total matter-energy supply.
The incentive to search for alternative models of dark
energy [26–28] stems from the fact that the CDM model
is affected by strong theoretical shortcomings [29] whereas
the model is incredibly compatible with a broad range of
data [30]. The validity of GR at large astrophysical and
cosmological scales has never been confirmed but merely
assumed [31]. Nonetheless dark energy models are
primarily built on the implicit assumption that Einstein’s GR is
the correct theory of gravity. Therefore, it is conceivable
that both the existing cosmic acceleration and the missing
relic are nothing else but a signal of a breakdown of GR. In
this sense, GR could fail in representing self-consistent
pictures both at ultraviolet (early universe) and infrared scales
(late universe). Hence, one possible way to explain the
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