General scalar–tensor cosmology: analytical solutions via noether symmetry

The European Physical Journal C, Feb 2017

We analyze the cosmology of a general scalar–tensor theory which encompasses generalized Brans–Dicke theory, Gauss–Bonnet gravity, non-minimal derivative gravity, generalized Galilean gravity and also the general k-essence 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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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. - 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 curre (...truncated)


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Erfan Massaeli, Meysam Motaharfar, Hamid Reza Sepangi. General scalar–tensor cosmology: analytical solutions via noether symmetry, The European Physical Journal C, 2017, pp. 124, Volume 77, Issue 2, DOI: 10.1140/epjc/s10052-017-4682-3