Multi-scalar field cosmological model and possible solutions using Noether symmetry approach

2021 ◽  
Author(s):  
Santu Mondal ◽  
Roshni Bhaumik ◽  
Sourav Dutta ◽  
Subenoy Chakraborty
Keyword(s):  
Scalar Field ◽  
Cosmological Model ◽  
Potential Function ◽  
Evolution Equations ◽  
Scalar Fields ◽  
Noether Symmetry ◽  
Kinetic Term ◽  
View Point ◽  
Symmetry Approach ◽  
Augmented Space

In this work, a cosmological model is considered having two scalar fields minimally coupled to gravity with a mixed kinetic term. The model is characterized by the coupling function and the potential function which are assumed to depend on one of the scalar fields. Instead of choosing these functions phenomenologically here, they are evaluated assuming the existence of Noether symmetry. By appropriate choice of a point transformation in the augmented space, one of the variables in the Lagrangian becomes cyclic and the evolution equations become much simpler to have solutions. Finally, the solutions are analyzed from cosmological view point.

scholarly journals Noether symmetry approach for Dirac–Born–Infeld cosmology

2015 ◽  
Vol 12 (05) ◽  
pp. 1550065 ◽  
Author(s):  
Salvatore Capozziello ◽  
Mariafelicia De Laurentis ◽  
Ratbay Myrzakulov
Keyword(s):  
Scalar Field ◽  
Cosmological Model ◽  
Exact Solutions ◽  
Interaction Potential ◽  
Noether Symmetry ◽  
Symmetry Approach ◽  
Canonical Scalar Field

We consider the Noether Symmetry Approach for a cosmological model derived from a tachyon scalar field T with a Dirac–Born–Infeld Lagrangian and a potential V(T). Furthermore, we assume a coupled canonical scalar field ϕ with an arbitrary interaction potential B(T, ϕ). Exact solutions are derived consistent with the accelerated behavior of cosmic fluid.

scholarly journals Quantization of Einstein-aether scalar field cosmology

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
N. Dimakis ◽  
T. Pailas ◽  
A. Paliathanasis ◽  
G. Leon ◽  
Petros A. Terzis ◽  
...  
Keyword(s):  
Scalar Field ◽  
Classical Solution ◽  
Potential Function ◽  
Scalar Fields ◽  
Inflationary Model ◽  
Cosmological Theory ◽  
Local Functions ◽  
Arbitrary Potential ◽  
Scalar Field Cosmology ◽  
First Time

AbstractWe present, for the first time, the quantization process for the Einstein-aether scalar field cosmology. We consider a cosmological theory proposed as a Lorentz violating inflationary model, where the aether and scalar fields interact through the assumption that the aether action constants are ultra-local functions of the scalar field. For this specific theory there is a valid minisuperspace description which we use to quantize. For a particular relation between the two free functions entering the reduced Lagrangian the solution to the Wheeler–DeWitt equation as also the generic classical solution are presented for any given arbitrary potential function.

Brans–Dicke type teleparallel scalar–tensor theory

2017 ◽  
Vol 32 (34) ◽  
pp. 1750183 ◽  
Author(s):  
Mustafa Salti ◽  
Oktay Aydogdu ◽  
Hilmi Yanar ◽  
Figen Binbay
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Scalar Field ◽  
Noether Symmetry ◽  
Scalar Tensor Theory ◽  
Minimal Coupling ◽  
Energy Effect ◽  
New Model ◽  
Symmetry Approach ◽  
Tensor Theory

The teleparallel alternative of general relativity which is based on torsion instead of curvature is considered as the gravitational sector to explore the dark universe. Inspired from the well-known Brans–Dicke gravity, here, we introduce a new proposal for the galactic dark energy effect. The new model includes a scalar field with self-interacting potential and a non-minimal coupling between the gravity and scalar field. Additionally, we analyze the idea via the Noether symmetry approach and thermodynamics.

A study of dynamical equations for non-minimally coupled scalar field using Noether symmetric approach

2016 ◽  
Vol 31 (19) ◽  
pp. 1650116 ◽  
Author(s):  
Sourav Dutta ◽  
Madan Mohan Panja ◽  
Subenoy Chakraborty
Keyword(s):  
Scalar Field ◽  
Infinitesimal Generator ◽  
Einstein Gravity ◽  
Matter Content ◽  
The Self ◽  
Noether Symmetry ◽  
Dynamical Equations ◽  
Augmented Space ◽  
Constants Of Motion ◽  
Scalar Field Cosmology

Non-minimally coupled scalar field cosmology has been studied in this work within the framework of Einstein gravity. In the background of homogeneous and isotropic Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime non-minimally coupled scalar field having self-interacting potential is taken as the source of the matter content. The constraint of imposing Noether symmetry on the Lagrangian of the system not only determines the infinitesimal generator (the symmetry vector) but also the coupling function and the self-interacting potential for the scalar field. By choosing appropriately a point transformation in the augmented space, one of the transformed variables is cyclic for the Lagrangian. Finally, using constants of motion, the solutions are analyzed.

scholarly journals Scalar field cosmology — geometry of dynamics

2014 ◽  
Vol 11 (02) ◽  
pp. 1460012 ◽  
Author(s):  
Marek Szydłowski ◽  
Orest Hrycyna ◽  
Aleksander Stachowski
Keyword(s):  
Phase Space ◽  
Scalar Field ◽  
Dynamical Systems ◽  
Potential Function ◽  
Structural Stability ◽  
Saddle Points ◽  
Scalar Fields ◽  
Fine Tuning ◽  
Scalar Field Cosmology ◽  
Structurally Stable

We study the Scalar Field Cosmology (SFC) using the geometric language of the phase space. We define and study an ensemble of dynamical systems as a Banach space with a Sobolev metric. The metric in the ensemble is used to measure a distance between different models. We point out the advantages of visualization of dynamics in the phase space. It is investigated the genericity of some class of models in the context of fine tuning of the form of the potential function in the ensemble of SFC. We also study the symmetries of dynamical systems of SFC by searching for their exact solutions. In this context, we stressed the importance of scaling solutions. It is demonstrated that scaling solutions in the phase space are represented by unstable separatrices of the saddle points. Only critical point itself located on two-dimensional stable submanifold can be identified as scaling solution. We have also found a class of potentials of the scalar fields forced by the symmetry of differential equation describing the evolution of the Universe. A class of potentials forced by scaling (homology) symmetries was given. We point out the role of the notion of a structural stability in the context of the problem of indetermination of the potential form of the SFC. We characterize also the class of potentials which reproduces the ΛCDM model, which is known to be structurally stable. We show that the structural stability issue can be effectively used is selection of the scalar field potential function. This enables us to characterize a structurally stable and therefore a generic class of SFC models. We have found a nonempty and dense subset of structurally stable models. We show that these models possess symmetry of homology.

scholarly journals Noether symmetry approach in f (T, B) teleparallel gravity with a fermionic field

2021 ◽  
Vol 2090 (1) ◽  
pp. 012058
Author(s):  
Yerlan Myrzakulov ◽  
Sabit Bekov ◽  
Kairat Myrzakulov
Keyword(s):  
Cosmological Model ◽  
Teleparallel Gravity ◽  
Noether Symmetry ◽  
Accelerated Expansion ◽  
Late Time ◽  
Fermionic Field ◽  
Symmetry Approach ◽  
Expansion Of The Universe ◽  
Isotropic Cosmological Model ◽  
The Universe

Abstract In this work, we consider a homogeneous and isotropic cosmological model of the universe in f (T, B) gravity with non-minimally coupled fermionic field. In order to find the form of the coupling function F(Ψ), the potential function V (Ψ) of the fermionic field and the function f (T, B), we found through the Noether symmetry approach. The results obtain are coincide with the observational data that describe the late-time accelerated expansion of the universe.

Classical and quantum cosmology in f(T)-gravity theory: A Noether symmetry approach

2021 ◽  
Author(s):  
Roshni Bhaumik ◽  
Sourav Dutta ◽  
Subenoy Chakraborty
Keyword(s):  
Quantum Cosmology ◽  
Functional Form ◽  
Gravity Theory ◽  
Noether Symmetry ◽  
Field Equations ◽  
Time Model ◽  
Symmetry Approach ◽  
Walker Metric ◽  
Augmented Space ◽  
Space Time Model

In the framework of [Formula: see text]-gravity theory, classical and quantum cosmology has been studied in this work for Friedmann Lemaitre Robertson Walker Metric (FLRW) space-time model. The Noether symmetry, a point-like symmetry of the Lagrangian, is used to the physical system and a specific functional form of [Formula: see text] is determined. A point transformation in the 2D augmented space restricts one of the variables to be cyclic so that the Lagrangian as well as the field equations are simplified so that they are solvable. Lastly, for quantum cosmology, the WD equation is constructed and a possible solution has been evaluated.

scholarly journals COSMOLOGICAL MODEL OF INTERACTING TACHYON FIELD

2012 ◽  
Vol 27 (17) ◽  
pp. 1250086 ◽  
Author(s):  
V. K. SHCHIGOLEV ◽  
M. P. ROTOVA
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Cosmological Model ◽  
Energy Flow ◽  
Field Model ◽  
Scalar Fields ◽  
Tachyon Field ◽  
First Order ◽  
Different Types ◽  
Phantom Fields

In this paper we investigate a tachyon field model in cosmology, provided its interaction with the quintessence or phantom fields. The model takes into account this interaction beyond the usual approach, in which the interaction is phenomenologically described by the energy flow between the matter components. In our model, the interaction of tachyon field with a canonical scalar field is taken into account through the interaction potential in the total Lagrangian of the system, like in the case of two or more canonical scalar fields. We obtain the different types of exact solution for the model by employing the so-called "first order formalism" procedures.

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