Narrow Results

In this paper, we consider a cosmological model of hyperbolic inflation involving two-scalar fields. By examining the Noether symmetries of the corresponding Lagrangian in the context of a spatially flat Friedmann–Lemaître–Robertson–Walker spacetime, we identify conserved quantities or first integrals corresponding to specific cases. These conserved quantities facilitate the derivation of novel solutions to the field equations, offering new perspectives on the dynamics of two-field inflationary models.

We investigate the Noether symmetries of the minimal surface Lagrangian for four classes of metrics in Gödel-type spacetimes. Then, calculating the Noether symmetries for all classes, namely, classes I, II, III and IV, we determine the conserved fields corresponding to each class, allowing us to derive a comprehensive characterization of the minimal surface equations for Gödel-type spacetimes.

The aim of this paper is to explore Noether symmetries of Bianchi type II universe in the modified teleparallel $f(T)$ gravity, where $f(T)$ is a function of the torsion scalar $T$. In a physical context, the selection of Noether symmetries provides constraints that are helpful in building conservation laws. Some of the well-known examples of such laws are the conservation of energy and momentum. In this study, initially, we explore certain classes of Bianchi type II universe considering linear as well as nonlinear $f(T)$ gravity models. In view of such models, equations of motion of the $f(T)$ gravity have been solved in twelve cases. In each of the cases, we apply the definition of Noether symmetry which tends to a set of nineteen equations. Upon solving these equations, we reach the fact that the Bianchi type II universe in the background of $f(T)$ gravity admits only four Noether vector fields (NVFs). As a result, the physical entities which we observe are the conservation of linear and generalized momentum.

Metric variation of higher order theory of gravity requires fixing of the Ricci scalar in addition to the metric tensor at the boundary. Fixing Ricci scalar at the boundary implies that the classical solutions are fixed once and forever to the de Sitter or anti-de Sitter (dS/AdS) solutions. Here, we justify such requirement from the standpoint of Noether symmetry.

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.

We discuss Noether symmetry approach in the modified theory of gravity with Gauss–Bonnet (GB) interaction-f(G) including an ideal fluid in Friedmann–Lemaître–Robertson–Walker (FLRW) background. It yields functional form of f(G) from the symmetry. The existence of Noether symmetry gives the scale factor in two cases, but these are not satisfied by field equations in general. In another case, the solution of field equations shows late-time transition to an accelerating expansion when matter is dust, however the solution including dust and radiation is always in accelerating era.

This paper investigates the existence of Noether symmetries of some anisotropic homogeneous universe models in non-minimally coupled f(R, T) gravity (R and T represent Ricci scalar and trace of the energy–momentum tensor). We evaluate symmetry generators and the corresponding conserved quantities for two models of this theory admitting direct and indirect non-minimal curvature–matter coupling. We also discuss exact solutions for dust as well as non-dust matter distribution and study the physical behavior of some cosmological parameters through these solutions. For dust distribution, the exact solution corresponds to power-law expansion and Einstein universe while exponential expansion appears for non-dust matter. The graphical analysis of these solutions and cosmological parameters provide consistent results with recent observations about accelerated cosmic expansion. We conclude that Noether symmetry generators and conserved quantities exist for both models.

This paper is aimed to study the group invariant solutions of the evolution equations in Brans–Dicke cosmology. In this context, we have considered the flat homogeneous Brans–Dicke (BD) scalar field in the background of flat homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model and have used Lie and Noether symmetry on the augmented system. From Lie symmetry we have determined the unknown potential for two different values of the equation of state parameter w. Then assuming that the Lagrangian admits a Noether symmetry, an analytic solution of the system is obtained in both old and new coordinate systems.

In this paper, we have studied Noether symmetries of locally rotationally symmetric (LRS) Bianchi type V spacetimes. Solving the determining equations of Noether symmetries, it is concluded that the dimension of Noether algebra for these spacetimes is 5, 6, 7, 9, 10, 11 or 17. For all Noether symmetry generators, we have presented the corresponding conservation laws and the Lie algebra. Moreover, some physical implications of the obtained metrics are discussed, which include the study of different energy conditions.

This paper deals with the symmetry analysis of the Einstein Cartan Theory [E. Cartan, C. R. Acad. Sci. (Paris)174, 593 (1922); E. Cartan, Ann. Sci. Ec. Norm. Super40, 325 (1923)] which is an extension of the general relativity and it accounts for the spacetime torsion [S. Basilakos et al., Phys. Rev. D88, 103526 (2013)]. We begin by applying Noether theorem [S. Capozziello, La Rivista del Nuovo Cimento (1978–1999) 19(4), 1 (1996)] to the Lagrangian of the FRW type cosmology with torsion and choose a point transformation: $(a,\varphi ,N)\to (u,v,W)$, such that one of the transformed variables is cyclic [S. Capozziello, M. De Laurentis and S. D. Odintsov, Eur. Phys. J. C72, 2068 (2012)] for the Lagrangian. Then using the conserved charge [S. Capozziello, M. De Laurentis and S. D. Odintsov, Eur. Phys. J. C72, 2068 (2012)], which is obtained by applying Noether theorem, and the constant of motion, we get the solutions and conclude that due to the presence of torsion, the FRW type cosmology is in the de Sitter phase [D. Kranas, C. G. Tsagas, J. D. Barrow and D. Iosifidis, Eur. Phys. J. C79, 341 (2019)].

Under conformal transformation, $f(\Re )$ theory of gravity in Palatini formalism leads to a Brans–Dicke type of scalar-tensor equivalent theory with a wrong sign in the effective kinetic energy term. This means that the effective scalar acts as the dark energy and so late-time cosmic acceleration in the matter-dominated era is accountable. However, we unveil some aspects of Palatini formalism, which reveals the fact that the formalism is not suitable to explain the cosmological evolution of the early universe with $f(\Re )$ gravity alone. Additionally, it is noticed that some authors, in an attempt to explore Noether symmetry of the theory changed the sign of the kinetic term and hence obtained the wrong answer. Here, we make the correction and unmask a very interesting aspect of symmetry analysis. Mathematical inequivalence between Jordan’s and Einstein’s frame in Palatini $f(\Re )$ theory has also been revealed.

The phenomena-like Hawking radiation, the collapse of black holes, and neutron stars decrease the curvature of spacetime continuously with the passage of time. The time conformal factor adds some curvature to nonstatic spacetime. In this article, some novel classes of nonstatic plane-symmetric spacetimes are explored by introducing a time conformal factor in the exact plane-symmetric spacetimes in such a way that their symmetric structure remains conserved. This technique re-scales the energy contents of the corresponding spacetimes, which comes with a re-scaled part in each spacetime. The invariant quantities corresponding to the Noether symmetries are also calculated.

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.

In the background of homogeneous and isotropic flat FLRW spacetime, both classical and quantum cosmologies have been studied for teleparallel dark energy (DE) model. Using Noether symmetry analysis, not only the symmetry vector but also the coupling function in the Lagrangian and the potential of the scalar field have been determined. Also symmetry analysis identifies a cyclic variable in the Lagrangian along the symmetry vector and as a result the Lagrangian simplifies to a great extent so that classical solution is obtained. Subsequently, in quantum cosmology Wheeler–DeWitt (WD) equation has been constructed and the quantum version of the conserved momenta corresponding to Noether symmetry identifies the periodic part of the wave function of the universe and as a result the WD equation becomes solvable. Finally, quantum description shows finite nonzero probability at the classical big bang singularity.

This paper investigates the Noether versus Killing symmetries and their associated conservation laws of Bianchi type-V spacetimes. The study is carried out using the Maple RIFSIMP package, which converts a set of nonlinear differential equations into the reduced involutive form (RIF). This technique generates an RIF tree, where each branch is solved to obtain the explicit forms of Noether symmetries. Separate RIF trees are used to represent each group. We derive a general expression for the Noether symmetry connected to homothety, and then we investigate this Noether symmetry in each separate group. To explore whether dark energy is associated with Bianchi type-V spacetime, we examine the energy density of each spacetime obtained in association with the Ricci scalar. The symmetries of the larger groups, 11- and 17-dimensional, are presented separately in the tables.

This research paper is two-fold. In the first part, we study Noether and Killing symmetries in Bianchi Type-III spacetimes, along with the associated conservation laws. The study uses the Maple RIFSIMP package to transform a set of nonlinear differential equations into a simpler form called the reduced involutive form (RIF). This method generates a RIF tree, where each branch is solved to find the explicit forms of Noether symmetries. We also examine the Noether symmetry related to homothety and analyze this symmetry separately within each group. In the second part, we investigate the behavior of an anisotropic fluid under the influence of a magnetic field, which is assumed to be aligned along the z-axis. The anisotropic fluid model is consistent with the inherent anisotropy of Bianchi Type-III, which may be amplified by the presence of the magnetic field. We also study how this magnetic field affects the fluid’s physical properties and explore the conditions under which the fluid may approach isotropy.

This work deals with chameleon field cosmology (a scalar field nonminimally coupled to cold dark matter) in the background of flat Friedmann–Lemaitre–Robertson–Walker (FLRW) space–time. Both classical and quantum cosmology have been investigated using Noether symmetry analysis of the underlying physical system. The Wheeler–DeWitt (WD) equation has been constructed on the minisuperspace and solutions have been obtained using conserved charge.

The present cosmological model consists of two scalar fields which are minimally coupled to gravity and having a mixed kinetic term. In the background of homogeneous and isotropic FLRW space–time the present model is characterized by the coupling function and the potential function which are functions of one of the scalar fields. Using symmetries of the 3D augmented space, homothetic and killing vectors are determined. Finally, quantum cosmology has been formulated for the present model and the wave function of the universe has been evaluated.

This work deals with Einstein–æther scalar–tensor gravity in the background of homogeneous and isotropic flat FLRW space–time model. The Noether symmetry vector identifies a transformation in the augmented space so that the field equations become solvable. The cosmological solutions are analyzed from the observational point of view. Finally, for quantum cosmology, the Wheeler–DeWitt (WD) equation has been formulated and solutions have been determined by identifying the periodic nature of the wave function using conserved (Noether) charge.

A modified fourth-order gravity theory namely the $f(T,B)$ theory is considered in flat FLRW model to investigate both classical and quantum cosmology. The field equations are reduced to second-order differential equations by considering the technique of Lagrange multiplier. Noether symmetry analysis has been used both for obtaining classical solution and the wave function of the Universe in quantum cosmology. Finally the cosmological solutions are examined from observational view point.