arXiv subjects

Hossein Shojaie

Publications and source records attributed to Hossein Shojaie.

14 recordsLinked to original sources

arXiv2023

A spherically symmetric gravitational solution of nearly conformally flat metric~measure~space

In this manuscript, we study the nearly flat approximation of a conformally invariant gravitational theory in metric measure space (MMS). In addition, we investigate the transformation of the energy-momentum tensor in this context and obtain the vacuum solution of MMS and its weak field limit in the spherically symmetric coordinates. We show that while it is already a vacuum solution, it can simulate dark matter when restricted to the framework of general relativity, i.e., a symmetry-broken conformal frame. This is done by employing a density function which is an essential part of MMS. We derive an equation for the density function for a general profile of a rotation curve obtained from observations. Specifically, the density function corresponding to two well-known profiles PSS and NFW are provided.

gr-qc↗

arXiv2021

Study of the de Sitter space-time and its behavior at infinity

The aim of this manuscript is to review the studies about de Sitter solution and the null infinity of asymptotically flat and de Sitter space-times. Thus, after introducing the de Sitter space-time, the symmetry group is described. Also precise definitions of asymptotically flat and de Sitter space-times are reviewed. Henceforth, the null infinities and the asymptotic symmetry groups of these two space-times are considered, which lead to the Fefferman-Graham approach and the Penrose-Newman formalism.

gr-qc↗

arXiv2020

Asymptotically flat boundary conditions for the $U(1)^3$ model for Euclidean Quantum Gravity

A generally covariant $U(1)^3$ gauge theory describing the $G_N \to 0$ limit of Euclidean general relativity is an interesting test laboratory for general relativity, specially because the algebra of the Hamiltonian and diffeomorphism constraints of this limit is isomorphic to the algebra of the corresponding constraints in general relativity. In the present work, we study boundary conditions and asymptotic symmetries of the $U(1)^3$ model and show that while asymptotic spacetime translations admit well-defined generators, boosts and rotations do not. Comparing with Euclidean general relativity, one finds that exactly the non-Abelian part of the $SU(2)$ Gauss constraint which is absent in the $U(1)^3$ model plays a crucial role in obtaining boost and rotation generators.

gr-qc↗

arXiv2019

Asymptotic conformal symmetry at spatial infinity

In this paper, the effects of adding spatial conformal symmetry to the asymptotic symmetry group of an asymptotically conformally flat spacetime are studied. It is shown that, in addition to the BMS group, only the dilations of the spatial conformal generators keep the corresponding boundary conditions conformally invariant under hypersurface deformations. We prove that in order to attain (i) a well-defined symplectic structure and (ii) a finite and (iii) integrable conserved charge, these conditions are satisfied simultaneously when admitting Regge-Teitelboim and twisted Henneaux-Troessaert parity conditions, where the latter also contain supertranslation invariance. The conserved dilation charge contains nonzero terms independent of the field variables, giving a nonvanishing effect on the boundary. The dilation symmetry also modifies the ADM mass, which is another physical effect of the conformal symmetry.

gr-qc↗

arXiv2019

Large Gauge Symmetries of an Asymptotically de Sitter Horizon: An Extended First Law of Thermodynamics

In this paper, we show that a universe with a dynamical cosmological constant approaching pure de Sitter at timelike infinity, enjoys an infinite dimensional symmetry group at its horizon. This group is larger than the usual $SO(4,1)$ of pure de Sitter. The charges associated with the asymptotic symmetry generators are non-integrable, and we demonstrate that they promote an extended version of the first law of thermodynamics. This contains four pairs of conjugate variables. The pair $(Θ,Λ)$ corresponding to the change in the cosmological constant and its conjugate volume $Θ$. The contribution of the surface tension of the horizon and its conjugate parameter surface area make a pair $(σ, A)$. The usual conjugate variables $ (T, S) $, $ (Ω, J) $ and a term $ \partial_v δS $ corresponding to entropy production, are included. In addition, this extended first law describes the non-conservative behaviour of the asymptotic charges in non-equilibrium.

hep-th↗

arXiv2016

Metric Measure Space as a Framework for Gravitation

In this manuscript, we show how conformal invariance can be incorporated in a classical theory of gravitation, in the context of metric measure space. Metric measure space involves a geometrical scalar $f$, dubbed as density function, which here appears as a conformal degree of freedom. In this framework, we present conformally invariant field equations, the relevant identities and geodesic equations. In metric measure space, the volume element and accordingly the operators with integral based definitions are modified. For instance, the divergence operator in this space differs from the Riemannian one. As a result, a gravitational theory formulated in this space has a generalized second Bianchi identity and a generalized conservation of energy-momentum tensor. It is shown how, by using the generalized identity for conservation of energy-momentum tensor, one can obtain a conformally invariant geodesic equation. By comparison of the geodesic equations in metric measure space with the Bohmian trajectories, in both relativistic and non-relativistic regimes, a relation between density function $f$ and the quantum potential is proposed. This suggests metric measure space to be considered as a suitable framework for geometric description of Bohm's quantum mechanics. On the other hand, as it is known, Weyl geometry is one of the main approaches to construct conformally invariant gravitational models. Regarding the fact that the connection in the integrable Weyl space is modified and in metric measure space remains the same as it is in the Riemann space, the mathematical analogy between these two spaces is also discussed.

gr-qc↗

arXiv2016

An FLRW Cosmology with a Chameleon Field

In this manuscript, the field equations of a chameleon field in which the matter Lagrangian term is a general function of the scalar field as well as matter field, are derived. The equations are then expressed in Friedmann--Lemaître--Robertson--Walker~(FLRW) framework and the associated phase portraits and a power law solution are discussed in details. It is shown that why non-minimal coupling between the chameleon and matter fields leads to an energy transfer between the fields which consequently, affects the expansion rate of the universe. The transfer direction is determined by the second law of thermodynamics. The solution indicates that an accelerating expansion of the universe can be described as a result of the energy flow from the chameleon field to matter field.

gr-qc↗

arXiv2015

A Conformally Invariant Theory of Gravitation in Metric Measure Space

In this manuscript, a conformally invariant theory of gravitation in the context of metric measure space is studied. The proposed action is invariant under both diffeomorphism and conformal transformations. Using the variational method, a generalization of the Einstein equation is obtained, wherein the conventional tensors are replaced by their conformally invariant counterparts, living in metric measure space. The invariance of the geometrical part of the action under a diffeomorphism leads to a generalized contracted second Bianchi identity. In metric measure space, the covariant derivative is the same as it is in the Riemannian space. Hence, in contrast to the Weyl space, the metricity and integrability are maintained. However, it is worth noting that in metric measure space the divergence of a tensor is not simply the contraction of the covariant derivative operator with the tensor that it acts on. Despite the fact that metric measure space and integrable Weyl space, are constructed based on different assumptions, it is shown that some relations in these spaces, such as the contracted second Bianchi identity, are completely similar.

gr-qc↗

arXiv2012

Pioneer Anomaly in Perturbed FRW Metric

In this manuscript, it is shown that the Pioneer anomaly is the local evidence for an expanding universe. In other words, its value is a direct measure of the Hubble constant while its sign shows the expanding behavior of the dynamics of the universe. This analysis is obtained by studying the radial geodesic deviation of the light rays in the perturbed Friedmann-Robertson-Walker metric in the Newtonian gauge.

astro-ph.CO↗

arXiv2012

The Variable-c Cosmology as a Solution to Pioneer Anomaly

It is shown that the Pioneer anomaly is a natural consequence of variable speed of light cosmological models wherein the speed of light is assumed to be a power-law function of the scale factor (or cosmic time). In other words, the Pioneer anomaly can be regarded as a non-gravitational effect of the continuously decreasing speed of light which indicates itself as an anomalous light propagation time delay in local frames. This time delay is accordingly interpreted as an additional Doppler blue shift.

astro-ph.CO↗

arXiv2011

On Dynamics of Brans--Dicke Theory of Gravitation

We study longstanding problem of cosmological clock in the context of Brans-Dicke theory of gravitation. We present the Hamiltonian formulation of the theory for a class of spatially homogenous cosmological models. Then, we show that formulation of the Brans-Dicke theory in the Einstein frame allows how an identification of an appropriate cosmological time variable, as a function of the scalar field in the theory, can be emerged in quantum cosmology. The classical and quantum results are applied to the Friedmann-Robertson-Walker cosmological models.

gr-qc↗

arXiv2010

FRW Cosmology From Five Dimensional Vacuum Brans-Dicke Theory

We follow approach of induced matter theory for 5D vacuum BD, introduce induced matter and potential in 4D hypersurfaces, and employ generalized FRW type solution. We confine ourselves to scalar field and scale factors be functions of the time. This makes the induced potential, by its definition, vanishes. When the scale factor of fifth dimension and scalar field are not constants, 5D eqs for any geometry admit a power law relation between scalar field and scale factor of fifth dimension. Hence the procedure exhibits that 5D vacuum FRW like eqs are equivalent, in general, to corresponding 4D vacuum ones with the same spatial scale factor but new scalar field and coupling constant. We show that 5D vacuum FRW like eqs or its equivalent 4D vacuum ones admit accelerated solutions. For constant scalar field, eqs reduce to usual FRW eqs with typical radiation dominated universe. For this situation we obtain dynamics of scale factors for any geometry without any priori assumption. For nonconstant scalar fields and spatially flat geometries, solutions are found to be power law and exponential ones. We also employ weak energy condition for induced matter, that allows negative/positive pressures. All types of solutions fulfill WEC in different ranges. The power law solutions with negative/positive pressures admit both decelerating and accelerating ones. Some solutions accept shrinking extra dimension. By considering nonghost scalar fields and recent observational measurements, solutions are more restricted. We illustrate that accelerating power law solutions, which satisfy WEC and have nonghost fields, are compatible with recent observations in ranges -4/3 < ω</- -1.3151 and 1.5208 </- n < 1.9583 for dependence of fifth dimension scale factor with usual scale factor. These ranges also fulfill condition nonghost fields in the equivalent 4D vacuum BD eqs.

gr-qc↗

arXiv2007

A varying-c cosmology

We develop a new model for the Universe based on two key assumptions: first, the inertial energy of the Universe is a constant, and second, the total energy of a particle, the inertial plus the gravitational potential energy produced by the other mass in the Universe, is zero. This model allows the speed of light and the total mass of the Universe to vary as functions of cosmological time, where we assume the gravitational constant to be a constant. By means of these assumptions, the relations between the scale factor and the other parameters are derived. The Einstein equation, by making it compatible with varying-$c$, is used and the Friedmann equations in this model are obtained. Assuming the matter content of the Universe to be perfect fluids, the model fixes $γ$ to be 2/3. That is, the whole Universe always exhibits a negative pressure. Moreover, the behavior of the scale factor is the same for any value of the curvature. It is also shown that the Universe began from a big bang with zero initial mass and expands forever even with positive curvature, but it is always decelerating. At the end, solutions to some famous problems, mainly of the standard big bang model, and an explanation for the observational data about the accelerating Universe are provided.

gr-qc↗

arXiv2006

A cosmology with variable c

A new varying-$c$ cosmological model constructed using two additional assumptions, which was introduced in our previous work, is briefly reviewed and the dynamic equation of the model is derived distinctly from a semi-Newtonian approach. The results of this model, using a $Λ$ term and an extra energy-momentum tensor, are considered separately. It is shown that the Universe began from a hot Big Bang and expands forever with a constant deceleration parameter regardless of its curvature. Finally, the age, the radius, and the energy content of the Universe are estimated and some discussion about the type of the geometry of the Universe is provided.

gr-qc↗