Dimensional Cosmological Model Research Articles

On n-Dimensional Maxwell and Dirac Equations in Curved Space-Time and Its Applications in SO(P,Q) Group Theoretic Image Processing

Maxwell equations in p time and q spatial dimensions are formulated. Properties of the Green’s function for the associated (p,q)-wave operator are derived based on contour integration. The notions of electric and magnetic fields in (p,q)-dimensions is explored by analogy with four dimensional physics and the problem of far field computation of the radiation field generated by charges and currents in \((1,n-1)\) space-time is analyzed. SO(p,q) invariance properties of the Maxwell equations are deduced and used to formulate SO(p,q)-group theoretic image processing problems in (p,q)-dimensions. Dirac’s equation in (p,q)-dimensional space-time is derived using the Clifford algebra of the Dirac gamma matrices. SO(p,q)-invariance of the Dirac equation based on the spinor representation of \(SO(p,q)\) is mentioned. The Maxwell’s equations in (p,q)-dimensional curved space-time is analyzed using perturbation theory in the context of maximally symmetric spaces which play a fundamental role in \((p,q)\)-dimensional cosmological models for homogeneous and isotropic spaces. The Einstein-Maxwell equations for (p,q)-dimensional gravity and electromagnetism is studied and used to derive the equations of motion of point charges carrying mass moving under mutual gravitational and electromagnetic interactions in general relativity. Finally, Dirac’s equation in (p,q)-dimensional curved space-time interacting with the (p,q)-dimensional electromagnetic field is looked at. \(U(1)\)-Gauge, local SO(p,q) Lorentz and diffeomorphism invariance of this equation is analyzed. Local \(SO(p,q)\) invariance of the curved space-time Dirac equation is deduced based on transformation properties of the Dirac matrices under the spinor representation. The appendix presents some applications of group representation theoretic statistical image processing on a manifold to the situation when the image field is described by the six component electromagnetic field tensor on which the Lorentz group acts.

A Probe into a (2 + 1)-Dimensional Combined Cosmological Model in f(R, T) Gravity

This research is an extension of our earlier published (2+1) dimensional cosmological models in f(R,T) gravity with Λ(R,T) (IOP Conf. Ser. J. Phys. Conf. Ser. 2019, 1258, 012026). A different class of cosmological space model is studied under modified theories of f(R,T) gravity, where the cosmological constant Λ is expressed as a function of the Ricci scalar R and the trace of the stress-energy momentum tensor T. We call such a model as “Λ(R,T) gravity”. Such a specific form of Λ(R,T) has been defined in the dust as well as in the perfect fluid case. We intend to search for a combined model that satisfies the equation of state for dark energy matter or quintessence matter or perfect matter fluid. Some geometric and intrinsic physical properties of the model are also described. The energy conditions, pressure and density are discussed both when Λ=Λ(r) is a function of the radial parameter r, as well as when Λ is zero. We study the effective mass function and also the gravitational redshift function, both of which are found to be positive as per the latest observations. The cosmological model is studied in f(R,T) modified theory of gravity, where the gravitational Lagrangian is expressed both in terms of the Ricci scalar R and the trace of the stress-energy tensor T. The equation of state parameter is discussed in terms of ω corresponding to the three cases mentioned above. The behaviour of the cosmological constant is separately examined in the presence of quintessence matter, dark energy matter and perfect fluid matter.

A Life in Mathematical Physics: Conference in Honour of Tekin Dereli

1. IntroductionThe friends and colleagues of Prof. Dr. Tekin Dereli came together to celebrate his 72nd birthday and the 50th year of his mathematical physics career. The three-days event took place online over the Zoom on 26-28 November 2021. His scientific and scholarly achievements, his kindness as a colleague, his thoughtful guidance of students and his service to the physics community in Turkey as a whole and last but not the least his open and easy accessibility to anyone needing his expert counseling have been appreciated by all.¨ We are grateful to the Turkish Academy of Sciences (TUBA) for sponsoring the online, open-access publication of the proceedings as a special issue in The Journal of Physics: Conference Series.2. Biography of Tekin DereliTekin Dereli was born in Ankara in 1949 where he completed his early education at Ankara Science High School in 1967. He earned his Bachelor’s degree in physics with high honors in 1971 at the Middle East Technical University (METU), where he also completed his PhD in 1976, with a thesis entitled “Fermions in Yang-Mills Potentials”. He gave his habilitation in 1981 with a thesis on “Dynamics of Neutrinos in Gravitational Fields” (in Turkish). His academic career began at METU as an instructor in 1973, where he later became an associate professor. He was promoted to professorship in 1987 at Ankara University and then returned to METU in 1993. He was invited to Ko¸c University as Professor of Physics in 2001 where he worked till 2021.Tekin Dereli held various research positions abroad, being always on-leave from METU. These include a visiting scientist position at Yale University during 1974-1975 under the hosting of Feza Gürsey and a research associate position at Brandeis University during 1976-1977 under the hosting of Stanley Deser. He collaborated with Peter C. Aichelburg as Einstein-Memorial Foundation Fellow at the Institute for Theoretical Physics, University of Vienna during 1977-1978. He was SRC Research Associate at Lancaster University between 1979-1981 where a long and fruitful collaboration with Robin W. Tucker has begun. He had been an Associate Member of ICTP between 1986-1991 and Alexander von Humboldt Foundation Fellow at Karlsruhe University during 1988-1989 under the hosting of Julius Wess.Tekin Dereli’s research interests cover a broad range of subjects. He published papers on magnetic monopoles in Yang-Mills gauge field theories, supersymmetry and supergravity, the role of quaternions and octonions in physics. He studied Clifford algebras and spin structures associated with the space-time. He worked on generalised theories of gravity, both in higher and lower dimensions than four, emphasizing their differential geometric gauge structure. In particular he investigated various aspects of black hole and gravitational wave solutions.Furthermore he constructed higher dimensional cosmological models. Tekin Dereli also worked on dualities in physics and mathematics in general and deformation quantisation in the context of the Landau problem.List of Scientific Bibliography of Tekin Dereli (1975-2021), Theses Supervised by Tekin Dereli, Alphabetical List of Contributors, Organising Committee are available in this pdf.

The linear stability of the n + 1 dimensional FLRW spacetimes

Here we prove the linear stability of a family of ‘n + 1’-dimensional cosmological models of general relativity locally isometric to the Friedmann Lemaître Robertson Walker (FLRW) spacetimes including a positive cosmological constant. We show that the solutions to the linearized Einstein–Euler field equations around a class of FLRW metrics with compact spatial topology (negative Einstein spaces and in particular hyperbolic for n = 3) arising from regular initial data remain uniformly bounded and decay to a family of metrics with constant negative spatial scalar curvature. To accomplish the result, we express the Einstein–Euler system in constant mean extrinsic curvature spatial harmonic gauge and linearize about the chosen FLRW background. Utilizing a Hodge decomposition of the fluid’s n-velocity one-form, the linearized system becomes elliptic–hyperbolic (and non-autonomous) in the CMCSH gauge facilitating an application of an energy type argument. Utilizing the estimates derived from the associated elliptic equations, we first prove the uniform boundedness of an energy functional (controlling an appropriate norm of the data) in the expanding direction. Utilizing the uniform boundedness, we later obtain a sharp decay estimate which suggests accelerated expansion (for Λ > 0) of this particular Universe model may be sufficient to control the non-linearities (including possible shock formation) of the Einstein–Euler system in a potential future proof of the fully non-linear stability. In addition, the rotational and harmonic parts of the fluid’s n-velocity field only couple to the remaining degrees of freedom in higher orders, which once again indicates a straightforward extension of current analysis to the fully non-linear setting in the sufficiently small data limit. In addition, our results require a certain integrability condition on the expansion factor and a suitable range of the adiabatic index γ ad ( i.e. in the physically relevant ‘3 + 1’ Universe) if the barotropic equation of state p = (γ ad − 1)ρ is chosen.

Five dimensional cosmological model in the form of Tsallis HDE

Here, in the context of Tsallis holographic dark energy, the Kaluza-Klein five dimensional metric is explored. The time based deceleration parameter is found by solving the field equations using the hybrid scale factor. It depicts the universe from the initial stages of deceleration to the current state of acceleration. The model’s physical features are also addressed.

Accelerating universe in higher dimensional space time: an alternative approach

We have discussed here a higher dimensional cosmological model and explained the recent acceleration with a Chaplygin type of gas. Dimensional reduction of extra space is possible in this case. Our solutions are general in nature because all the well known results of 4D Chaplygin driven cosmology are recovered when $d = 0$. We have drawn the best fit graph using the data obtained by the differential age method (CC) and it is seen that the graph favours only one extra dimension. That means the Chaplygin gas is apparently dominated by a 5D world. Relevant to point out that the final equation in this case are highly nonlinear in nature. Naturally it is not possible to obtain explicit solution of the 4D scale factor with time. To circumvent this difficulty, we consider a first order approximation of the key equation which has made it possible to get time explicit solution of 4D scale factor in exact form as well as the expression of extra dimensions. It may be pointed out that for large four dimensional scale factor this solution mimics $\Lambda$CDM model. An analysis of flip time is also studied both analytically and graphically in some detail. It clearly shows that early \emph{flip} occurs for higher dimensions. It is also seen that the rate of dimensional reduction is faster for higher dimensions. So we may conclude that the effect of compactification of extra dimension helps the acceleration.

Sub-horizon modes and growth index in a linear scalar cosmological perturbations

We test a four dimensional cosmological model embedded in a five dimensional bulk space by means of the dynamical Nash-Greene theorem. In a fluid approach, we apply a joint likelihood analysis to the data with the Markov Chain Monte Carlo (MCMC) method for cosmological parameter estimation. We use recent datasets as the “Gold 2018” growth-rate data, the Planck2018/varLambda CDM data on the cosmic microwave background (CMB) anisotropies, the Baryon acoustic oscillations (BAO) measurements, the Pantheon Supernovae type Ia and the data on the Hubble parameter H(z) with redshift ranging from 0.01< z < 2.3. Performing the Information Criterion (IC) analysis, we find that the present model is in very good agreement with observations with a close statistical equivalence with wCDM cosmologies at 1-sigma level with a slightly larger growth profiles. By modifications of CLASS(EFCLASS) code, we make a comparison between the models on their unlensed CMB TT temperature spectra. Moreover, the proposed model presents a low power spectrum by the reduction of the ISW effect at lower multipoles. We also find that the overall percentage relative difference of the growth index varDelta gamma (%) is up to 1.4% as compared to wCDM pattern in sub-horizon scales.

Five dimensional cosmological model in the form of Tsallis HDE

Five dimensional cosmological model in the form of Tsallis HDE

A higher dimensional cosmological model for the search of dark energy source

With due consideration of reasonable cosmological assumptions within the limit of the present cosmological scenario, we have analyzed a spherically symmetric metric in 5D setting within the framework of Lyra manifold. The model universe is predicted to be a DE model, dominated by vacuum energy. The model represents an oscillating model, each cycle evolving with a big bang and ending at a big crunch, undergoing a series of bounces. The universe is isotropic and undergoes super-exponential expansion. The value of Hubble’s parameter is measured to be [Formula: see text] which is very close to [Formula: see text], the value estimated by the latest Planck 2018 result. A detailed discussion on the cosmological parameters obtained is also presented with graphs.

(2+1) dimensional cosmological models in f(R, T) gravity with (R, T)

We intend to study a new class of cosmological models in f(R, T) modified theories of gravity, hence define the cosmological constant as a function of the trace of the stress energy-momentum-tensor T and the Ricci scalar R, and name such a model Λ(R, T) gravity where we have specified a certain form of Λ(R, T). Λ(R, T) is also defined in the perfect fluid and dust case. Some physical and geometric properties of the model are also discussed. The pressure, density and energy conditions are studied both when Λ is a positive constant and when Λ = Λ(t), i.e a function of cosmological time, t. We study behavior of some cosmological quantities such as Hubble and deceleration parameters. The model is innovative in the sense that it has been described in terms of both R and T and display better understanding of the cosmological observations.

Integrable higher-dimensional cosmology with separable variables in an Einstein-dilaton-antisymmetric field theory

We consider a $D$-dimensional cosmological model with a dilaton field and two $(D-d-1)$-form field strengths which have nonvanishing fluxes in extra dimensions. Exact solutions for the model with a certain set of couplings are obtained by separation of three variables. Some of the solutions describe accelerating expansion of the $d$-dimensional space. Quantum cosmological aspects of the model are also briefly mentioned.

Energy Conditions of the Five Dimensional with NMDC and Acelerating Universe

The Energy condition is studied for five dimensional cosmological model with nonminimal derivative coupling (NMDC) between scalar field and curvature tensor. We assume that the scale factors of three dimensional space (a(t)) and the extra dimension (b(t)) is related by b(t) = (a(t))γ, where γ is a constant. We apply the Null Energy Condition (NEC), Weak Energy Condition (WEC), Strong Energy Condition (SEC) and Dominant Energy Condition (DEC) to our model and investigate some constraint in order the energy condition violated. The constraint that we found is appropriate with cosmological model in which the four-dimensional universe expands with positive acceleration and the extra dimension decays.

Qualitative evolution in $$\textit{f(R)}$$ f ( R ) cosmologies

We investigate the qualitative evolution of (D+1)-dimensional cosmological models in f(R) gravity for the general case of the function f(R). The analysis is specified for various examples, including the (D+1)-dimensional generalization of the Starobinsky model, models with polynomial and exponential functions. The cosmological dynamics are compared in the Einstein and Jordan representations of the corresponding scalar-tensor theory. The features of the cosmological evolution are discussed for Einstein frame potentials taking negative values in certain regions of the field space.

Spherically symmetric five dimensional cosmological model in scale covariant theory of gravitation

A higher dimensional cosmological model filled with perfect fluid source in the frame work of scale covariant theory of gravitation proposed by Canuto et al. (Phys. Rev. Lett. 39:429, 1977) is considered. A determinate solution of the field equations is obtained using a relation between the metric potentials. The physical behavior of the model is discussed by computing the physical and kinematical parameters of the model.

Five dimensional FRW bulk viscous cosmological models in Brans–Dicke theory of gravitation

Five dimensional FRW space-time is considered in the presence of bulk viscous fluid in the frame work of Brans and Dicke (Phys. Rev. 124:925, 1961) scalar–tensor theory of gravitation. To obtain determinate solution of the field equations we have used a power law between scalar field and the scale factor of the universe. Radiating flat, closed and open models are also presented. Physical properties of the models are also discussed.

General solution of a cosmological model induced from higher dimensions using a kinematical constraint

In a recent study Akarsu and Dereli (Gen. Relativ. Gravit. 45:1211, 2013) discussed the dynamical reduction of a higher dimensional cosmological model which is augmented by a kinematical constraint characterized by a single real parameter, correlating and controlling the expansion of both the external (physical) and internal spaces. In that paper explicit solutions were found only for the case of three dimensional internal space ( $$n=3$$ ). Here we derive a general solution of the system using Lie group symmetry properties, in parametric form for arbitrary number $$n=1,2,3,\ldots $$ of internal dimensions. We also investigate the dynamical reduction of the model as a function of cosmic time $$t$$ for various values of $$n$$ and generate parametric plots to discuss cosmologically relevant results.

Holography in (2 + 1)−dimensional Cosmological Model with Generalized Equation of State

In this paper we examine the cosmic holographic principle suggested by Fischler and Susskind (1998) in (2 + 1)−dimensional cosmological models by using generalized equation of state of a more general form, p = (γ−1)(ρ+ρ0), where γ and ρ0 are two parameters. It is shown that the holographic principle is satisfied in all flat and open universes. For (2 + 1)−dimensional closed universe by applying the method proposed by Kaloper, N. and Linde, A. Phys. Rev. D 60, 103509 (1999), we find that the holographic principle cannot be realized in general.

Higher Dimensional Cosmological Models with Bulk Viscous Fluid

In the present study, we have investigated (n + 2)-dimensional non-static FRW models with zero curvature in presence of bulk viscosity in the framework of general relativity. To get deterministic solutions, we employed the conditions ζ = ζ0θ (where ζ0 is a constant) and Λ = aS−m (where a and m are constants). Physical and Kinematical parameters of the models are discussed. In the paper, an attempt is made to compare (n + 2)-dimensional FRW models with four dimensional ones, which for n = 2 reduce to four dimensional FRW models. We also established a relation connecting energy density and the radiation temperature in the radiation dominated era. It is also seen that the presence of bulk viscosity accelerates the expansion of the universe, which is in agreement with recent observations.

Higher dimensional cosmological models: An alternative explanation for late time cosmic acceleration

Einstein's equations have been solved for a homogeneous, anisotropic 1 + 3 + D dimensional universe. We have studied the late time acceleration of the universe in this model. The content of the universe is assumed to be such that it exerts zero pressure in visible dimensions and in extra dimensions, the equation of state is given. The parameters of the model are fixed by comparing with observational data on supernovae. We have shown that late time acceleration occurs in the universe with q0 and ztr being approximately 0.46 and 0.76 respectively.

Cosmological magnetogenesis from extra-dimensional Gauss-Bonnet gravity

Generation of primordial magnetic fields during inflation typically requires the breaking of conformal invariance of the Electromagnetic action. In this paper this has been achieved naturally in a higher dimensional cosmological model with a Gauss-Bonnet term in the action. The evolution of the scale factor of the extra dimension (whose dynamics is influenced by the Gauss-Bonnet term) acts as the cause for the breaking of conformal invariance. Different cases have been investigated, each of which is characterized by the number of higher dimensions, the value of the Gauss-Bonnet parameter, and the cosmological constant. Many of the scenarios considered are highly constrained by the requirements that the cosmic evolution is stable, that the normal dimensions expand and that there is no back reaction due to growing electric fields. However there do exist scenarios which satisfy the above requirements and are well suited for magnetogenesis. In particular, a scenario where the number of extra dimensions $D=4$ and the cosmological constant is non-zero, turns out to be best suited for generating primordial magnetic fields. It is shown that for these values of parameters, a scale invariant magnetic field of the order of $10^{-10}-10^{-9}$ $G$ can be produced. Even in these most favorable scenarios, the higher dimensional space expands during inflation at the same rate as the normal dimension. Hence if a mechanism could freeze the evolution of the higher dimension, this seems to be a viable mechanism to produce acceptable primordial magnetic fields.