Noncommutative Double Scalar Fields in FRW Cosmology as Cosmical Oscillators

We investigate effects of noncommutativity of phase space generated by two scalar fields conformally coupled to curvature in FRW cosmology. We restrict deformation of minisuperspace to noncommutativity between scalar fields and between their canonical conjugate momenta. The investigation is carried out by means of comparative analysis of mathematical properties of time evolution of variables in classical model and wave function of universe in quantum level. We find that impose of noncommutativity causes more ability in tuning time solutions of scalar fields and hence, has important implications in evolution of universe. We get that noncommutative parameter in momenta sector is the only responsible parameter for noncommutative effects in flat universes. A distinguishing feature of noncommutative solutions of scalar fields is that they can be simulated with well known harmonic oscillators, depend on values of spatial curvature. Namely free, forced and damped harmonic oscillators corresponding to flat, closed and open universes. In this respect, we call them cosmical oscillators. In closed universes, when noncommutative parameters are small, cosmical oscillators have analogous effect with familiar beating effect in sound phenomenon. The existence of non-zero constant potential does not change solutions of scalar fields, but modifies scale factor. An interesting feature of well behaved solutions of wave functions is that functional form of its radial part is the same as commutative ones provided that given replacement of constants, caused by noncommutative parameters, is performed. Further, Noether theorem has been employed to explore effects of noncommutativity on underlying symmetries in commutative frame. Two of six Noether symmetries of flat universes, in general, are retained in noncommutative case, and one out of three ones in non flat universes.Comment: 21 pages, 5 figure

Thermodynamic Properties of Regular Phantom Black Hole

The Regular Phantom Black Holes (RPBH)s are of theoretical and observational importance, and some properties have been studied. In this work, we study some of the thermodynamical properties such as entropy, and temperature, ... in three asymptotically spacetimes: flat, de--Sitter (dS), and Anti-de Sitter (AdS). Many of the RPBH properties, including horizon radius, are (directly or indirectly) dependent on a scale parameter b. Due to the slightly different structure from Schwarzschild--metrics, the method to express relations between thermodynamical variables requires a new function of the scale parameter. We also imply the local and global thermodynamic stability through the Heat Capacity (HC) and Gibbs Energy (GB), respectively. The calculations and graphs show the results, in the flat background, are very similar to Schwarzschild ones. Also, some results show that the asymptotically AdS-RPBH is more compatible with physical laws than the dS and flat backgrounds

Magnetic Dipole and Noncommutativity

The noncommutativity concept has wide range of applications in physical and mathematical theories. Noncommutativity in the position-time coordinates concerns the microscale structure of space-time. the noncommutativity is an intrinsic property of the space-time and it could be different from usual properties when one encounters the high energy phenomena. on the other hand, the space-time is assumed to be as a background for the occurrence of physical events. therefore, it is not far-fetched to expect the emergence of new physics or dynamics when the fine geometric structure of space-time is deformed. In this work, we consider a common form of this deformation and try to answer the question as: a physical (or dynamical) model can be described by the noncommutative effects?. This can also be asked this way: dose the noncommutativity could have a physical manifestations in the nature?. Our model here is a magnetic dipole.Comment: 17 pages, 4 figure

About the Power Spectrum Of Primordial Gravitational Waves

The primordial gravitational waves have been generated by inflationary amplification of the primordial (quantum) fluctuations. It is true that they have not been recorded directly so far, but their spectrum can help a lot in solving the basic puzzles of the early universe as Inflation (high) energy scale. In the present work, we give a straightforward method to calculate the spectral energy density of the relic gravitons different from that used in e. g. \cite{ mirza04,Latham 2005, Yuki 2006}. The evolution equations are written in terms of the scale factor (instead of conformal time) and are obtained through the Lagrange formalism (instead of the transfer function). The presence of the Hubble parameter allows to calculate the power spectrum in the different dynamical regimes. The corresponding diagram shows in the universe including Cosmological Constant the spectral energy density is noticeably enhanced.Comment: 6 pages, 1 figur, 1 tabl

About Gravitomagnetism

The gravitomagnetic field is the force exerted by a moving body on the basis of the intriguing interplay between geometry and dynamics which is the analog to the magnetic field of a moving charged body in electromagnetism. The existence of such a field has been demonstrated based on special relativity approach and also by special relativity plus the gravitational time dilation for two different cases, a moving infinite line and a uniformly moving point mass, respectively. We treat these two approaches when the applied cases are switched while appropriate key points are employed. Thus, we demonstrate that the strength of the resulted gravitomagnetic field in the latter approach is twice the former. Then, we also discuss the full linearized general relativity and show that it should give the same strength for gravitomagnetic field as the latter approach. Hence, through an exact analogy with the electrodynamic equations, we present an argument in order to indicate the best definition amongst those considered in this issue in the literature. Finally, we investigate the gravitomagnetic effects and consequences of different definitions on the geodesic equation including the second order approximation terms.Comment: 16 pages, a few amendments have been performed and a new section has been adde

Noncommutativity Effects in FRW Scalar Field Cosmology

We study effects of noncommutativity on the phase space generated by a non-minimal scalar field which is conformally coupled to the background curvature in an isotropic and homogeneous FRW cosmology. These effects are considered in two cases, when the potential of scalar field has zero and nonzero constant values. The investigation is carried out by means of a comparative detailed analysis of mathematical features of the evolution of universe and the most probable universe wave functions in classically commutative and noncommutative frames and quantum counterparts. The influence of noncommutativity is explored by the two noncommutative parameters of space and momentum sectors with a relative focus on the role of the noncommutative parameter of momentum sector. The solutions are presented with some of their numerical diagrams, in the commutative and noncommutative scenarios, and their properties are compared. We find that impose of noncommutativity in the momentum sector causes more ability in tuning time solutions of variables in classical level, and has more probable states of universe in quantum level. We also demonstrate that special solutions in classical and allowed wave functions in quantum models impose bounds on the values of noncommutative parameters.Comment: 13 pages, 5 figure

The Power Spectrum Of Gravitational Waves In Anisotropic Universe

One of the predictions from simple inflation models is a stochastic background of gravitational waves (or literally what is called the Primordial Gravitational Waves (\textbf{PGW})) with a nearly scale--invariant spectrum. In this work, we consider these waves arising from perturbing the Anisotropic background (Bianchi type--I) metric by focus on their power spectrums.The intended frameworks are the Einstein's and modified gravity frames. The investigations indicate that in the modified gravity context, the results have more ability to adapt to physical conditions or constraints. Especially, the scale--invariant character of the spectrum is much more pronounced in the modified framework.Comment: This paper is same with the paper to Identifier arXiv:2007.0669