Inflationary Universe in Deformed Phase Space Scenario

We consider a noncommutative (NC) inflationary model with a homogeneous scalar field minimally coupled to gravity. The particular NC inflationary setting produces entirely new consequences. We first analyze the free field case and subsequently examine the situation where the scalar field is subjected to a polynomial and exponential potentials. We propose to use a canonical deformation between momenta, in a spatially flat FLRW universe, and while the Friedmann equation remains unaffected the Friedmann acceleration equation (and thus the Klein-Gordon equation) is modified by an extra term linear in the NC parameter. This concrete noncommutativity on the momenta allows interesting dynamics that other NC models seem not to allow. Let us be more precise. This extra term behaves as the sole explicit pressure that under the right circumstances implies a period of accelerated expansion of the universe. We find that in the absence of the scalar field potential, and in contrast with the commutative case, in which the scale factor always decelerates, we obtain an inflationary phase for small negative values of the NC parameter. Subsequently, the period of accelerated expansion is smoothly replaced by an appropriate deceleration phase providing an interesting model regarding the graceful exit problem in inflationary models. Moreover, in the case of the free scalar field, we show that not only the horizon problem is solved but also there is some resemblance between the evolution equation of the scale factor associated to our model and that for the $R^2$ (Starobinsky) inflationary model. Therefore, our herein NC model not only can be taken as an appropriate scenario to get a successful kinetic inflation, but also is a convenient setting to obtain inflationary universe possessing the graceful exit when scalar field potentials are present.Comment: 15 pages, 9 figures, Accepted to publish in Annals of Physic

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

Classical Trace Anomaly

We seek an analogy of the mathematical form of the alternative form of Einstein's field equations for Lovelock's field equations. We find that the price for this analogy is to accept the existence of the trace anomaly of the energy-momentum tensor even in classical treatments. As an example, we take this analogy to any generic second order Lagrangian and exactly derive the trace anomaly relation suggested by Duff. This indicates that an intrinsic reason for the existence of such a relation should perhaps be, classically, somehow related to the covariance of the form of Einstein's equations.Comment: Version 2: 21 pages, TeX file (using phyzzx.tex), added new section and references. Version 3: Just replaced Abstrac

Quantum mechanics and geodesic deviation in the brane world

We investigate the induced geodesic deviation equations in the brane world models, in which all the matter forces except gravity are confined on the 3-brane. Also, the Newtonian limit of induced geodesic deviation equation is studied. We show that in the first Randall-Sundrum model the Bohr-Sommerfeld quantization rule is as a result of consistency between the geodesic and geodesic deviation equations. This indicates that the path of test particle is made up of integral multiples of a fundamental Compton-type unit of length $h/mc$.Comment: 5 pages, no figure

Horizon Problem Remediation via Deformed Phase Space

We investigate the effects of a special kind of dynamical deformation between the momenta of the scalar field of the Brans-Dicke theory and the scale factor of the FRW metric. This special choice of deformation includes linearly a deformation parameter. We trace the deformation footprints in the cosmological equations of motion when the BD coupling parameter goes to infinity. One class of the solutions gives a constant scale factor in the late time that confirms the previous result obtained via another approach in the literature. This effect can be interpreted as a quantum gravity footprint in the coarse grained explanation. The another class of the solutions removes the big bang singularity, and the accelerating expansion region has an infinite temporal range which overcomes the horizon problem. After this epoch, there is a graceful exiting by which the universe enters in the radiation dominated era.Comment: 13 pages, 2 figures, to appear in GER

Boundary Term in Metric f(R) Gravity: Field Equations in the Metric Formalism

The main goal of this paper is to get in a straightforward form the field equations in metric f(R) gravity, using elementary variational principles and adding a boundary term in the action, instead of the usual treatment in an equivalent scalar-tensor approach. We start with a brief review of the Einstein-Hilbert action, together with the Gibbons-York-Hawking boundary term, which is mentioned in some literature, but is generally missing. Next we present in detail the field equations in metric f(R) gravity, including the discussion about boundaries, and we compare with the Gibbons-York-Hawking term in General Relativity. We notice that this boundary term is necessary in order to have a well defined extremal action principle under metric variation.Comment: 12 pages, title changes by referee recommendation. Accepted for publication in General Relativity and Gravitation. Matches with the accepted versio

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 < \omega </- -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.Comment: 18 pages, 16 figures, 11 table

Chameleonic Generalized Brans--Dicke model and late-time acceleration

In this paper we consider Chameleonic Generalized Brans--Dicke Cosmology in the framework of FRW universes. The bouncing solution and phantom crossing is investigated for the model. Two independent cosmological tests: Cosmological Redshift Drift (CRD) and distance modulus are applied to test the model with the observation.Comment: 20 pages, 15 figures, to be published in Astrophys. Space Sci. (2011

Naked Singularity Formation In f(R) Gravity

We study the gravitational collapse of a star with barotropic equation of state $p=w\rho$ in the context of $f({\mathcal R})$ theories of gravity. Utilizing the metric formalism, we rewrite the field equations as those of Brans-Dicke theory with vanishing coupling parameter. By choosing the functionality of Ricci scalar as $f({\mathcal R})=\alpha{\mathcal R}^{m}$, we show that for an appropriate initial value of the energy density, if $\alpha$ and $m$ satisfy certain conditions, the resulting singularity would be naked, violating the cosmic censorship conjecture. These conditions are the ratio of the mass function to the area radius of the collapsing ball, negativity of the effective pressure, and the time behavior of the Kretschmann scalar. Also, as long as parameter $\alpha$ obeys certain conditions, the satisfaction of the weak energy condition is guaranteed by the collapsing configuration.Comment: 15 pages, 4 figures, to appear in GR

Zitterbewegung in External Magnetic Field: Classic versus Quantum Approach

We investigate variations of the Zitterbewegung frequency of electron due to an external static and uniform magnetic field employing the expectation value quantum approach, and compare our results with the classical model of spinning particles. We demonstrate that these two so far compatible approaches are not in agreement in the presence of an external uniform static magnetic field, in which the classical approach breaks the usual symmetry of free particles and antiparticles states, i.e. it leads to CP violation. Hence, regarding the Zitterbewegung frequency of electron, the classical approach in the presence of an external magnetic field is unlikely to correctly describe the spin of electron, while the quantum approach does, as expected. We also show that the results obtained via the expectation value are in close agreement with the quantum approach of the Heisenberg picture derived in the literature. However, the method we use is capable of being compared with the classical approach regarding the spin aspects. The classical interpretation of spin produced by the altered Zitterbewegung frequency, in the presence of an external magnetic field, are discussed.Comment: 16 pages, no figure