Possible Contributions to the Bulk Casimir Energy in Heterotic M-theory

Some possible ways for the study of the contributions of some background fields to the bulk Casimir energy have been probed in the framework of the 5D heterotic M-theory

On the Masses of the Universal hypermultiplets in heterotic M-theory

The reduced 5D Heterotic M-theory has a deeply rich structure. For every Calabi-yau compactification, there exists a gravitational hypermultiplet $(g_{\mu\nu},\psi_{\mu},A_{\mu})$ and a universal hypermultiplet. In this paper we derive the formulae for the masses of the scalar sector of the universal hypermultiplet $(V,\sigma,\zeta,\bar{\zeta})$ in the framework of 5D Heterotic M-theory.Comment: AIP Conf. Proc. 201

Ricci-Gauss-Bonnet holographic dark energy in Chern-Simons modified gravity: A flat FLRW quintessence-dominated universe

We discuss the recently suggested Ricci-Gauss-Bonnet holographic dark energy in Chern-Simons modified gravity. We have tested some general forms of the scale factor $a(t)$, and used two physically reasonable forms which have been proved to be consistent with observations. Both solutions predict a sign flipping in the evolution of cosmic pressure which is positive during the early-time deceleration and negative during the late-time acceleration. This sign flipping in the evolution of cosmic pressure helps in explaining the cosmic deceleration-acceleration transition, and it has appeared in other cosmological models in different contexts. However, the current work shows a pressure singularity which needs to be explained. The evolution of the equation of state parameter $\omega(t)$ shows the same asymptotic behavior for both solutions indicating a quintessence-dominated universe in the far future. We also note that $\omega(t)$ goes to negative values (leaving the decelerating dust-dominated era at $\omega=0$) at exactly the same time the pressure becomes negative. Again, there is another singularity in the behavior of $\omega(t)$ which happens at the same cosmic time of the pressure singularity.Comment: 13 pages, 9 figure

Crossing the phantom divide line in universal extra dimensions

We investigate the cosmic acceleration and the evolution of dark energy across the cosmological constant boundary in universal extra dimensions UED. We adopt an empirical approach to solve the higher-dimensional cosmological equations so that the deceleration parameter $q$ is consistent with observations. The expressions for the jerk and deceleration parameters are independent of the number of dimensions $n$. The behavior of pressure in $4$D shows a positive-to-negative transition corresponding to the deceleration-to-acceleration cosmic transition. This pressure behavior helps in providing an explanation to the cosmic deceleration-acceleration transition although the reason behind the transition itself remains unknown. In the conventional $4$D cosmology, there is a no-go theorem prevents the EoS parameter of a single perfect fluid in FRW geometry to cross the $\omega=-1$ boundary. The current model includes a single homogenous but anisotropic perfect fluid in a homogenous FRW metric with two different scale factors in the ordinary $4$D and the UED. In contrast to the conventional $4$D cosmology, we have found that the dark energy evolution in UED shows $\omega=-1$ crossing. however, the no-go theorem is still respected in $4$D where the EoS parameter doesn't cross the $\omega=-1$ boundary.Comment: 9 pages, 6 figures, 1 tabl

Space-time singularities and the theory of retracts

In previous publications, we have started investigating some possible applications to the retraction theory in gravitational physics and showed that it can be very useful in providing proofs and explaining the topological bases. In the current work, we investigate the role of the retraction theory in the mathematical study of space-time singularities and suggest a topological restriction on the formation of singularities. Although we present a toy model using a 5D cosmological metric as an example, the current study applies for any collapsing system under the influence of gravity such as a massive star or the whole universe. After showing that the cosmological space-time $M$ can be retracted into lower dimensional circles $S_i \subset M$, we prove the existence of a homotopy between this retraction and the identity map which defines a deformation retract on $M$. Since a circle doesn't deformation retract onto a point but it does retract to a point, the defined deformation retract stops any circle $S_i$ from retracting into a point which means no singularity is formed. The paper underlines the role of algebraic topology in the mathematical study of space-time singularities and represents a new application of the retraction theory in mathematical physics.Comment: 11 page

Bianchi Type-VV cosmology in f(R,T)f(R,T) gravity with Λ(T)\Lambda(T)

A new class of cosmological models in $f(R, T)$ modified theories of gravity proposed by Harko et al. (2011), where the gravitational Lagrangian is given by an arbitrary function of Ricci scalar $R$ and the trace of the stress-energy tensor $T$, have been investigated for a specific choice of $f(R, T) = f_{1}(R) + f_{2}(T)$ by considering time dependent deceleration parameter. The concept of time dependent deceleration parameter (DP) with some proper assumptions yield the average scale factor $a(t) = \sinh^{\frac{1}{n}}(\alpha t)$, where $n$ and $\alpha$ are positive constants. For $0 < n \leq 1$, this generates a class of accelerating models while for $n > 1$, the models of universe exhibit phase transition from early decelerating phase to present accelerating phase which is in good agreement with the results from recent astrophysical observations. Our intention is to reconstruct $f(R,T)$ models inspired by this special law for the deceleration parameter in connection with the theories of modified gravity. In the present study we consider the cosmological constant $\Lambda$ as a function of the trace of the stress energy-momentum-tensor, and dub such a model "$\Lambda(T)$ gravity" where we have specified a certain form of $\Lambda(T)$. Such models may display better uniformity with the cosmological observations. The statefinder diagnostic pair $\{r,s\}$ parameter has been embraced to characterize different phases of the universe. We also discuss the physical consequences of the derived models.Comment: 16 pages, 10 figures. I have removed the over la

Deformation Retract and Folding of the 5D Schwarzchild Field

In this article we introduce some types of the deformtion retracts of the $5D$ Schwarzchild space making use of Lagrangian equations. The retraction of this space into itself and into geodesics has been presented. The relation between folding and deformation retract of this space has been achieved. A relation for energy conservation similar to the one obtained in four dimensions has been obtained for the five dimensional case.Comment: 10 pages, 0 figure

Topological Origin of Holographic Principle: Application to wormholes

In this paper, we suggest a mathematical representation to the holographic principle through the theory topological retracts. We found that the topological retraction is the mathematical analogs of the hologram idea in modern quantum gravity and it can be used to explore the geometry of the hologram boundary. An example has been given on the five dimensional (5D) wormhole space-time $W$ which we found it can retract to lower dimensional circles $S_i \subset W$. In terms of the holographic principle, the description of this volume of space-time $W$ is encoded on the lower-dimensional circle which is the region boundary.Comment: 8 pages and 2 figure

A stable flat entropy-corrected FRW universe

In this paper, a general entropy-corrected FRW cosmological model has been presented in which a deceleration-to-acceleration transition occurs according to recent observations. We found that the case for the flat universe ($k=0$), supported by observations, is the most stable one where it successfully passes all stability tests. The stability of the model has been studied through testing the sound speed, the classical and the new nonlinear energy conditions. The model predicts a positive pressure during the early-time decelerating epoch, and a negative pressure during the late-time accelerating epoch in a good agreement with cosmic history and dark energy assumption. We have investigated all possible values of the prefactors $\alpha$ and $\beta$ in the corrected entropy-area relation to find the best values required for a stable flat universe. We have also made use of the evolution of the equation of state parameters $\omega(t)$ in predicting the correct values of $\alpha$ and $\beta$. The jerk and density parameters have been calculated where a good agreement with observations and $\Lambda$CDM model has been obtained. Two dark energy proposals have been investigated in this model, the entropy-corrected holographic dark energy and the modified holographic Ricci dark energy.Comment: 17 pages, 18 figure

Globally Optimal Cooperation in Dense Cognitive Radio Networks

The problem of calculating the local and global decision thresholds in hard decisions based cooperative spectrum sensing is well known for its mathematical intractability. Previous work relied on simple suboptimal counting rules for decision fusion in order to avoid the exhaustive numerical search required for obtaining the optimal thresholds. However, these simple rules are not globally optimal as they do not maximize the overall global detection probability by jointly selecting local and global thresholds. Instead, they maximize the detection probability for a specific global threshold. In this paper, a globally optimal decision fusion rule for Primary User signal detection based on the Neyman- Pearson (NP) criterion is derived. The algorithm is based on a novel representation for the global performance metrics in terms of the regularized incomplete beta function. Based on this mathematical representation, it is shown that the globally optimal NP hard decision fusion test can be put in the form of a conventional one dimensional convex optimization problem. A binary search for the global threshold can be applied yielding a complexity of O(log2(N)), where N represents the number of cooperating users. The logarithmic complexity is appreciated because we are concerned with dense networks, and thus N is expected to be large. The proposed optimal scheme outperforms conventional counting rules, such as the OR, AND, and MAJORITY rules. It is shown via simulations that, although the optimal rule tends to the simple OR rule when the number of cooperating secondary users is small, it offers significant SNR gain in dense cognitive radio networks with large number of cooperating users