International Journal of Modern Physics A

We give here an overview of recent developments in high energy physics and cosmology and their interconnections that relate to unification, and discuss prospects for the future. Thus there are currently three empirical data that point to supersymmetry as an underlying symmetry of particle physics: the unification of gauge couplings within supersymmetry, the fact that nature respects the supersymmetry prediction that the Higgs boson mass lie below 130 GeV, and vacuum stability up to the Planck scale with a Higgs boson mass at $\sim$125 GeV while the Standard Model does not do that. Coupled with the fact that supersymmetry solves the big hierarchy problem related to the quadratic divergence to the Higgs boson mass square along with the fact that there is no alternative paradigm that allows us to extrapolate physics from the electroweak scale to the grand unification scale consistent with experiment, supersymmetry remains a compelling framework for new physics beyond the Standard Model. The large loop correction to the Higgs boson mass in supersymmetry to lift the tree mass to the experimentally observable value, indicates a larger value of the scale of weak scale supersymmetry, making the observation of sparticles more challenging but still within reach at the LHC for the lightest ones. Recent analyses show that a high energy LHC (HE-LHC) operating at 27 TeV running at its optimal luminosity of $2.5\times 10^{35}{\mathrm{\text{cm}}}^{-2}{\mathrm{\text{s}}}^{-1}$ can reduce the discovery period by several years relative to HL-LHC and significantly extend the reach in parameter space of models. In the coming years several experiments related to neutrino physics, searches for supersymmetry, on dark matter and dark energy will have direct impact on the unification frontier. Thus the discovery of sparticles will establish supersymmetry as a fundamental symmetry of nature and also lend direct support for strings. Further, discovery of sparticles associated with missing energy will constitute discovery of dark matter with LSP being the dark matter. On the cosmology front more accurate measurement of the equation of state, i.e. $p=w\rho$, will shed light on the nature of dark energy. Specifically, $w>-1$ will likely indicate the existence of a dynamical field, possibly quintessence, responsible for dark energy and $w<-1$ would indicate an entirely new sector of physics. Further, more precise measurements of the ratio $r$ of tensor to scalar power spectrum, of the scalar and tensor spectral indices $n_s$ and $n_t$ and of non-Gaussianity will hopefully allow us to realize a Standard Model of inflation. These results will be a guide to further model building that incorporates unification of particle physics and cosmology.

We propose a generalization of Schramm–Loewner evolution (SLE) that has internal degrees of freedom described by an affine Lie superalgebra. We give a general formulation of SLE corresponding to representation theory of an affine Lie superalgebra whose underlying finite-dimensional Lie superalgebra is basic classical type, and write down stochastic differential equations on internal degrees of freedom in case that the corresponding affine Lie superalgebra is $\widehat{𝔬𝔰𝔭(1|2)}$. We also demonstrate computation of local martingales associated with the solution from a representation of $\widehat{𝔬𝔰𝔭(1|2)}$.

We continue the study undertaken in Ref. 16 of the exceptional Jordan algebra $J=J_3^8$ as (part of) the finite-dimensional quantum algebra in an almost classical space–time approach to particle physics. Along with reviewing known properties of $J$ and of the associated exceptional Lie groups we argue that the symmetry of the model can be deduced from the Borel–de Siebenthal theory of maximal connected subgroups of simple compact Lie groups.

We consider the history of the universe from a possible big bang or a bounce into a late period of a unified interacting dark energy–dark matter model. The model is based on the Two Measures Theories (TMT) which introduces a metric independent volume element and this allows us to construct a unification of dark energy and dark matter. A generalization of the Two Measures Theories gives a diffusive nonconservative stress-energy–momentum tensor in addition to the conserved stress-energy tensor which appear in Einstein equations. These leads to a formulation of interacting DE–DM dust models in the form of a diffusive-type interacting Unified Dark Energy and Dark Matter scenario. The deviation from $\mathrm{\Lambda }$CDM is determined by the diffusion constant $C_2$. For $C_2=0$ the model is indistinguishable from $\mathrm{\Lambda }$CDM. Numerical solutions of the theories show that in some $C_2\ne 0$ the evolution of the early universe is governed by Stiff equation of state or the universe bounces to hyper-inflation. But all of those solutions have a final transition to $\mathrm{\Lambda }$CDM as a stable fixed point for the late universe.

In this paper, we revisit our model-independent methods developed for reconstructing properties of Weakly Interacting Massive Particles (WIMPs) by using measured recoil energies from direct Dark Matter detection experiments directly and take into account more realistically non-negligible threshold energy. All expressions for reconstructing the mass and the (ratios between the) spin-independent and the spin-dependent WIMP–nucleon couplings have been modified. We focus on low-mass ($m_{\chi }\lesssim 15$ GeV) WIMPs and present the numerical results obtained by Monte Carlo simulations. Constraints caused by non-negligible threshold energy and technical treatments for improving reconstruction results will also be discussed.

The power spectrum of the momentum distributions of particles have been estimated with Optical Glauber and Monte Carlo Glauber initial conditions for relativistic heavy ion collisions. The evaluation procedure adopted in this work is analogous to the one used in the calculation of power spectrum in Cosmic Microwave Background Radiation (CMBR). The power spectrum due to perturbations in the phase space distribution of the particles has also been evaluated. The perturbation in phase space has been evolved through the Boltzmann transport equation in an expanding quark–gluon plasma (QGP) background. The expansion of the QGP has been treated within the purview of (3+1)-dimensional relativistic hydrodynamics. We observe that the nonequilibrium effects introduced as perturbations in the phase space distributions can be traced through its variation with temperature which is distinctly different from the case of vanishing perturbation. A relation has been derived between the power spectrum and the flow harmonics.

In this paper we study the quantization of a massless scalar field in a rotating frame. In particular, we obtain the Casimir energy in a space–time with one extra compactified dimension for a rotating observer. We consider a uniformly rotating system on the circle S¹ and present an equation for spin-0 bosons where noninertial effects can be taken into account. It is shown that the spectrum of the scalar field depends on the angular velocity of the rotating system and in this way, positive and negative modes can be defined through an appropriate choice of the angular velocity. We show that noninertial effects restrict the physical region of the space–time where particles can be placed, and furthermore that the Casimir energy in the space–time with one extra compactified dimension is shifted by these effects. In addition, we pointed out that rotating effects modify the length of the extra dimension for a co-rotating observer in this kind of space–time.