International Journal of Modern Physics D

A critical review of the standard paradigm for the origin of Galactic cosmic rays (CRs) is presented. Recent measurements of local and far-away CRs reveal unexpected behaviors, which challenge the commonly accepted scenario. These recent findings are discussed, together with long-standing open issues. Despite the progress made thanks to ever-improving observational techniques and theoretical investigations, at present our understanding of the origin and of the behavior of CRs remains incomplete. We believe it is still unclear whether a modification of the standard paradigm, or rather a radical change of the paradigm itself is needed in order to interpret all the available data on CRs within a self-consistent scenario.

This is a mini-review about the rapidly growing subject of dual holographic complexity (HC) for subsystems in conformal field theory (CFT) using a subregion volume enclosed by the entangled area in the dual bulk theory. This proposal is named as HC = volume. We use this proposal to compute the HC for different geometries in bulk theory. Because this HC quantity diverges as a result of the existence of the UV cutoff in the CFT, we proposed a suitable regularization scheme by subtracting the contribution of the background (pure) AdS spacetime from the deformation of the AdS geometry. Furthermore, the time-dependent geometries are investigated using the AdS/CFT proposal and hence, we proposed a time-dependent copy for HC in such nonstatic geometries. As an attempt to make a relation between HC and holographic entanglement entropy (HEE), inspired from the pure geometrical origins, we showed that HC and HEE which are duals to different volumes/areas in the bulk theory would be connected in a universal form for a general deformation AdS geometry (called holographic Cavalieri principle). As a pioneering idea we build a holographic model for $P-V$ critically in black holes via regularized HC as the dual thermodynamic volume. The second-order phase transitions in two-dimensional holographic superconductors is explained by using the regularized HC as an order parameter. All the results presented in this mini-review are collected from the list of published works of the first author of this paper. In several cases, we gave further explanation and clarification to make the ideas more understandable to the community. Other proposals for complexity like complexity as on shell action are not included in this review paper.

In this work, we compare the thermodynamical viability of two types of noncanonical scalar field models with kinetic corrections: the square kinetic and square root kinetic corrections. In modern cosmology, the generalized second law of thermodynamics (GSLT) plays an important role in deciding thermodynamical compliance of a model as one cannot consider a model to be viable if it fails to respect GSLT. Hence, for comparing thermodynamical viability, we examine the validity of GSLT for these two models. For this purpose, by employing the Unified first law (UFL), we calculate the total entropy of these two models in apparent and event horizons. The validity of GSLT is then examined from the autonomous systems as the original expressions of total entropy are very complicated. Although, at the background level, both models give interesting cosmological dynamics, however, thermodynamically we found that the square kinetic correction is more realistic as compared to the square root kinetic correction. More precisely, the GSLT holds for the square kinetic correction throughout the evolutionary history except only during the radiation epoch where the scalar field may not represent a true description of the matter content. On the other hand, the square root kinetic model fails to satisfy the GSLT in major cosmological eras.

This paper investigates the Tsallis holographic dark energy (THDE) model in accordance with the apparent horizon as an infrared cut-off, in a non flat universe. The cosmological evolution of the deceleration parameter and equation of state of THDE model are calculated. The evolutionary trajectories are plotted for the THDE model for distinct values of the Tsallis parameter $\delta$ besides distinct spatial curvature contributions, in the statefinder $(r,s)$ parameter-pairs and ${\omega }_D\text{–}{\omega }_D^{\prime }$ plane, considering the present value of dark energy (DE) density parameter ${\mathrm{\Omega }}_{D0}$, ${\mathrm{\Omega }}_{D0}=0.72$, in the light of $\mathrm{\text{WMAP}}+e\mathrm{\text{CMB}}+\mathrm{\text{BAO}}+H_0$ observational data. The statefinder and ${\omega }_D\text{–}{\omega }_D^{\prime }$ plane plots specify the feature of the THDE and demonstrate the separation between this framework and other models of DE.

We propose yet another solution to the initial condition problem of inflation associated with homogeneity beyond the horizon at the onset of inflation, in cases where inflation is preceded by a radiation era. One may argue that causality will allow for smoothness over the causal horizon scale $H^{-1}$, but for thermal inflationary scenarios, the background inflaton field will only be correlated over the thermal correlation length $\zeta \sim T^{-1}$ which is much smaller than $H^{-1}$. We argue, with examples, that if the number of relativistic degrees of freedom in the preinflationary era is very large $(>10^4)$ then the thermal correlation length can be of the order of the causal horizon size alleviating the initial conditions problem of inflation.

In general relativity, there is no dispersion in gravitational waves, while some modified gravity theories predict dispersion phenomena in the propagation of gravitational waves. In this paper, we demonstrate that this dispersion will induce an observable deviation of waveforms if the orbits have large eccentricities. The mechanism is that the waveform modes with different frequencies will be emitted at the same time due to the existence of eccentricity. During the propagation, because of the dispersion, the arrival time of different modes will be different, then produce the deviation and dephasing of waveforms compared with general relativity. This kind of dispersion phenomena related with extreme-mass-ratio inspirals could be observed by space-borne detectors, and the constraint on the graviton mass could be improved. Moreover, we find that the dispersion effect may also be constrained by ground detectors better than the current result if a highly eccentric intermediate-mass-ratio inspirals be observed.

In this paper, we study the cosmological evolution of the universe filled with a perfect fluid in the Eddington-inspired-Born–Infeld gravity. Applying an alternative method in which the evolution of the scale factor for this theory is linked to the cosmographic parameters, we obtain a dynamical dark energy solution where the singularity (through a regular bounce or a loitering phase) still can be avoided for $\kappa >0$ with $w>0$. For the range $-1<w<0$, the results lead us to universes that experience an unlimited rate of expansion with finite density. Also, we obtain a possible maximum value of $H=4.338\times 10^{-43}/t_{\text{Planck}}$ at the cosmic bounce point.

We study the resolution of certain cosmological singularity in the context of higher-spin three-dimensional gravity. We consider gravity coupled to a spin-3 field realized as Chern–Simons theory with gauge group $SL(3,ℂ)$. In this context, we elaborate and extend a singularity resolution scheme proposed by Krishnan and Roy. We discuss the resolution of a big bang singularity in the case of gravity coupled to a spin-4 field realized as Chern–Simons theory with gauge group $SL(4,ℂ)$. In all these cases, we show the existence of gauge transformations that do not change the holonomy of the Chern–Simons gauge potential and lead to metrics without the initial singularity. We argue that such transformations always exist in the context of gravity coupled to a spin-$N$ field when described by Chern–Simons with gauge group $SL(N,ℂ)$.

We study the gravitomagnetism in the Scalar-Vector-Tensor theory or Moffat’s Modified theory of Gravity (MOG). We compute the gravitomagnetic field that a slow-moving mass distribution produces in its Newtonian regime. We report that the consistency between the MOG gravitomagnetic field and that predicted by the Einstein’s gravitational theory and measured by Gravity Probe B, LAGEOS and LAGEOS 2, and with a number of GRACE and Laser Lunar ranging measurements requires $\left|\alpha \right|<0.0013$.

The evolutionary pictures for phantom field in loop quantum cosmology are discussed in this paper. Comparing the dynamical behaviors of the phantom field with one of the canonical scalar fields in loop quantum cosmology scenario, we found that the $H-\rho$ phase trajectories are the same, but the $\varphi -\dot{\varphi }$ phase-spaces are very different, and the phantom field with considering potentials can drive neither super inflation nor slow-roll inflation in loop quantum cosmology (LQC) scenario. While the universe is filled with multiple dark fluids, to ensure that the condition $V\le {\rho }_{\mathrm{\text{c}}}$ does not violate, the energy density of dark matter ${\rho }_{\mathrm{\text{DM}}}$ and the equation-of-state of phantom field ${\omega }_{\mathrm{\text{Ph}}}$ should satisfy the condition ${\rho }_{\mathrm{\text{DM}}}/{\rho }_{\mathrm{\text{c}}}>(-1-{\omega }_{\mathrm{\text{Ph}}})/(1-{\omega }_{\mathrm{\text{Ph}}})$ at the bounce point. If this constraint condition holds, the universe can enter an inflationary stage, and it is possible to unify the description of phantom field, dark matter and inflation. We introduced a toy model which has the same form of the general Chaplygin gas to unify the dark energy, dark matter and slow-roll inflation, and the slow-roll inflation of the toy model has also been discussed.

A scalar-tensor model with Gauss–Bonnet and nonminimal kinetic couplings is considered, in which ghost modes are eliminated via a Lagrange multiplier constraint. A reconstruction procedure is devised for the scalar potential and Lagrange multiplier, valid for any given cosmological scenario. In particular, inflationary and dark energy cosmologies of different types (power-law, Little-Rip, de Sitter, quasi-de Sitter) are reconstructed in such models. It is shown that, for various choices of the kinetic coupling terms, it is possible to obtain a viable inflationary phenomenology compatible with the most accurate values of the observational indices.

Models of static wormholes within the $f(R,T)$ extended theory of gravity are investigated, in particular the family $f(R,T)=R+\lambda T$, with $T=\rho +P_r+2P_l$ being the trace of the energy–momentum tensor. Models corresponding to different relations for the pressure components (radial and lateral), and several equations-of-state (EoS), reflecting different matter content, are worked out explicitly. The solutions obtained for the shape functions of the generated wormholes obey the necessary metric conditions, as manifested in other studies in the literature. The respective energy conditions reveal the physical nature of the wormhole models thus constructed. It is found, in particular, that for each of those considered, the parameter space can be divided into different regions, in which the exact wormhole solutions fulfill the null energy conditions (NEC) and the weak energy conditions (WEC), respectively, in terms of the lateral pressure. Moreover, the dominant energy condition (DEC) in terms of both pressures is also valid, while $\rho +P_r+2P_l=0$. A similar solution for the theory $P_r={\omega }_1\rho +{\omega }_2{\rho }^2$ is found numerically, where ${\omega }_1$ and ${\omega }_2$ are either constant or functions of $r$, leading to the result that the NEC in terms of the radial pressure is also valid. For nonconstant ${\omega }_i$ models, attention is focused on the behavior ${\omega }_i\propto r^m$. To finish, the question is addressed, how $f(R)=R+\alpha R^2$ will affect the wormhole solutions corresponding to fluids of the form $P_r={\omega }_1\rho +{\omega }_2{\rho }^2$, in the three cases such as NEC, WEC and DEC. Issues concerning the nonconservation of the matter energy–momentum tensor, the stability of the solutions obtained, and the observational possibilities for testing these models are discussed in Sec. 6.

This paper deals with a nonminimally coupled scalar field in the background of homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker (FLRW) flat spacetime. As Einstein field equations are coupled second-order nonlinear differential equations, it is very hard to find exact solutions. By suitable choice of variables, we transform Einstein field equations to an autonomous system and critical points are determined. We use center manifold theory to characterize nonhyperbolic critical points and are found to be saddle in nature. We discuss possible bifurcation scenarios, which indicate the existence of the cosmological bouncing model.

We generalize the basic theory of mimetic gravity by extending its purview to the general metric-compatible geometries that admit torsion, in addition to curvature. This essentially implies reinstating the mimetic principle of isolating the conformal degree of freedom of gravity in presence of torsion, by parametrizing both the physical metric and torsion in terms of the scalar ‘mimetic’ field and the metric and torsion of a fiducial space. We assert the requisite torsion parametrization from an inspection of the fiducial space Cartan transformation which, together with the conformal transformation of the fiducial metric, preserves the physical metric and torsion. In formulating the scalar–tensor equivalent Lagrangian, we consider an explicit contact coupling of the mimetic field with torsion, so that the former can manifest itself geometrically as the source of a torsion mode, and most importantly, give rise to a viable ‘dark universe’ picture from a mimicry of an evolving dust-like cosmological fluid with a nonzero pressure. A further consideration of higher derivatives of the mimetic field in the Lagrangian leads to physical bounds on the mimetic–torsion coupling strength, which we determine explicitly.

Extensions of the gravity theory in order to obtain traceless field equations have been widely considered in the literature. The leading example of such class of theories is the unimodular gravity, but there are other possibilities like the mimetic gravity and the Rastall gravity with a coupling parameter $\lambda =1/2$. The unimodular gravity proposal is a very interesting approach in order to address the cosmological constant problem. When coupled to matter, such theories may imply that the energy–momentum tensor is not divergence free anymore. In this paper, a unimodular type theory will be developed by evading the conservation $T_{;\mu }^{\mu \nu }=0$. The cosmological consequences of the later, both at background as well as for scalar and tensor perturbations, are explored. Possible further extensions of this approach are discussed as well as its connection with the traditional unimodular gravity.