Narrow Results

This paper explores a cosmological reconstruction scheme in the background of $f(Q)$ gravity theory from a Holographic perspective. The basic motivation for this work is that the reconstruction is performed from a holographic origin, which has its roots in the black hole thermodynamics and quantum gravity. Dark energy models inspired by holographic prescription are used to reconstruct the $f(Q)$ gravity models. Two such models, namely, the Granda–Oliveros holographic dark energy model and its generalization, the Chen-Jing model, are considered for the study. Different scale factors are used and a thorough reconstruction scheme is set up using the dark energy models. The observationally constrained values of the free model parameters have been used to form the reconstructed models. Finally, a thorough investigation of the energy conditions has been performed to check the cosmological viability of the reconstructed $f(Q)$ models. As an outcome, we get some very promising and cosmologically viable $f(Q)$ models that present some interesting properties and demand further investigation. Finally, a method is discussed how the constructed $f(Q)$ models can be reconciled with a generalized holographic dark energy.

We present a new class of time-dependent solution to the ten-dimensional type 0 effective action. Given a generic potential of tachyon field, there exist phases where tachyon is either frozen at local extremals or free to propagate along flat directions. In the latter phase, a cosmology model is proposed where the tachyon plays the role of time.

We study the age problem of the universe with the holographic dark energy (DE) model introduced in Ref. 37, and test the model with some known old high redshift objects (OHRO). The parameters of the model have been constrained using the SNIa, CMB and BAO data set. We found that the age of the old quasar APM 08 279+5255 at z = 3.91 can be described by the model.

Based on the shooting method, we numerically investigate the properties of holographic paramagnetism-ferromagnetism phase transition in the presence of higher-order Gauss–Bonnet (GB) correction terms on the gravity side. On the matter field side, however, we consider the effects of Power-Maxwell (PM) nonlinear electrodynamics on the phase transition of this system. For this purpose, we introduce a massive 2-form coupled to PM field, and neglect the effects of 2-form fields and gauge field on the background geometry. We observe that increasing the strength of both the power parameter $q$ and GB coupling constant $\alpha$ decreases the critical temperature of holographic model, and leads to the harder formation of magnetic moment in the black hole background. Interestingly, we find out that at low temperatures, the spontaneous magnetization and ferromagnetic phase transition happen in the absence of external magnetic field. In this case, the critical exponent for magnetic moment has the mean field value, $1/2$, regardless of the values of $q$ and $\alpha$. In the presence of external magnetic field, however, the magnetic susceptibility satisfies the Curie–Weiss law.

Using a holographic proposal for the geometric entropy we study its behavior in the geometry of Schwarzschild black holes in global AdS_p for p = 3, 4, 5. Holographically, the entropy is determined by a minimal surface. On the gravity side, due to the presence of a horizon on the background, generically there are two solutions to the surfaces determining the entanglement entropy. In the case of AdS₃, the calculation reproduces precisely the geometric entropy of an interval of length l in a two-dimensional conformal field theory with periodic boundary conditions. We demonstrate that in the cases of AdS₄ and AdS₅ the sign of the difference of the geometric entropies changes, signaling a transition. Euclideanization implies that various embedding of the holographic surface are possible. We study some of them and find that the transitions are ubiquitous. In particular, our analysis renders a very intricate phase space, showing, for some ranges of the temperature, up to three branches. We observe a remarkable universality in the type of results we obtain from AdS₄ and AdS₅.

We investigate the holographic superconductor model constructed in the (2+1)-dimensional AdS soliton background in the probe limit. With analytical methods, we obtain the formula of critical phase transition points with respect to the scalar mass. We also generalize this formula to higher-dimensional space–time. We mention that these formulas are precise compared to numerical results. In addition, we find a correspondence between the value of the charged scalar field at the tip and the scalar operator at infinity around the phase transition points.

We propose a holographic tachyon model of dark energy with interaction between the components of the dark sector. The correspondence between the tachyon field and the holographic dark energy densities allows the reconstruction of the potential and the dynamics of the tachyon scalar field in a flat Friedmann–Robertson–Walker universe. We show that this model can describe the observed accelerated expansion of our universe with a parameter space given by the most recent observational results.

The energy density of the holographic dark energy (HDE) is based on the area law of entropy, and thus any modification of the area law leads to a modified holographic energy density. Inspired by the entropy expression associated with the apparent horizon of a Friedmann–Robertson–Walker (FRW) universe in DGP braneworld, we propose a new model for the HDE in the framework of DGP brane cosmology. We investigate the cosmological consequences of this new model and calculate the equation of state (EoS) parameter by choosing the Hubble radius, $L=H^{-1}$, as the system’s IR cutoff. Our study show that, due to the effects of the extra dimension (bulk), the identification of IR cutoff with Hubble radius, can reproduce the present acceleration of the universe expansion. This is in contrast to the ordinary HDE in standard cosmology which leads to the zero EoS parameter in the case of choosing the Hubble radius as system’s IR cutoff in the absence of interaction between dark matter (DM) and dark energy (DE).

We analytically study the properties of a $(2+1)$-dimensional $s$-wave holographic superconductor in the presence of exponential nonlinear (EN) electrodynamics. We consider the case in which the scalar and gauge fields back react on the background metric. Employing the analytical Sturm–Liouville method, we find that in the black hole background, the nonlinear electrodynamics correction will affect the properties of the holographic superconductors. We find that with increasing both backreaction and nonlinear parameters, the scalar hair condensation on the boundary will develop more difficult. We obtain the relation connecting the critical temperature with the charge density. Our analytical results support that, even in the presence of the nonlinear electrodynamics and backreaction, the phase transition for the holographic superconductor still belongs to the second-order and the critical exponent of the system always takes the mean-field value $1/2$.

We use the deep learning algorithm to learn the Reissner–Nordström (RN) black hole metric by building a deep neural network. Plenty of data are determined in boundary of AdS and we propagate them to the black hole horizon through AdS metric and equation of motion (e.o.m). We label these data according to the values near the horizon, and together with initial data they constitute a data set. Then we construct corresponding deep neural network and train it with the data set to obtain the Reissner–Nordström (RN) black hole metric. Finally, we discuss the effects of learning rate, batch-size and initialization on the training process.

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.

It has been investigated that the crystal loss effect on the dynamical evolutions of rigid holographic bright solitons in photorefractive dissipative systems based on two-wave mixing. Numerical results show that the stability of rigid holographic bright solitons in such systems depends strongly on the crystal loss. The soliton formed at a given crystal loss can propagate stably in the crystal over a distance that is long enough; the input solitary beam can evolve into a stable soliton and propagate in the crystal when the crystal loss drift is quite small, whereas it will not evolve into a stable soliton and its intensity becomes increase or decrease with propagation distance if the loss difference is big enough. A potential application of these properties of rigid holographic solitons in optical attenuators or repeaters is discussed.