Narrow Results

We study the brane with arbitrary tension σ on the edge of various black holes with AdS asymptotics. We investigate Friedmann equations governing the motion of the brane universes and match the Friedmann equation to Cardy entropy formula.

According to the formal holographic principle, a modification to the assumption of holographic principle in Verlinder's investigation of entropy force is obtained. A more precise relation between entropy and area in the holographic system is proposed. With the entropy corrections to the area-relation, we derivate Newton's laws and Einstein equation with a static spherically symmetric holographic screen. Furthermore, we derived the correction terms to the modified Friedmann equation of the FRW universe starting from the holographic principle and the Debye model.

We derive the spatially flat rainbow-Friedmann equation from de Broglie–Bohm interpretation in canonical quantum cosmology. Our result shows that the spatially flat rainbow-Friedmann equations of early and late-time universe are having different forms. The spatially flat rainbow-Friedmann equation of early universe which is obtained in this paper is quite different from the one which was initially derived by Magueijo and Smolin [Class. Quantum Grav.21, 1725 (2004)]. However, the spatially flat rainbow-Friedmann equation for late-time universe obtained in this paper is found to be the same as the one derived by Magueijo and Smolin (for the case $k=0$ and Newton’s gravitational constant $G(E)=G_0)$. The new spatially flat rainbow-Friedmann equation obtained in this paper could provide an alternative way in understanding the evolution of the early rainbow universe.

In various gravity theories, Friedmann equations can be cast to a form of the first law of thermodynamics in a Friedmann–Robertson–Walker (FRW) cosmological setup. However, this result failed in recent infrared (IR) modified Hořava–Lifshitz (HL) gravity. The difficulty stems from the fact that HL gravity is Lorentz-violating. Motivated by this problem, we use the Misner–Sharp mass to investigate the thermodynamics near the apparent horizon in HL cosmology. We find that the Friedmann equations can be derived from the first law of thermodynamics. The Misner–Sharp mass used here inherits the specific properties of HL gravity since it is directly from the gravitational action of HL theory. We also prove that the first law of thermodynamics with logarithmic entropy still holds at the apparent horizon in FRW. The results suggest that the general prescription of deriving the field equation from thermodynamics still works in the HL cosmology.

We recently formulated a model of the universe based on an underlying W3-symmetry. It allows the creation of the universe from nothing and the creation of baby universes and wormholes for spacetimes of dimension 2, 3, 4, 6 and 10. Here we show that the classical large time and large space limit of these universes is one of exponential fast expansion without the need of a cosmological constant. Under a number of simplifying assumptions, our model predicts that w = −1.2 in the case of four-dimensional spacetime. The possibility of obtaining a w-value less than −1 is linked to the ability of our model to create baby universes and wormholes.

Using the generalized procedure proposed by S. F. Wu et al.²³ recently, we construct the first law of thermodynamics on apparent horizon in a general braneworld model with curvature correction terms on the brane and in the bulk, respectively. The explicit entropy formular of apparent horizon in the general braneworld is worked out. We also discuss the masslike function which associated with a new type first law of thermodynamics of the general braneworld in detail. We analyze the difference between the conventional thermodynamics and the new type thermodynamics on apparent horizon. At last, the discussions about the physical meanings of the masslike function have also been given.

In the context of the Brans–Dicke scalar tensor theory of gravitation, the cosmological Friedmann equation which relates the expansion rate H of the universe to the various fractions of energy density is analyzed rigorously. It is shown that the Brans–Dicke scalar tensor theory of gravitation brings a negligible correction to the matter density component of the Friedmann equation. Besides, in addition to Ω_Λ and Ω_M in the standard Einstein cosmology, another density parameter, Ω_Δ, is expected by the theory inevitably. Some cosmological consequences of such nonfamiliar cases are examined as far as recent observational results are concerned. Theory implies that if Ω_Δ is found to be nonzero, data can favor this model and hence this theory turns out to be the most powerful candidate in place of the standard Einstein cosmological model with cosmological constant. Such a replacement will enable more accurate predictions for the rate of change of the Newtonian gravitational constant in the future.

Considering the results from Hořava–Lifshitz (HL) theory, a more precise relation between the number of bits and area in the holographic system is proposed. With this corrected relation and Debye model, two modified Friedmann equations are derived from the Hawking temperature and the Unruh temperature separately in entropic force. These equations could be better in describing the whole evolution of the Universe.

In this paper, we investigate the effect modified dispersion relation (MDR) on the entropy-area relation of FRW universe, leading to the modification of Friedmann equations. In this regard, we show that limitations imposed by MDR leads to certain modifications of bouncing universe thermodynamics.

Rainbow gravity can be a suitable model to study the Friedmann–Robertson–Walker (FRW) universe in the realm of high energy physics. In rainbow gravity the radius of the apparent horizon is modified and it is used to derive the surface gravity and the temperature on the horizon. Inspired by the modified Friedmann equation in rainbow gravity and adopting the viewpoint that there is a deep connection between Friedmann equation and the first law of thermodynamics, the entropy on the horizon is obtained. It is interesting to be noted that the thermodynamical properties of the FRW universe depend on the energy of the probe, which is used by an observer to investigate the spacetime. Finally, it is shown that the validity of the generalized second law (GSL) of thermodynamics can be considered as a useful instrument to restrict the choice of rainbow gravity functions.

Though the expansion of a simple FLRW dust ball would always decelerate in Newtonian gravitational dynamics, in GR, when the dust ball’s radius insufficiently exceeds the Schwarzschild value, its expansion instead accelerates because the dominant gravitational time-dilation braking of its expansion speed weakens as it expands. But in “comoving coordinates” the fixing of the 00 component of the metric tensor to unity completely eliminates gravitational time dilation, which is reflected by the purely Newtonian Friedmann equation of motion in those “coordinates” for the dust-ball. For a particular dust-ball initial condition Oppenheimer and Snyder remedied the GR-inconsistent Newtonian behavior in “comoving coordinates” by their famed tour-de-force analytic transformation to GR-compatible “standard” coordinates. Recent extension of their transformation to arbitrary dust-ball initial conditions enables the derivation of GR-consistent equations of motion in “standard” coordinates for all shell radii of any simple FLRW dust ball. These non-Newtonian equations of motion not only show that a dust ball’s expansion always accelerates when its radius insufficiently exceeds the Schwarzschild value, but also that for a range of initial conditions the dust ball’s expansion never ceases to accelerate (although that acceleration asymptotically decreases toward zero), apparently eliminating any need for a nonzero “dark energy” cosmological constant.

This volume assumes pre-requisite knowledge of basic cosmology and of standard methods of mathematical physics. This chapter presents just a brief review of essential elements of the expansion history of the Universe (more exhaustive expositions are available in standard textbooks such as those cited in the previous chapter).

Cosmological N-body simulations play an important role in modern cosmology by providing vital information regarding the evolution of the dark matter: its clustering and motion, and properties of dark matter halos. The simulations are instrumental for the transition of the theoretical cosmology from an inspiring but speculative part of astronomy to the modern precision cosmology. In spite of more than 50 yrs of development, N-body methods are still a thriving field with the invention of more powerful methods providing more accurate theoretical predictions. Here, we review different numerical methods (PM, Tree, AMR) and ideas used in this field.