In this paper, we study the physical meaning of the wavefunction of the universe. With the continuity equation derived from the Wheeler-DeWitt (WDW) equation in the minisuperspace model, we show that the quantity $rho(a)=|psi(a)|^2$ for the universe
is inversely proportional to the Hubble parameter of the universe. Thus, $rho(a)$ represents the probability density of the universe staying in the state $a$ during its evolution, which we call the dynamical interpretation of the wavefunction of the universe. We demonstrate that the dynamical interpretation can predict the evolution laws of the universe in the classical limit as those given by the Friedmann equation. Furthermore, we show that the value of the operator ordering factor $p$ in the WDW equation can be determined to be $p=-2$.
We study the quantization of the Einstein-Hilbert action for a small true vacuum bubble without matter or scalar field. The quantization of action induces an extra term of potential called quantum potential in Hamilton-Jacobi equation, which gives ex
panding solutions including the exponential expansion solutions of the scalar factor $a$ for the bubble. We show that exponential expansion of the bubble continues with a short period (about a Planck time $t_p$), no matter whether the bubble is closed, flat or open. The exponential expansion ends spontaneously when the bubble becomes large, i.e., the scalar factor $a$ of the bubble approaches a Planck length $l_p$. We show that it is quantum potential of the small true vacuum bubble that plays the role of the scalar field potential suggested in the slow-roll inflation model. With the picture of quantum tunneling, we calculate particle creation rate during inflation, which shows that particles created by inflation have the capability of reheating the universe.
An interesting idea is that the universe could be spontaneously created from nothing, but no rigorous proof has been given. In this paper, we present such a proof based on the analytic solutions of the Wheeler-DeWitt equation (WDWE). Explicit solutio
ns of the WDWE for the special operator ordering factor p=-2 (or 4) show that, once a small true vacuum bubble is created by quantum fluctuations of the metastable false vacuum, it can expand exponentially no matter whether the bubble is closed, flat or open. The exponential expansion will end when the bubble becomes large and thus the early universe appears. With the de Broglie-Bohm quantum trajectory theory, we show explicitly that it is the quantum potential that plays the role of the cosmological constant and provides the power for the exponential expansion of the true vacuum bubble. So it is clear that the birth of the early universe completely depends on the quantum nature of the theory.
In both classical and quantum world, information cannot appear or disappear. This fundamental principle, however, is questioned for a black hole, by the acclaimed information loss paradox. Based on the conservation laws of energy, charge, and angular
momentum, we recently show the total information encoded in the correlations among Hawking radiations equals exactly to the same amount previously considered lost, assuming the non-thermal spectrum of Parikh and Wilczek. Thus the information loss paradox can be falsified through experiments by detecting correlations, for instance, through measuring the covariances of Hawking radiations from black holes, such as the manmade ones speculated to appear in LHC experiments. The affirmation of information conservation in Hawking radiation will shine new light on the unification of gravity with quantum mechanics.
Information about the collapsed matter in a black hole will be lost if Hawking radiations are truly thermal. Recent studies discover that information can be transmitted from a black hole by Hawking radiations, due to their spectrum deviating from exa
ct thermality when back reaction is considered. In this paper, we focus on the spectroscopic features of Hawking radiation from a Schwarzschild black hole, contrasting the differences between the nonthermal and thermal spectra. Of great interest, we find that the energy covariances of Hawking radiations for the thermal spectrum are exactly zero, while the energy covariances are non-trivial for the nonthermal spectrum. Consequently, the nonthermal spectrum can be distinguished from the thermal one by counting the energy covariances of successive emissions, which provides an avenue towards experimentally testing the long-standing information loss paradox.
A recent article by Mathur attempts a precise formulation for the paradox of black hole information loss [S. D. Mathur, arXiv:1108.0302v2 (hep-th)]. We point out that a key component of the above work, which refers to entangled pairs inside and outsi
de of the horizon and their associated entropy gain or information loss during black hole evaporation, is a presumptuous false outcome not backed by the very foundation of physics. The very foundation of Mathurs above work is thus incorrect. We further show that within the framework of Hawking radiation as tunneling the so-called small corrections are sufficient to resolve the information loss problem.
For Hawking radiation, treated as a tunneling process, the no-hair theorem of black hole together with the law of energy conservation is utilized to postulate that the tunneling rate only depends on the external qualities (e.g., the mass for the Schw
arzschild black hole) and the energy of the radiated particle. This postulate is justified by the WKB approximation for calculating the tunneling probability. Based on this postulate, a general formula for the tunneling probability is derived without referring to the concrete form of black hole metric. This formula implies an intrinsic correlation between the successive processes of the black hole radiation of two or more particles. It also suggests a kind of entropy conservation and thus resolves the puzzle of black hole information loss in some sense.
