No Arabic abstract
We present a short review of possible applications of the Wheeler-De Witt equation to cosmological models based on the low-energy string effective action, and characterised by an initial regime of asymptotically flat, low energy, weak coupling evolution. Considering in particular a class of duality-related (but classically disconnected) background solutions, we shall discuss the possibility of quantum transitions between the phases of pre-big bang and post-big bang evolution. We will show that it is possible, in such a context, to represent the birth of our Universe as a quantum process of tunneling or anti-tunneling from an initial state asymptotically approaching the string perturbative vacuum.
Lectures by the author at the 1986 Cargese summer school modestly corrected and uploaded for greater accessibility. Some of the authors views on the quantum mechanics of cosmology have changed from those presented here but may still be of historical interest. The material on the Born-Oppenheimer approximation for solving the Wheeler-DeWitt equation and the work on the classical geometry limit and the approximation of quantum field theory in curved spacetime are still of interest and of use.
I show that a generic quantum phenomenon can drive cosmic acceleration without the need for dark energy or modified gravity. When treating the universe as a quantum system, one typically focuses on the scale factor (of an FRW spacetime) and ignores many other degrees of freedom. However, the information capacity of the discarded variables will inevitably change as the universe expands, generating quantum bias (QB) in the Friedmann equations [Phys. Lett. A 382, 36, 2555 (2018)|arXiv:1707.05789]. If information could be stored in each Planck-volume independently, this effect would give rise to a constant acceleration $10^{120}$ times larger than that observed, reproducing the usual cosmological constant problem. However, once information capacity is quantified according to the holographic principle, cosmic acceleration is far smaller and depends on the past behaviour of the scale factor. I calculate this holographic quantum bias, derive the semiclassical Friedmann equations, and obtain their general solution for a spatially-flat universe containing matter and radiation. Comparing these QB-CDM solutions to those of $Lambda$CDM, the new theory is shown to be falsifiable, but nonetheless consistent with current observations. In general, realistic QB cosmologies undergo phantom acceleration ($w_mathrm{eff}<-1$) at late times, predicting a Big Rip in the distant future.
In this paper, we study the dynamics of k-essence in loop quantum cosmology (LQC). The study indicates that the loop quantum gravity (LQG) effect plays a key role only in the early epoch of the universe and is diluted at the later stage. The fixed points in LQC are basically consistent with that in standard Friedmann-Robertson-Walker (FRW) cosmology. For most of the attractor solutions, the stability conditions in LQC are in agreement with that for the standard FRW universe. But for some special fixed point, more tighter constraints are imposed thanks to the LQG effect.
We revisit spatially flat FLRW cosmology in light of recent advances in standard model relativistic fluid dynamics. Modern fluid dynamics requires the presence of curvature-matter terms in the energy-momentum tensor for consistency. These terms are linear in the Ricci scalar and tensor, such that the corresponding cosmological model is referred to as ``Ricci cosmology. No cosmological constant is included, there are no inflaton fields, bulk viscosity is assumed to be zero and we only employ standard Einstein gravity. Analytic solutions to Ricci cosmology are discussed, and we find that it is possible to support an early-time inflationary universe using only well-known ingredients from the Standard Model of physics and geometric properties of space-time.
We compute the spectrum of relic gravitons in a model of string cosmology. In the low- and in the high-frequency limits we reproduce known results. The full spectrum, however, also displays a series of oscillations which could give a characteristic signature at the planned LIGO/VIRGO detectors. For special values of the parameters of the model the signal reaches its maximum already at frequencies accessible to LIGO and VIRGO and it is close to the sensitivity of first generation experiments.