(Loop) quantum gravity and the inflationary scenario

Quantum gravity, as a fundamental theory of space-time, is expected to reveal how the universe may have started, perhaps during or before an inflationary epoch. It may then leave a potentially observable (but probably miniscule) trace in cosmic large-scale structures that seem to match well with predictions of inflation models. A systematic quest to derive such tiny effects using one approach, loop quantum gravity, has, however, led to unexpected obstacles. Such models remain incomplete, and it is not clear whether loop quantum gravity can be consistent as a full theory. But some surprising effects appear to be generic and would drastically alter our understanding of space-time at large density. These new high-curvature phenomena are a consequence of a widening gap between quantum gravity and ordinary quantum-field theory on a background.     

High-energy gravity and the very early universe

It is suggested that gravity may not be asymptotically free at short distances because of the interaction of the graviton with matter. If gravity indeed becomes strong at high energies, a revolutionary change of our present theory on the early universe would seem to be necessary. During the first extremely small fraction of a second in the big-bang universe, gravity would have been so strong that it might not have been described by Einstein's theory of general relativity. The possibility of abnormally strong gravity at high energies or short distances is discussed in some detail. A possible explanation is proposed for the nonvanishing mean baryon number density of the universe. It is also pointed out that the universe may well escape from the catastrophic singularity of Penrose and Hawking.     

Fluctuations in the inflationary universe

In the usual treatment of the inflationary universe, it is assumed that the expectation value of some component of the Higgs field develops a non-zero symmetry breaking value Φ₀. However, in the models normally considered, the expectation value of Φ will be zero at all times because Φ and ?Φ are equally probable. To overcome this difficulty, we calculate the effective action as a function of 〈Φ²〉 rather than 〈Φ〉. This also solves the infra-red problem associated with a Coleman-Weinberg condition in de Sitter space. The expectation value of Φ² grows linearly with time at first and then as (t₂ ? t^?1). The irregularities in the resulting universe are smaller than those predicted by previous authors, though in the case of the standard SU(5) GUT they are still bigger than the limit set by the microwave background.     

Friedmann universe in a quantum gravity model

It is shown that, in a model theory of gravity, which quantises only the conformal part, the Robertson-Walker universe has a nonsingular evolution. The method also shows that there arises a lower bound to the physical length scale in any static metric with positive curvature.     

Limits on inflationary models of the universe

It is shown that there are severe limits on any model in which the universe undergoes a period of exponential expansion in the early stages. If one requires that the exponential expansion is long enough to account for the spatial flatness of the universe and that it should not create larger density fluctuations than are observed, it follows that the Hubble constant during the exponential expansion cannot be greater than 6 × 10^?5 of the Planck mass. This rules out all models in which the Hubble constant is of the order of the Planck mass. It is shown that one can satisfy the limits with a model containing a massive scalar field if the mass of the field is less than about 10¹⁴ GeV.     

Cosmological perturbations in the inflationary universe

In the framework of the gauge-invariant formalism the problem of the evolution of adiabatic perturbations in the metric for the theory of gravity with higher derivatives, which contains inflation, has been solved. The results are compared with the case when inflation arises due to a scalar field. The restrictions on the parameters of the models are given.     

Baryon asymmetry in the inflationary universe

It is shown that the baryon asymmetry in the inflationary universe under certain constraints on the masses of superheavy bosons can be larger than that in the standard baryosynthesis scenario. An important property of the model considered is that the final baryon asymmetry does not depend on initial conditions in the early universe in contrast to what occurs in the standard scenario based on B?L conserving GUTs.     

Quantum fluctuations in the new inflationary universe

The evolution of quantum fluctuations of a scalar field in de Sitter space is analyzed in the context of the new inflationary scenario. The duration of the inflationary phase is estimated and the problem of density perturbations resulting from quantum fluctuations of the Higgs field is discussed.     

Gravitational pressure,apparent horizon and thermodynamics of FLRW universe in the teleparallel gravity

In the context of the teleparallel equivalent of general relativity the concept of gravitational pressure and gravitational energy-momentum arisen in a natural way. In the case of a Friedmann–Lemaitre–Robertson–Walker space FLRW we obtain the total energy contained inside the apparent horizon and the radial pressure over the apparent horizon area. We use these definitions to written a thermodynamics relation \(T_{A}dS_{A} = dE_{A}+P_{A}dV_{A}\) at the apparent horizon, where \(E_{A}\) is the total energy inside the apparent horizon, \(V_{A}\) is the areal volume of the apparent horizon, \(P_{A}\) is the radial pressure over the apparent horizon area, \(S_{A}\) is the entropy which can be assumed as one quarter of the apparent horizon area only for a non stationary apparent horizon. We identify \(T_{A}\) as the temperature at the surface of the apparent horizon. We shown that for all expanding accelerated FLRW model of universe the radial pressure is positive.     

The fractal dimension of the inflationary universe

In cosmological scenarios of the new inflationary type, inflation never ends completely. The total volume of inflating regions grows exponentially with time, and they form a self-similar fractal of dimension slightly less than 3.     

Coleman-Weinberg theory and the new inflationary universe scenario

It is argued that a new inflationary universe scenario, which provides a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems, can be naturally implemented in the context of grand unified theories of the type of the Coleman-Weinberg theory.     

Fate of order parameter in the inflationary universe

We evaluate the friction term of the evolution equation of the order parameter in the new inflationary universe scenario. It is shown that the friction force is too weak so that the order parameter travels many time around minima of the Coleman-Weinberg potential. It causes unwanted large scale inhomogeneities. Reheating of the universe is also discussed.     

Scalar field fluctuations in the expanding universe and the new inflationary universe scenario

The behaviour of the scalar fied fluctuations in the exponentially expanding universe and their role in the new inflationary universe scenario are investigated.     

Generalized uncertainty principle, modified dispersion relations and the early universe thermodynamics

In this paper, we study the effects of Generalized Uncertainty Principle (GUP) and Modified Dispersion Relations (MDRs) on the thermodynamics of ultra-relativistic particles in early universe. We show that limitations imposed by GUP and particle horizon on the measurement processes, lead to certain modifications of early universe thermodynamics.     

An inflationary scenario taking into account of possible dark energy effects in the early universe

We investigate the possible effect of cosmological-constant type dark energy during the inflation period of the early universe. This is accommodated by a new dispersion relation in de Sitter space. The modified inflation model of a minimally coupled scalar field is still able to yield an observation-compatible scale-invariant primordial spectrum, simultaneously having the potential to generate a spectrum with lower power at large scales. A qualitative match to the WMAP 7-year data is presented. We obtain an Ω _Λ of the same order of that in the Λ-CDM model. Possible relations between the de Sitter scenario and Doubly Special Relativity (DSR) are also discussed.