Predictions in eternal inflation

Il Nuovo Cimento B

Physical Review D

Eternal inflation is studied in the context of warm inflation. We focus on different tools to analyze the effects of dissipation and the presence of a thermal radiation bath on the fluctuation-dominated regime, for which the self-reproduction of Hubble regions can take place. The tools we explore are the threshold inflaton field and threshold number of e-folds necessary to establish a self-reproduction regime and the counting of Hubble regions, using generalized conditions for the occurrence of a fluctuation-dominated regime. We obtain the functional dependence of these quantities on the dissipation and temperature. A Sturm-Liouville analysis of the Fokker-Planck equation for the probability of having eternal inflation and an analysis for the probability of having eternal points are performed. We have considered the representative cases of inflation models with monomial potentials of the form of chaotic and hilltop ones. Our results show that warm inflation tends to initially favor the onset of a self-reproduction regime for smaller values of the dissipation. As the dissipation increases, it becomes harder than in cold inflation (i.e., in the absence of dissipation) to achieve a self-reproduction regime for both types of models analyzed. The results are interpreted and explicit analytical expressions are given whenever that is possible.

Eternal Inflation, 2019

In generic models of cosmological inflation, the geometry of spacetime is highly inhomogeneous on scales of many Hubble sizes, consisting of infinitely many causally disconnected “pocket universes.” The values of cosmological observables and even of the low-energy coupling constants and particle masses may vary among the pocket universes. String-theoretic landscape models present a similar structure of a “multiverse” where an infinite number of de Sitter, asymptotically flat (Minkowski), and anti-de Sitter pocket universes are nucleated via quantum tunneling. Since observers on Earth have no information about their location within the eternally inflating multiverse, the main question in this context has been that of obtaining statistical predictions for quantities observed at a “random” location. In this book, I discuss the long-standing technical and conceptual problems arising within this statistical framework, known collectively as the “measure problem” in multiverse cosmology. After reviewing various existing approaches and mathematical techniques developed in the past two decades for studying these issues, I describe a new proposal for a measure in the multiverse, called the reheating-volume (RV) measure. The RV measure is based on approximating an infinite multiverse by a family of progressively larger but finite multiverses. Such multiverses occur seldom but are allowed by all cosmological “multiverse” models. I give a detailed description of the new measure and its applications to generic models of eternal inflation of random-walk type and to landscape scenarios. The RV prescription is formulated differently for scenarios with eternal inflation of the random walk type and for landscape scenarios. For models of random-walk inflation, the RV cutoff considers events where one has a finite (although large) total reheating volume to the future of an initial Hubble patch. For landscape scenarios, I propose to calculate the distribution of observable quantities in a landscape that is conditioned in probability to nucleate a finite total number of bubbles to the future of an initial bubble. In each case I show in a mathematically rigorous manner that the RV measure yields well-defined results that are invari- ant with respect to general coordinate transformations, independent of the initial conditions at the beginning of inflation, and free of the “youngness paradox” and the “Boltzmann brain” problems affecting some of the previously proposed measures. I derive analytic formulas for RV-regulated probability distributions that is suitable for numerical computations.

1997

The physics of the inflationary universe requires the study of the out of equilibrium evolution of quantum fields in curved spacetime. We present the evolution for both the geometry and the matter (described by the quantum inflaton field) by means of the non-perturbative large N limit combined with semi-classical gravitational dynamics including the back-reaction of quantum fluctuations self-consistently for a new inflation scenario. We provide a criterion for the validity of the classical approximation and a full analysis of the case in which spinodal quantum fluctuations drive the evolution of the scale factor. Under carefully determined conditions, we show that the full field equations may be well approximated by those of a single composite field which obeys the classical equation of motion in all cases. The de Sitter stage is found to be followed by a matter dominated phase. We compute the spectrum of scalar density perturbations and argue that the spinodal instabilities are responsible for a 'red' spectrum with more power at longer wavelengths. A criterion for the validity of these models is provided and contact with the reconstruction program is established. * To appear in the Proceedings of SEWM'97 † Laboratoire Associé au CNRS UA280.

Lecture Notes in Physics, 1986

The dynamics of a large-scale quasi-homogeneous scalar field producing the de Sitter (inflationary) stage in the early universe is strongly affected by small-scale quantum fluctuations of the same scalar field and, in this way, becomes stochastic. The evolution of the corresponding large-scale space-time metric follows that of the scalar field and is stochastic also. The Fokker-Planck equation for the evolution of the large-scale scalar field is obtained and solved for an arbitrary scalar field potential. The average duration of the de-Sitter stage in the new inflationary scenario is calculated (only partial results on this problem were known earlier). Applications of the developed formalism to the chaotic inflationary scenario and to quantum inflation are considered. In these cases, the main unsolved problem lies in initial pre-inflationary conditions.

2013

The inflationary phase of the Universe is explored by proposing a toy model related to the scalar field, termed as {\it inflaton}. The potential part of the energy density in the said era is assumed to have a constant vacuum energy density part and a variable part containing the inflaton. The prime idea of the proposed model constructed in the framework of the closed Universe is based on a fact that the inflaton is the root cause of the orientation of the space. According to this model the expansion of the Universe in the inflationary epoch is not approximately rather exactly exponential in nature and thus it can solve some of the fundamental puzzles, viz. flatness as well as horizon problems. It is also predicted that the constant energy density part in the potential may be associated to the dark energy, which is eventually different from the vacuum energy, at least in the inflationary phase of the Universe. However, the model keeps room for the end of inflationary era.

Physical Review D, 2000

Models of inflationary cosmology can lead to variation of observable parameters ("constants of Nature") on extremely large scales. The question of making probabilistic predictions for today's observables in such models has been investigated in the literature. Because of the infinite thermalized volume resulting from eternal inflation, it has proven difficult to obtain a meaningful and unambiguous probability distribution for observables, in particular due to the gauge dependence. In the present paper, we further develop the gaugeinvariant procedure proposed in a previous work for models with a continuous variation of "constants". The recipe uses an unbiased selection of a connected piece of the thermalized volume as sample for the probability distribution. To implement the procedure numerically, we develop two methods applicable to a reasonably wide class of models: one based on the Fokker-Planck equation of stochastic inflation, and the other based on direct simulation of inflationary spacetime. We present and compare results obtained using these methods.

Physical Review D, 2001

I study a stochastic approach to the recently introduced fresh inflation model for super Hubble scales. I find that the state loses its coherence at the end of the fresh inflationary period as a consequence of the damping of the interference function in the reduced density matrix. This fact should be a consequence of (a) the relative evolution of both the scale factor and the horizon and (b) the additional thermal and dissipative effects. This implies a relevant difference with respect to supercooled inflationary scenarios which require a very rapid expansion of the scale factor to the give decoherence of super Hubble fluctuations.

Physics Letters B, 2006

Using the Ponce de Leon background metric, which describes a 5D universe in an apparent vacuum:Ḡ AB = 0, we study the effective 4D evolution of both, the inflaton and gauge-invariant scalar metric fluctuations, in the recently introduced model of space time matter inflation.

Physical Review D, 1996

is extremely sensitive to the choice of the time coordinate t. For example, cutoffs at a fixed proper time and at a fixed scale factor give drastically different results . An alternative procedure [1] is to introduce a cutoff at the time t (j) c when all but a small fraction ε of the co-moving volume destined to thermalize into regions of type j has thermalized. The value of ε is taken to be the same for all types of thermalized regions, and for all universes in the ensemble, but the corresponding cutoff times t (j) c are generally different. The limit ε → 0 is taken after calculating the probability distribution for the constants. It was shown in that the resulting probabilities are rather insensitive to the choice of time parametrization.