Ewan D. Stewart

A More accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation

Formulae are derived for the spectra of scalar curvature perturbations and gravitational waves produced during inflation, special cases of which include power law inflation, natural inflation in the small angle approximation and inflation in the slow roll approximation.Abstract Formulae are derived for the spectra of scalar curvature perturbations and gravitational waves produced during inflation, special cases of which include power law inflation, natural inflation in the small angle approximation and inflation in the slow roll approximation.

A New delta N formalism for multi-component inflation

The δN formula that relates the final curvature perturbation on comoving slices to the inflaton perturbation on flat slices after horizon crossing is a powerful and intuitive tool for computing the curvature perturbation spectrum from inflation. However, it is customarily assumed further that the conventional slow-roll condition is satisfied, and satisfied by all components, during horizon crossing. In this paper, we develop a new δN formalism for multi-component inflation that can be applied in the most general situations. This allows us to generalize the idea of general slow-roll inflation to the multi-component case, in particular only applying the general slow-roll condition to the relevant component. We compute the power spectrum of the curvature perturbation in multi-component general slow-roll inflation, and find that under quite general conditions it is invertible.

Mutated hybrid inflation

Abstract A new model of inflation is described. An unusual form for the inflationary potential of obtained because the inflation corresponds to a non-trivial path in the configuration space of the two real scalar fields of the model. The model predicts a spectral index n = 1 − 3/2 N ≅ 0.97 for the density perturbations and negligible gravitational waves.

Euclidean quantum gravity and stochastic inflation

In this paper, we compare dispersions of a scalar field in Euclidean quantum gravity and stochastic inflation. We use Einstein gravity with a minimally coupled scalar field and a quadratic potential. We restrict our attention to small mass and small field cases. In Euclidean approach, we introduce the ground state wave function which is approximated by instantons. In stochastic approach, we introduce probability distribution of Hubble patches that can be approximated by a locally homogeneous universes up to a smoothing scale. We are assuming that the ground state wave function should correspond the stationary state of the probability distribution of the stochastic universe. By comparing the dispersion of both approaches, we conclude mainly three results. (1) For a statistical distribution with a certain value, we can find a corresponding instanton in the Euclidean side and it should be a complex-valued instanton. (2) The finite scale factor of the Euclidean approach corresponds the smoothing scale of the stochastic side; the universe is homogeneous up to the scale factor. (3) In addition, as the mass increases a critical value, both approaches break at the same time. Hence, generation of inhomogeneity in stochastic approach and the instability of classicality in Euclidean approach are related.

Inflationary models with a flat potential enforced by non-Abelian discrete gauge symmetries

Non-abelian discrete gauge symmetries can provide the inflaton with a flat potential even when one takes into account gravitational strength effects. The discreteness of the symmetries also provide special field values where inflation can end via a hybrid type mechanism. An interesting feature of this method is that it can naturally lead to extremely flat potentials and so, in principle, to inflation at unusually low energy scales. Two examples of effective field theories with this mechanism are given, one with a hybrid exit and one with a mutated hybrid exit. They include an explicit example in which the single field consistency condition is violated.

Inflation model building in moduli space

A self-consistent modular cosmology scenario and its testability in view of future CMB experiments are discussed. Particular attention is drawn to the enhanced symmetric points in moduli space which play crucial roles in our scenario. The running and moreover the running of running for the cosmic perturbation spectrum are also analyzed.

Anthropic Likelihood for the Cosmological Constant and the Primordial Density Perturbation Amplitude

Weinberg et al. calculated the anthropic likelihood of the cosmological constant using a model assuming that the number of observers is proportional to the total mass of gravitationally collapsed objects, with mass greater than a certain threshold, at t \rightarrow \infty. We argue that Weinbergs model is biased toward small \Lambda, and to try to avoid this bias we modify his model in a way that the number of observers is proportional to the number of collapsed objects, with mass and time equal to certain preferred mass and time scales. Compared to Weinbergs model, this model gives a lower anthropic likelihood of \Lambda_0 (T_+(\Lambda_0) ~ 5%). On the other hand, the anthropic likelihood of the primordial density perturbation amplitude from this model is high, while the likelihood from Weinbergs model is low. Furthermore, observers will be affected by the history of the collapsed object, and we introduce a method to calculate the anthropic likelihoods of \Lambda and Q from the mass history using the extended Press-Schechter formalism. The anthropic likelihoods for

Wronskian Formulation of the Spectrum of Curvature Perturbations

\Lambda

General solutions for tunneling of scalar fields with quartic potentials in de Sitter space

and Q from this method are similar to those from our single mass constraint model, but, unlike models using the single mass constraint which always have degeneracies between \Lambda and Q, the results from models using the mass history are robust even if we allow both \Lambda and Q to vary. In the case of Weinbergs flat prior distribution of \Lambda (pocket based multiverse measure), our mass history model gives T_+(\Lambda_0) ~ 10%, while the scale factor cutoff measure and the causal patch measure give T_+(\Lambda_0) \geq 30%.

False vacuum inflation with Einstein gravity

We present a new formulation for the evaluation of the primordial spectrum of curvature perturbations generated during inflation, using the fact that the Wronskian of the scalar field perturbation equation is constant. In the literature, there are many works on the same issue focusing on a few specific aspects or effects. Here we deal with the general multi-component scalar field, and show that our new formalism gives a method for evaluating the final amplitude of the curvature perturbation systematically and economically. The advantage of the new method is that one only has to solve a single mode of the scalar field perturbation equation backwards in time from the end of inflation to the stage at which the perturbation is within the Hubble horizon, at which the initial values of the scalar field perturbations are given. We also clarify the relation of the new method with the new, recently developed δN formalism.