Stochastic inflation revisited: non-slow-roll statistics and DBI inflation

@article{Tolley2008StochasticIR,
  title={Stochastic inflation revisited: non-slow-roll statistics and DBI inflation},
  author={Andrew J. Tolley and Mark Wyman},
  journal={Journal of Cosmology and Astroparticle Physics},
  year={2008},
  volume={2008},
  pages={028}
}
  • A. Tolley, M. Wyman
  • Published 14 January 2008
  • Physics
  • Journal of Cosmology and Astroparticle Physics
Stochastic inflation describes the global structure of the inflationary universe by modeling the super-Hubble dynamics as a system of matter fields coupled to gravity where the sub-Hubble field fluctuations induce a stochastic force into the equations of motion. The super-Hubble dynamics are ultralocal, allowing us to neglect spatial derivatives and treat each Hubble patch as a separate universe. This provides a natural framework in which to discuss probabilities on the space of solutions and… 

Figures from this paper

A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
TLDR
A path-integral derivation of Langevin equations is developed, which solves conceptual issues of the heuristic approach made at the level of the classical equations of motion, and allows in principle to compute corrections to the stochastic formalism.
Stochastic inflation in phase space: Is slow roll a stochastic attractor?
An appealing feature of inflationary cosmology is the presence of a phase-space attractor, "slow roll", which washes out the dependence on initial field velocities. We investigate the robustness of
A Tail of Eternal Inflation
Non-trivial inflaton self-interactions can yield calculable signatures of primordial nonGaussianity that are measurable in cosmic surveys. Surprisingly, we find that the phase transition to slow-roll
Stochastic inflationary dynamics beyond slow-roll and consequences for primordial black hole formation
We consider the impact of quantum diffusion on inflationary dynamics during an ultra-slow-roll phase, which can be of particular significance for the formation of primordial black holes. We show, by
Enhanced Inflation in the Dirac-Born-Infeld framework
We consider the Einstein equations within the Dirac-Born-Infield (DBI) scenario for a spatially flat Friedmann-Robertson-Walker (FRW) spacetime without a cosmological constant. We derive the
Hamiltonian formalism for cosmological perturbations: the separate-universe approach
The separate-universe approach provides an effective description of cosmological perturbations at large scales, where the universe can be described by an ensemble of independent, locally homogeneous
The hand-made tail: non-perturbative tails from multifield inflation
Abstract It is becoming increasingly clear that large but rare fluctuations of the primordial curvature field, controlled by the tail of its probability distribution, could have dramatic effects on
Stochastic inflation and primordial black holes
During inflation, vacuum quantum fluctuations are amplified and stretched to astrophysical distances. They give rise to fluctuations in the cosmic microwave background (CMB) temperature and
A symmetric DBI action theory and its applications to inflationary cosmology
The Dirac-Born-Infeld (DBI) field theory in string theory is important and can provide the field of the universe’s inflation. At the same time, it provides a causal mechanism for generating the
Stochastic tunneling for strongly non-Gaussian inflationary theories
We reconsider the dynamics of stochastic or thermal tunneling in theories like Dirac-Born-Infeld inflation that have non-minimal kinetic terms and, as a result, strongly non-Gaussian perturbations.
...
...

References

SHOWING 1-10 OF 79 REFERENCES
Stochastic inflation and nonlinear gravity.
  • Salopek, Bond
  • Physics
    Physical review. D, Particles and fields
  • 1991
TLDR
It is argued that the most reasonable choice of time hypersurfaces for the Langevin system during inflation is {ital T}=ln({ital Ha}), where {ital H} and {ital a} are the local values of the Hubble parameter and the scale factor, since {italT} is the natural time for evolving the short-wavelength scalar field fluctuations in an inhomogeneous background.
Self-reproduction in k-inflation
We study cosmological self-reproduction in models of inflation driven by a scalar field {phi} with a noncanonical kinetic term (k-inflation). We develop a general criterion for the existence of
Formalizing the slow-roll approximation in inflation.
TLDR
This work proposes a new measure of inflation, based upon contraction of the comoving Hubble length as opposed to the usual $e$-foldings of physical expansion, and derives relevant formulae from an infinite hierarchy of slow-roll parameters.
STOCHASTIC DE SITTER (INFLATIONARY) STAGE IN THE EARLY UNIVERSE
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
Solving stochastic inflation for arbitrary potentials
A perturbative method for solving the Langevin equation of inflationary cosmology in the presence of backreaction is presented. In the Gaussian approximation, the method permits an explicit
Super Hubble nonlinear perturbations during inflation
We show that the nonlinear evolution of long-wavelength perturbations may be important in a wide class of inflationary scenarios. We develop a solution for the evolution of such nonlinear
Nonlinear evolution of long-wavelength metric fluctuations in inflationary models.
  • Salopek, Bond
  • Physics
    Physical review. D, Particles and fields
  • 1990
TLDR
This work describes a formalism for following the nonlinear propagation of long-wavelength metric and scalar-field fluctuations and performs an expansion in spatial gradients of the Arnowitt-Deser-Misner equations and retains only terms up to first order.
Langevin analysis of eternal inflation
It has been widely claimed that inflation is generically eternal to the future, even in models where the inflaton potential monotonically increases away from its minimum. The idea is that quantum
...
...