Path Integral for Stochastic Inflation: Non-Perturbative Volume Weighting, Complex Histories, Initial Conditions and the End of Inflation

Cosmological Measures without Volume Weighting

Many cosmologists (myself included) have advocated volume weighting for the cosmological measure problem, weighting spatial hypersurfaces by their volume. However, this often leads to the Boltzmann brain problem, that almost all observations would be by momentary Boltzmann brains that arise very briefly as quantum fluctuations in the late universe when it has expanded to a huge size, so that our observations (too ordered for Boltzmann brains) would be highly atypical and unlikely. Here it is suggested that volume weighting may be a mistake. Volume averaging is advocated as an alternative. One …

Non-thermal Histories and Implications for Structure Formation

We examine the evolution of cosmological perturbations in a non-thermal post-inflationary history with a late-time matter domination period prior to BBN. Such a cosmology could arise naturally in the well-motivated moduli scenario in the context of supersymmetry (SUSY) -- in particular in models of Split-SUSY. Sub-horizon dark matter perturbations grow linearly during the matter dominated phase before reheating and can lead to an enhancement in the growth of substructure on small scales, even in the presence of dark matter annihilations. This suggests that a new scale (the horizon size at rehe…

Replication Regulates Volume Weighting in Quantum Cosmology

Probabilities for observations in cosmology are conditioned both on the universe's quantum state and on local data specifying the observational situation. We show the quantum state defines a measure for prediction through such conditional probabilities that is well behaved for spatially large or infinite universes when the probabilities that our data is replicated are taken into account. In histories where our data are rare volume weighting connects top-down probabilities conditioned on both the data and the quantum state to the bottom-up probabilities conditioned on the quantum state alone. W…

Populating the Landscape: A Top Down Approach

We put forward a framework for cosmology that combines the string landscape with no boundary initial conditions. In this framework, amplitudes for alternative histories for the universe are calculated with final boundary conditions only. This leads to a top down approach to cosmology, in which the histories of the universe depend on the precise question asked. We study the observational consequences of no boundary initial conditions on the landscape, and outline a scheme to test the theory. This is illustrated in a simple model landscape that admits several alternative inflationary histories f…

The use of exp(iS[x]) in the sum over histories

The use of $\sum \exp(iS[x])$ as the generic form for a sum over histories in configuration space is discussed critically and placed in its proper context. The standard derivation of the sum over paths by discretizing the paths is reviewed, and it is shown that the form $\sum \exp(iS[x])$ is justified only for Schrodinger-type systems which are at most second order in the momenta. Extending this derivation to the relativistic free particle, the causal Green's function is expressed as a sum over timelike paths, and the Feynman Green's function is expressed both as a sum over paths which only go…

Volume Weighting the Measure of the Universe from Classical Slow-Roll Expansion

One of the most frustrating issues in early universe cosmology centers on how to reconcile the vast choice of universes in string theory and in its most plausible high energy sibling, eternal inflation, that jointly generate the string landscape with the fine-tuned and hence relatively small number of universes that have undergone a large expansion and can accommodate observers and, in particular, galaxies. We show that such observations are highly favored for any system whereby physical parameters are distributed at a high energy scale, due to the conservation of the Liouville measure and the…

轴子失准景观中的遗忘现象

Amnesia in the Axion Misalignment Landscape

该研究通过格点模拟探究暴胀前轴子失准景观的演化，发现meV质量范围存在敏感的“峰顶着陆”解，强自相互作用可使不同早期轴子历史产生相似晚期结构。

First study of reionization in tilted flat and untilted non-flat dynamical dark energy inflation models

We examine the effects of dark energy dynamics and spatial curvature on cosmic reionization by studying reionization in tilted spatially-flat and untilted non-flat XCDM and $ϕ$CDM dynamical dark energy inflation models that best fit the Planck 2015 cosmic microwave background (CMB) anisotropy and a large compilation of non-CMB data. We carry out a detailed statistical study, based on a principal component analysis and a Markov chain Monte Carlo analysis of a compilation of lower-redshift reionization data, to estimate the uncertainties in the cosmological model reionization histories. We find …

Effects and Detectability of Quasi-Single Field Inflation in the Large-Scale Structure and Cosmic Microwave Background

Quasi-single field inflation predicts a peculiar momentum dependence in the squeezed limit of the primordial bispectrum which smoothly interpolates between the local and equilateral models. This dependence is directly related to the mass of the isocurvatons in the theory which is determined by the supersymmetry. Therefore, in the event of detection of a non-zero primordial bispectrum, additional constraints on the parameter controlling the momentum-dependence in the squeezed limit becomes an important question. We explore the effects of these non-Gaussian initial conditions on large-scale stru…

反向随机膨胀

Time-reversed Stochastic Inflation

本文提出反向随机膨胀方法，通过反向福克-普朗克方程非微扰地推导量子时期内场值的概率分布，并推导出曲率涨落的新精确公式。

Roulette Inflation with Kähler Moduli and their Axions

We study 2-field inflation models based on the ``large-volume'' flux compactification of type IIB string theory. The role of the inflaton is played by a Kähler modulus τcorresponding to a 4-cycle volume and its axionic partner θ. The freedom associated with the choice of Calabi Yau manifold and the non-perturbative effects defining the potential V(τ, θ) and kinetic parameters of the moduli bring an unavoidable statistical element to theory prior probabilities within the low energy landscape. The further randomness of (τ, θ) initial conditions allows for a large ensemble of trajectories. Featur…

非微扰模量衰变与多组分暗物质

Non-Perturbative Modulus Decay and Multi-Component Dark Matter

本文研究模量凝聚体的非微扰衰变，发现Wino产生被抑制而轴子通道可能显著影响暗物质组分与暗辐射，需非线性研究验证。

Starting the Universe: Stable Violation of the Null Energy Condition and Non-standard Cosmologies

We present a consistent effective theory that violates the null energy condition (NEC) without developing any instabilities or other pathological features. The model is the ghost condensate with the global shift symmetry softly broken by a potential. We show that this system can drive a cosmological expansion with dH/dt > 0. Demanding the absence of instabilities in this model requires dH/dt <~ H^2. We then construct a general low-energy effective theory that describes scalar fluctuations about an arbitrary FRW background, and argue that the qualitative features found in our model are very gen…