arXiv subjects

Matthew C. Johnson

Publications and source records attributed to Matthew C. Johnson.

At least 73 records · Page 4Linked to original sources

arXiv2017

Constraining cosmological ultra-large scale structure using numerical relativity

Cosmic inflation, a period of accelerated expansion in the early universe, can give rise to large amplitude ultra-large scale inhomogeneities on distance scales comparable to or larger than the observable universe. The cosmic microwave background (CMB) anisotropy on the largest angular scales is sensitive to such inhomogeneities and can be used to constrain the presence of ultra-large scale structure (ULSS). We numerically evolve nonlinear inhomogeneities present at the beginning of inflation in full General Relativity to assess the CMB quadrupole constraint on the amplitude of the initial fluctuations and the size of the observable universe relative to a length scale characterizing the ULSS. To obtain a statistically significant number of simulations, we adopt a toy model in which inhomogeneities are injected along a preferred direction. We compute the likelihood function for the CMB quadrupole including both ULSS and the standard quantum fluctuations produced during inflation. We compute the posterior given the observed CMB quadrupole, finding that when including gravitational nonlinearities, ULSS curvature perturbations of order unity are allowed by the data, even on length scales not too much larger than the size of the observable universe. Our results illustrate the utility and importance of numerical relativity for constraining early universe cosmology.

astro-ph.CO↗

arXiv2017

Analyzing the cosmic variance limit of remote dipole measurements of the cosmic microwave background using the large-scale kinetic Sunyaev Zel'dovich effect

Due to cosmic variance we cannot learn any more about large-scale inhomogeneities from the primary cosmic microwave background (CMB) alone. More information on large scales is essential for resolving large angular scale anomalies in the CMB. Here we consider cross correlating the large-scale kinetic Sunyaev Zel'dovich (kSZ) effect and probes of large-scale structure, a technique known as kSZ tomography. The statistically anisotropic component of the cross correlation encodes the CMB dipole as seen by free electrons throughout the observable Universe, providing information about long wavelength inhomogeneities. We compute the large angular scale power asymmetry, constructing the appropriate transfer functions, and estimate the cosmic variance limited signal to noise for a variety of redshift bin configurations. The signal to noise is significant over a large range of power multipoles and numbers of bins. We present a simple mode counting argument indicating that kSZ tomography can be used to estimate more modes than the primary CMB on comparable scales. A basic forecast indicates that a first detection could be made with next-generation CMB experiments and galaxy surveys. This paper motivates a more systematic investigation of how close to the cosmic variance limit it will be possible to get with future observations.

astro-ph.CO↗

arXiv2017

Simulating the Universe(s) III: Observables for the full bubble collision spacetime

This is the third paper in a series establishing a quantitative relation between inflationary scalar field potential landscapes and the relic perturbations left by the collision between bubbles produced during eternal inflation. We introduce a new method for computing cosmological observables from numerical relativity simulations of bubble collisions in one space and one time dimension. This method tiles comoving hypersurfaces with locally-perturbed Friedmann-Robertson-Walker coordinate patches. The method extends previous work, which was limited to the spacetime region just inside the future light cone of the collision, and allows us to explore the full bubble-collision spacetime. We validate our new methods against previous work, and present a full set of predictions for the comoving curvature perturbation and local negative spatial curvature produced by identical and non-identical bubble collisions, in single scalar field models of eternal inflation. In both collision types, there is a non-zero contribution to the spatial curvature and cosmic microwave background quadrupole. Some collisions between non-identical bubbles excite wall modes, giving extra structure to the predicted temperature anisotropies. We comment on the implications of our results for future observational searches. For non-identical bubble collisions, we also find that the surfaces of constant field can readjust in the presence of a collision to produce spatially infinite sections that become nearly homogeneous deep into the region affected by the collision. Contrary to previous assumptions, this is true even in the bubble into which the domain wall is accelerating.

hep-th↗

arXiv2016

Estimating gravitational radiation from super-emitting compact binary systems

Binary black hole mergers are among the most violent events in the Universe, leading to extreme warping of spacetime and copious emission of gravitational radiation. Even though black holes are the most compact objects they are not necessarily the most efficient emitters of gravitational radiation in binary systems. The final black hole resulting from a binary black hole merger retains a significant fraction of the pre-merger orbital energy and angular momentum. A non-vacuum system can in principle shed more of this energy than a black hole merger of equivalent mass. We study these super-emitters through a toy model that accounts for the possibility that the merger creates a compact object that retains a long-lived time-varying quadrupole moment. This toy model can capture the merger of neutron stars, but it can also be used to consider more exotic compact binaries. We hope that this toy model can serve as a guide to more rigorous numerical investigations into these systems.

gr-qc↗

arXiv2015

Observable Signatures of a Classical Transition

Eternal inflation arising from a potential landscape predicts that our universe is one realization of many possible cosmological histories. One way to access different cosmological histories is via the nucleation of bubble universes from a metastable false vacuum. Another way to sample different cosmological histories is via classical transitions, the creation of pocket universes through the collision between bubbles. Using relativistic numerical simulations, we examine the possibility of observationally determining if our observable universe resulted from a classical transition. We find that classical transitions produce spatially infinite, approximately open Friedman-Robertson-Walker universes. The leading set of observables in the aftermath of a classical transition are negative spatial curvature and a contribution to the Cosmic Microwave Background temperature quadrupole. The level of curvature and magnitude of the quadrupole are dependent on the position of the observer, and we determine the possible range of observables for two classes of single-scalar field models. For the first class, where the inflationary phase has a lower energy than the vacuum preceding the classical transition, the magnitude of the observed quadrupole generally falls to zero with distance from the collision while the spatial curvature grows to a constant. For the second class, where the inflationary phase has a higher energy than the vacuum preceding the classical transition, the magnitude of the observed quadrupole generically falls to zero with distance from the collision while the spatial curvature grows without bound. We find that the magnitude of the quadrupole and curvature grow with increasing centre of mass energy of the collision, and explore variations of the parameters in the scalar field lagrangian.

astro-ph.CO↗

arXiv2015

Forecasting constraints from the cosmic microwave background on eternal inflation

We forecast the ability of cosmic microwave background (CMB) temperature and polarization datasets to constrain theories of eternal inflation using cosmic bubble collisions. Using the Fisher matrix formalism, we determine both the overall detectability of bubble collisions and the constraints achievable on the fundamental parameters describing the underlying theory. The CMB signatures considered are based on state-of-the-art numerical relativistic simulations of the bubble collision spacetime, evolved using the full temperature and polarization transfer functions. Comparing a theoretical cosmic-variance-limited experiment to the WMAP and Planck satellites, we find that there is no improvement to be gained from future temperature data, that adding polarization improves detectability by approximately 30%, and that cosmic-variance-limited polarization data offer only marginal improvements over Planck. The fundamental parameter constraints achievable depend on the precise values of the tensor-to-scalar ratio and energy density in (negative) spatial curvature. For a tensor-to-scalar ratio of $0.1$ and spatial curvature at the level of $10^{-4}$, using cosmic-variance-limited data it is possible to measure the width of the potential barrier separating the inflating false vacuum from the true vacuum down to $M_{\rm Pl}/500$, and the initial proper distance between colliding bubbles to a factor $π/2$ of the false vacuum horizon size (at three sigma). We conclude that very near-future data will have the final word on bubble collisions in the CMB.

astro-ph.CO↗

arXiv2015

Testing eternal inflation with the kinetic Sunyaev Zel'dovich effect

Perhaps the most controversial idea in modern cosmology is that our observable universe is contained within one bubble among many, all inhabiting the eternally inflating multiverse. One of the few way to test this idea is to look for evidence of the relic inhomogeneities left by the collisions between other bubbles and our own. Such relic inhomogeneities induces a coherent bulk flow over gigaparsec scales. Therefore, bubble collisions leave unique imprints in the cosmic microwave background (CMB) through the kinetic Sunyaev Zel'dovich (kSZ) effect, temperature anisotropies induced by the scattering of photons from coherently moving free electrons in the diffuse intergalactic medium. The kSZ signature produced by bubble collisions has a unique directional dependence and is tightly correlated with the galaxy distribution; it can therefore be distinguished from other contributions to the CMB anisotropies. An important advantage of the kSZ signature is that it peaks on arcminute angular scales, where the limiting factors in making a detection are instrumental noise and foreground subtraction. This is in contrast to the collision signature in the primary CMB, which peaks on angular scales much larger than one degree, and whose detection is therefore limited by cosmic variance. In this paper, we examine the prospects for probing the inhomogeneities left by bubble collisions using the kSZ effect. We provide a forecast for detection using cross-correlations between CMB and galaxy surveys, finding that the detectability using the kSZ effect can be competitive with constraints from CMB temperature and polarization data.

astro-ph.CO↗

arXiv2014

Testing Inflation with Large Scale Structure: Connecting Hopes with Reality

The statistics of primordial curvature fluctuations are our window into the period of inflation, where these fluctuations were generated. To date, the cosmic microwave background has been the dominant source of information about these perturbations. Large scale structure is however from where drastic improvements should originate. In this paper, we explain the theoretical motivations for pursuing such measurements and the challenges that lie ahead. In particular, we discuss and identify theoretical targets regarding the measurement of primordial non-Gaussianity. We argue that when quantified in terms of the local (equilateral) template amplitude $f_{\rm NL}^{\rm loc}$ ($f_{\rm NL}^{\rm eq}$), natural target levels of sensitivity are $Δf_{\rm NL}^{\rm loc, eq.} \simeq 1$. We highlight that such levels are within reach of future surveys by measuring 2-, 3- and 4-point statistics of the galaxy spatial distribution. This paper summarizes a workshop held at CITA (University of Toronto) on October 23-24, 2014.

astro-ph.CO↗

arXiv2014

Simulating the universe(s) II: phenomenology of cosmic bubble collisions in full General Relativity

Observing the relics of collisions between bubble universes would provide direct evidence for the existence of an eternally inflating Multiverse; the non-observation of such events can also provide important constraints on inflationary physics. Realizing these prospects requires quantitative predictions for observables from the properties of the possible scalar field Lagrangians underlying eternal inflation. Building on previous work, we establish this connection in detail. We perform a fully relativistic numerical study of the phenomenology of bubble collisions in models with a single scalar field, computing the comoving curvature perturbation produced in a wide variety of models. We also construct a set of analytic predictions, allowing us to identify the phenomenologically relevant properties of the scalar field Lagrangian. The agreement between the analytic predictions and numerics in the relevant regions is excellent, and allows us to generalize our results beyond the models we adopt for the numerical studies. Specifically, the signature is completely determined by the spatial profile of the colliding bubble just before the collision, and the de Sitter invariant distance between the bubble centers. The analytic and numerical results support a power-law fit with an index $1< κ\lesssim 2$. For collisions between identical bubbles, we establish a lower-bound on the observed amplitude of collisions that is set by the present energy density in curvature.

hep-th↗

arXiv2014

Simulating the universe(s): from cosmic bubble collisions to cosmological observables with numerical relativity

The theory of eternal inflation in an inflaton potential with multiple vacua predicts that our universe is one of many bubble universes nucleating and growing inside an ever-expanding false vacuum. The collision of our bubble with another could provide an important observational signature to test this scenario. We develop and implement an algorithm for accurately computing the cosmological observables arising from bubble collisions directly from the Lagrangian of a single scalar field. We first simulate the collision spacetime by solving Einstein's equations, starting from nucleation and ending at reheating. Taking advantage of the collision's hyperbolic symmetry, simulations are performed with a 1+1-dimensional fully relativistic code that uses adaptive mesh refinement. We then calculate the comoving curvature perturbation in an open Friedmann-Robertson-Walker universe, which is used to determine the temperature anisotropies of the cosmic microwave background radiation. For a fiducial Lagrangian, the anisotropies are well described by a power law in the cosine of the angular distance from the center of the collision signature. For a given form of the Lagrangian, the resulting observational predictions are inherently statistical due to stochastic elements of the bubble nucleation process. Further uncertainties arise due to our imperfect knowledge about inflationary and pre-recombination physics. We characterize observational predictions by computing the probability distributions over four phenomenological parameters which capture these intrinsic and model uncertainties. This represents the first fully-relativistic set of predictions from an ensemble of scalar field models giving rise to eternal inflation, yielding significant differences from previous non-relativistic approximations. Thus, our results provide a basis for a rigorous confrontation of these theories with cosmological data.

hep-th↗

arXiv2013

Hierarchical Bayesian Detection Algorithm for Early-Universe Relics in the Cosmic Microwave Background

A number of theoretically well-motivated additions to the standard cosmological model predict weak signatures in the form of spatially localized sources embedded in the cosmic microwave background (CMB) fluctuations. We present a hierarchical Bayesian statistical formalism and a complete data analysis pipeline for testing such scenarios. We derive an accurate approximation to the full posterior probability distribution over the parameters defining any theory that predicts sources embedded in the CMB, and perform an extensive set of tests in order to establish its validity. The approximation is implemented using a modular algorithm, designed to avoid a posteriori selection effects, which combines a candidate-detection stage with a full Bayesian model-selection and parameter-estimation analysis. We apply this pipeline to theories that predict cosmic textures and bubble collisions, extending previous analyses by using: (1) adaptive-resolution techniques, allowing us to probe features of arbitrary size, and (2) optimal filters, which provide the best possible sensitivity for detecting candidate signatures. We conclude that the WMAP 7-year data do not favor the addition of either cosmic textures or bubble collisions to the standard cosmological model, and place robust constraints on the predicted number of such sources. The expected numbers of bubble collisions and cosmic textures on the CMB sky within our detection thresholds are constrained to be fewer than 4.0 and 5.2 at 95% confidence, respectively.

astro-ph.CO↗

arXiv2012

A robust constraint on cosmic textures from the cosmic microwave background

Fluctuations in the cosmic microwave background (CMB) contain information which has been pivotal in establishing the current cosmological model. These data can also be used to test well-motivated additions to this model, such as cosmic textures. Textures are a type of topological defect that can be produced during a cosmological phase transition in the early universe, and which leave characteristic hot and cold spots in the CMB. We apply Bayesian methods to carry out a rigorous test of the texture hypothesis, using full-sky data from the Wilkinson Microwave Anisotropy Probe. We conclude that current data do not warrant augmenting the standard cosmological model with textures. We rule out at 95% confidence models that predict more than 6 detectable cosmic textures on the full sky.

astro-ph.CO↗

arXiv2012

Determining the outcome of cosmic bubble collisions in full General Relativity

Cosmic bubble collisions provide an important possible observational window on the dynamics of eternal inflation. In eternal inflation, our observable universe is contained in one of many bubbles formed from an inflating metastable vacuum. The collision between bubbles can leave a detectable imprint on the cosmic microwave background radiation. Although phenomenological models of the observational signature have been proposed, to make the theory fully predictive one must determine the bubble collision spacetime, and thus the cosmological observables, from a scalar field theory giving rise to eternal inflation. Because of the intrinsically non-linear nature of the bubbles and their collision, this requires a numerical treatment incorporating General Relativity. In this paper, we present results from numerical simulations of bubble collisions in full General Relativity. These simulations allow us to accurately determine the outcome of bubble collisions, and examine their effect on the cosmology inside a bubble universe. We confirm the validity of a number of approximations used in previous analytic work, and identify qualitatively new features of bubble collision spacetimes. Both vacuum bubbles and bubbles containing a realistic inflationary cosmology are studied. We identify the constraints on the scalar field potential that must be satisfied in order to obtain collisions that are consistent with our observed cosmology, yet leave detectable signatures.

hep-th↗

arXiv2011

Cycles in the Multiverse

Eternal inflation is a seemingly generic consequence of theories that give rise to accelerated expansion of the universe and possess multiple vacuum states. Making predictions in an eternally inflating universe is notoriously difficult because one must compare infinite quantities, and a wide variety of regulating procedures yield radically different results. This is the measure problem of eternal inflation. In this paper, we analyze models of eternal inflation which allow for the possibility of cyclic bubble universes: in each bubble, standard cosmological evolution is re-played over and over again. Eternal inflation can generically arise in cyclic models that include a dark energy dominated phase. In such models, several problematic consequences of standard regulating procedures, such as the youngness and Boltzmann Brain problems, are substantially alleviated. We discuss the implications for making predictions in cyclic models, as well as some general implications for understanding the measure problem in eternal inflation.

hep-th↗

arXiv2011

Out of equilibrium: understanding cosmological evolution to lower-entropy states

Despite the importance of the Second Law of Thermodynamics, it is not absolute. Statistical mechanics implies that, given sufficient time, systems near equilibrium will spontaneously fluctuate into lower-entropy states, locally reversing the thermodynamic arrow of time. We study the time development of such fluctuations, especially the very large fluctuations relevant to cosmology. Under fairly general assumptions, the most likely history of a fluctuation out of equilibrium is simply the CPT conjugate of the most likely way a system relaxes back to equilibrium. We use this idea to elucidate the spacetime structure of various fluctuations in (stable and metastable) de Sitter space and thermal anti-de Sitter space.

hep-th↗

arXiv2011

First Observational Tests of Eternal Inflation: Analysis Methods and WMAP 7-Year Results

In the picture of eternal inflation, our observable universe resides inside a single bubble nucleated from an inflating false vacuum. Many of the theories giving rise to eternal inflation predict that we have causal access to collisions with other bubble universes, providing an opportunity to confront these theories with observation. We present the results from the first observational search for the effects of bubble collisions, using cosmic microwave background data from the WMAP satellite. Our search targets a generic set of properties associated with a bubble collision spacetime, which we describe in detail. We use a modular algorithm that is designed to avoid a posteriori selection effects, automatically picking out the most promising signals, performing a search for causal boundaries, and conducting a full Bayesian parameter estimation and model selection analysis. We outline each component of this algorithm, describing its response to simulated CMB skies with and without bubble collisions. Comparing the results for simulated bubble collisions to the results from an analysis of the WMAP 7-year data, we rule out bubble collisions over a range of parameter space. Our model selection results based on WMAP 7-year data do not warrant augmenting LCDM with bubble collisions. Data from the Planck satellite can be used to more definitively test the bubble collision hypothesis.

astro-ph.CO↗

arXiv2011

First Observational Tests of Eternal Inflation

The eternal inflation scenario predicts that our observable universe resides inside a single bubble embedded in a vast inflating multiverse. We present the first observational tests of eternal inflation, performing a search for cosmological signatures of collisions with other bubble universes in cosmic microwave background data from the WMAP satellite. We conclude that the WMAP 7-year data do not warrant augmenting LCDM with bubble collisions, constraining the average number of detectable bubble collisions on the full sky to be less than 1.6 at 68% CL. Data from the Planck satellite can be used to more definitively test the bubble collision hypothesis.

astro-ph.CO↗

arXiv2009

Dynamical compactification from de Sitter space

We show that D-dimensional de Sitter space is unstable to the nucleation of non-singular geometries containing spacetime regions with different numbers of macroscopic dimensions, leading to a dynamical mechanism of compactification. These and other solutions to Einstein gravity with flux and a cosmological constant are constructed by performing a dimensional reduction under the assumption of q-dimensional spherical symmetry in the full D-dimensional geometry. In addition to the familiar black holes, black branes, and compactification solutions we identify a number of new geometries, some of which are completely non-singular. The dynamical compactification mechanism populates lower-dimensional vacua very differently from false vacuum eternal inflation, which occurs entirely within the context of four-dimensions. We outline the phenomenology of the nucleation rates, finding that the dimensionality of the vacuum plays a key role and that among vacua of the same dimensionality, the rate is highest for smaller values of the cosmological constant. We consider the cosmological constant problem and propose a novel model of slow-roll inflation that is triggered by the compactification process.

hep-th↗