Anthony Aguirre’s research while affiliated with University of California, Santa Cruz and other places

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. 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.

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.

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.

We explore the viability of a boson dark matter candidate with an asymmetry between the number densities of particles and antiparticles. A simple thermal field theory analysis confirms that, under certain general conditions, this component would develop a Bose-Einstein condensate in the early universe that, for appropriate model parameters, could survive the ensuing cosmological evolution until now. The condensation of a dark matter component in equilibrium with the thermal plasma is a relativistic process, hence the amount of matter dictated by the charge asymmetry is complemented by a hot relic density frozen out at the time of decoupling. Contrary to the case of ordinary WIMPs, dark matter particles in a condensate can be very light, $10^{-22}\,{\rm eV} \lesssim m \lesssim 10^2\,{\rm eV}$; the lower limit arises from constraints on small-scale structure formation, while the upper bound ensures that the density from thermal relics is not too large. Big-Bang nucleosynthesis constrains the temperature of decoupling to the scale of the QCD phase transition or above. This requires large dark matter-to-photon ratios and very weak interactions with standard model particles. Finally, we argue that a given boson particle that was in thermal equilibrium in the early universe may be in a condensate, or in the form of thermal relics, but we cannot have a combination of both contributing significantly to the mass density today.

We explore the viability of a boson dark matter candidate with an asymmetry between the number densities of particles and antiparticles. A simple thermal field theory analysis confirms that, under certain general conditions, this component would develop a Bose-Einstein condensate in the early universe that, for appropriate model parameters, could survive the ensuing cosmological evolution until now. The condensation of a dark matter component in equilibrium with the thermal plasma is a relativistic process, hence the amount of matter dictated by the charge asymmetry is complemented by a hot relic density frozen out at the time of decoupling. Contrary to the case of ordinary WIMPs, dark matter particles in a condensate must be lighter than a few tens of eV so that the density from thermal relics is not too large. Big-Bang nucleosynthesis constrains the temperature of decoupling to the scale of the QCD phase transition or above. This requires large dark matter-to-photon ratios and very weak interactions with standard model particles.

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 $1< \kappa \lesssim 2$. 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.

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 entire collision spacetime, from nucleation to reheating, inside each bubble. 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, in the Sachs-Wolfe approximation, 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 centre 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 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.

We perform a semi-classical analysis of the Emergent Universe scenario for inflation. Fixing the background, and taking the inflaton to be homogenous, we cast the inflaton's evolution as a one-dimensional quantum mechanics problem. We find that the tuning required over a long time scale for this inflationary scenario is unstable quantum mechanically. Considering the inflaton field value as a wavepacket, the spreading of the wavepacket destroys any chance of both starting and ending with a well-formed state. Thus, one cannot have an Einstein static universe to begin with that evolves into a well-defined beginning to inflation a long time later.

High frequency trading has led to widespread efforts to reduce information propagation delays between physically distant exchanges. Using relativistically correct millisecond-resolution tick data, we document a 3-millisecond decrease in one-way communication time between the Chicago and New York areas that has occurred from April 27th, 2010 to August 17th, 2012. We attribute the first segment of this decline to the introduction of a latency-optimized fiber optic connection in late 2010. A second phase of latency decrease can be attributed to line-of-sight microwave networks, operating primarily in the 6-11 GHz region of the spectrum, licensed during 2011 and 2012. Using publicly available information, we estimate these networks' latencies and bandwidths. We estimate the total infrastructure and 5-year operations costs associated with these latency improvements to exceed $500 million.

High frequency trading has led to widespread efforts to reduce information propagation delays between physically distant exchanges. Using relativistically correct millisecond-resolution tick data, we document a 3-millisecond decrease in one-way communication time between the Chicago and New York areas that has occurred from April 27th, 2010 to August 17th, 2012. We attribute the first segment of this decline to the introduction of a latency-optimized fiber optic connection in late 2010. A second phase of latency decrease can be attributed to line-of-sight microwave networks, operating primarily in the 6-11 GHz region of the spectrum, licensed during 2011 and 2012. Using publicly available information, we estimate these networks' latencies and bandwidths. We estimate the total infrastructure and 5-year operations costs associated with these latency improvements to exceed $500 million.