James B. Mertens

Departures from the Friedmann-Lemaitre-Robertston-Walker Cosmological Model in an Inhomogeneous Universe: A Numerical Examination

While the use of numerical general relativity for modeling astrophysical phenomena and compact objects is commonplace, the application to cosmological scenarios is only just beginning. Here, we examine the expansion of a spacetime using the Baumgarte-Shapiro-Shibata-Nakamura formalism of numerical relativity in synchronous gauge. This work represents the first numerical cosmological study that is fully relativistic, nonlinear, and without symmetry. The universe that emerges exhibits an average Friedmann-Lemaître-Robertson-Walker (FLRW) behavior; however, this universe also exhibits locally inhomogeneous expansion beyond that expected in linear perturbation theory around a FLRW background.

Gravitional radiation from first-order phase transitions in the presence of a fluid

First-order phase transitions are a source of stochastic gravitational radiation. Precision calculations of the gravitational waves emitted during these processes sourced by both the degrees of freedom undergoing the transition and the anisotropic stress of the ambient constituents have reached an age of maturity. Here we present numerical simulations of a scalar field coupled to a fluid for a set of models that represent different types of first-order phase transitions. We parametrize the final gravitational wave spectrum as a function of the ratio of the energies of the constituents and the coupling between the two sectors. In most of the cases we study, the field sector is the dominant source of gravitational radiation, but it is possible in certain scenarios for the fluid to have the most important contribution.

Integration of inhomogeneous cosmological spacetimes in the BSSN formalism

We present cosmological-scale numerical simulations of an evolving universe in full general relativity and introduce a new numerical tool, cosmograph, which employs the Baumgarte-Shapiro-Shibata-Nakamura formalism on a three-dimensional grid. Using cosmograph, we calculate the effect of an inhomogeneous matter distribution on the evolution of a spacetime. We also present the results of a set of standard stability tests to demonstrate the robustness of our simulations.

OBSERVABLE DEVIATIONS FROM HOMOGENEITY IN AN INHOMOGENEOUS UNIVERSE

How does inhomogeneity affect our interpretation of cosmological observations? It has long been wondered to what extent the observable properties of an inhomogeneous universe differ from those of a corresponding Friedman-Lemaitre-Robertson-Walker (FLRW) model, and how the inhomogeneities affect that correspondence. Here, we use numerical relativity to study the behavior of light beams traversing an inhomogeneous universe and construct the resulting Hubble diagrams. The universe that emerges exhibits an average FLRW behavior, but inhomogeneous structures contribute to deviations in observables across the observers sky. We also investigate the relationship between angular diameter distance and the angular extent of a source, finding deviations that grow with source redshift. These departures from FLRW are important path-dependent effects with implications for using real observables in an inhomogeneous universe such as our own.

Vacuum bubbles in the presence of a relativistic fluid

A bstractFirst order phase transitions are characterized by the nucleation and evolution of bubbles. The dynamics of cosmological vacuum bubbles, where the order parameter is independent of other degrees of freedom, are well known; more realistic phase transitions in which the order parameter interacts with the other constituents of the Universe is in its infancy. Here we present high-resolution lattice simulations that explore the dynamics of bubble evolution in which the order parameter is coupled to a relativistic fluid. We use a generic, toy potential, that can mimic physics from the GUT scale to the electroweak scale.

General relativistic corrections to the weak lensing convergence power spectrum

We compute the weak lensing convergence power spectrum,

A cosmologically motivated reference formulation of numerical relativity

C^{\kappa\kappa}(\theta)

The Limited Accuracy of Linearized Gravity

, in a dust-filled universe using fully non-linear general relativistic simulations. The spectrum is then compared to more standard, approximate calculations by computing the Bardeen (Newtonian) potentials in linearized gravity and utilizing the Born approximation. We find corrections to the angular power spectrum amplitude of order ten percent at very large angular scales,

Simulated reconstruction of the remote dipole field using the kinetic Sunyaev Zel’dovich effect

\ell ~ 2-3

Simulating the universe

, and percent-level corrections at intermediate angular scales of