John T. Giblin Jr

Gravitational waves from the end of inflation: Computational strategies

Parametric resonance or preheating is a plausible mechanism for bringing about the transition between the inflationary phase and a hot, radiation dominated universe. This epoch results in the rapid production of heavy particles far from thermal equilibrium and could source a significant stochastic background of gravitational radiation. Here, we present a numerical algorithm for computing the contemporary power spectrum of gravity waves generated in this post-inflationary phase transition for a large class of scalar-field driven inflationary models. We explicitly calculate this spectrum for both quartic and quadratic models of chaotic inflation, and low-scale hybrid models. In particular, we consider hybrid models with an inverted potential. These models have a very short and intense period of resonance which is qualitatively different from previous examples studied in this context, but we find that they lead to a similar spectrum of gravitational radiation.

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.

Gravitational-wave cosmology across 29 decades in frequency

Quantum fluctuations of the gravitational field in the early Universe, amplified by inflation, produce a primordial gravitational-wave background across a broad frequency band. We derive constraints on the spectrum of this gravitational radiation, and hence on theories of the early Universe, by combining experiments that cover 29 orders of magnitude in frequency. These include Planck observations of cosmic microwave background temperature and polarization power spectra and lensing, together with baryon acoustic oscillations and big bang nucleosynthesis measurements, as well as new pulsar timing array and ground-based interferometer limits. While individual experiments constrain the gravitational-wave energy density in specific frequency bands, the combination of experiments allows us to constrain cosmological parameters, including the inflationary spectral index n_t and the tensor-to-scalar ratio r. Results from individual experiments include the most stringent nanohertz limit of the primordial background to date from the Parkes Pulsar Timing Array, Ω_(GW)(f) < 2.3 × 10^(−10). Observations of the cosmic microwave background alone limit the gravitational-wave spectral index at 95% confidence to n_t ≲ 5 for a tensor-to-scalar ratio of r = 0.11. However, the combination of all the above experiments limits n_t < 0.36. Future Advanced LIGO observations are expected to further constrain n_t < 0.34 by 2020. When cosmic microwave background experiments detect a nonzero r, our results will imply even more stringent constraints on n_t and, hence, theories of the early Universe.

Thermal inflation and the gravitational wave background

We consider the impact of thermal inflation -- a short, secondary period of inflation that can arise in supersymmetric scenarios -- on the stochastic gravitational wave background. We show that while the primordial inflationary gravitational wave background is essentially unchanged at CMB scales, it is massively diluted at solar system scales and would be unobservable by a BBO style experiment. Conversely, bubble collisions at the end of thermal inflation can generate a new stochastic background. We calculate the likely properties of the bubbles created during this phase transition, and show that the expected amplitude and frequency of this signal would fall within the BBO range.

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.

Preheating with non-minimal kinetic terms

We present the first (3+1)-dimensional numerical simulations of scalar fields with nonminimal kinetic terms. As an example, we examine the existence and stability of preheating in the presence of a Dirac-Born-Infeld inflaton coupled to a canonical matter field. The simulations represent the full nonlinear theory in the presence of an expanding universe. We show that parametric resonance in the matter field along with self-resonance in the inflaton repopulate the universe with matter particles as efficiently as in traditional preheating.

Spacetime Embedding Diagrams for Spherically Symmetric Black Holes

We show that it is possible to embed the 1 + 1 dimensional reduction of certain spherically symmetric black hole spacetimes into 2 + 1 Minkowski space. The spacetimes of interest (Schwarzschild de-Sitter, Schwarzschild anti de-Sitter, and Reissner-Nordström near the outer horizon) represent a class of metrics whose geometries allow for such embeddings. The embedding diagrams have a dynamic character which allows one to represent the motion of test particles. We also analyze various features of the embedding construction, deriving the general conditions under which our procedure provides a smooth embedding. These conditions also yield an embedding constant related to the surface gravity of the relevant horizon.

Gauge field preheating at the end of inflation

Here we consider the possibility of preheating the Universe via the parametric amplification of a massless, U(1) abelian gauge field. We assume that the gauge field is coupled to the inflaton via a conformal factor with one free parameter. We present the results of high-resolution three-dimensional simulations of this model and show this mechanism efficiently preheats the Universe to a radiation-dominated final state.

Estimates of maximum energy density of cosmological gravitational-wave backgrounds

The recent claim by BICEP2 of evidence for primordial gravitational waves from inflation has focused interest on the potential for early-Universe cosmology using observations of gravitational waves. In addition to cosmic microwave background detectors, efforts are underway to carry out gravitational-wave astronomy over a wide range of frequencies including pulsar timing arrays (nHz), space-based detectors (mHz), and terrestrial detectors (∼10–2000 Hz). This multiband effort will probe a wide range of times in the early Universe (each corresponding to a different energy scale), during which gravitational-wave backgrounds may have been produced through processes such as phase transitions or preheating. In this letter, we derive a rule of thumb (not quite so strong as an upper limit) governing the maximum energy density of cosmological backgrounds. For most cosmological scenarios, we expect the energy density spectrum to peak at values of Ωgw(f) . 10. We discuss the applicability of this rule of thumb and the implications for gravitationalwave astronomy.