We consider gravitational wave production due to parametric resonance at the end of inflation, or "preheating". This leads to large inhomogeneities which source a stochastic background of gravitational waves at scales inside the comoving Hubble horizon at the end of inflation. We confirm that the present amplitude of these gravitational waves need not depend on the inflationary energy scale.We analyze an explicit model where the inflationary energy scale is ∼ 10 9 GeV, yielding a signal close to the sensitivity of Advanced LIGO and BBO. This signal highlights the possibility of a new observational "window" into inflationary physics, and provides significant motivation for searches for stochastic backgrounds of gravitational waves in the Hz to GHz range, with an amplitude on the order of Ωgw(k)h 2 ∼ 10 −11 . Finally, the strategy used in our numerical computations is applicable to the gravitational waves generated by many inhomogeneous processes in the early universe.A successful model of inflation must have a "graceful exit" that describes the transition from the accelerated phase to a thermalized universe [1]. A widely studied mechanism for achieving this is preheating (e.g. [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]). After inflation, the inflaton (or a related field) oscillates about the bottom of its potential, driving the resonant amplification of specific momentum modes of some coupled field(s). This renders the universe inhomogeneous, and the resulting spatial gradients source gravitational waves. For GUT inflation, the present peak frequency is between 1 MHz and 1 GHz [5,15]. It was conjectured that the characteristic frequency is inversely proportional to the inflationary scale, while the amplitude can be independent of this scale [15], leading to a signal potentially detectable by future iterations of LIGO and BBO. We confirm this conjecture by numerically computing the gravitational wave spectrum in a toy model of preheating following low scale inflation. While simple inflationary models typically involve GUT scale physics, many stringy models have a much lower inflationary scale, so this signal may eventually lead to new constraints on these models. The tools developed for this analysis will allow us to explore fully realistic preheating models in an expanding background. Furthermore, our computational strategy applies to any inhomogeneous phase in the universe, and may have applications beyond the present problem.Computational Strategy & Results: During parametric resonance, momentum modes of a field χ are pumped by an oscillating field φ. In simple models φ is the inflaton, but in hybrid models φ is the direction orthogonal to the inflationary trajectory which induces the "waterfall" transition [20,21]. In either case the lagrangian can be expressed asWe numerically simulate the nonlinear field evolution in a conformally rigid spacetime background. We can then compute the spatial parts of T µν at any given time. The tensor contribution to the metric perturbation and Einstein equations readwhere the ove...

We study the onset of the reheating epoch at the end of axion-driven inflation where the axion is coupled to an Abelian, U (1), gauge field via a Chern-Simons interaction term. We focus primarily on m 2 φ 2 inflation and explore the possibility that preheating can occur for a range of coupling values consistent with recent observations and bounds on the overproduction of primordial black holes. We find that for a wide range of parameters preheating is efficient. In certain cases the inflaton transfers all of its energy to the gauge fields within a few oscillations. In most cases, we find that the gauge fields on sub-horizon scales end preheating in an unpolarized state due to the existence of strong rescattering between the inflaton and gauge-field modes. We also present a preliminary study of an axion monodromy model coupled to U (1) gauge fields, seeing a similarly efficient preheating behavior as well as indications that the coupling strength has an effect on the creation of oscillons.1 Note that at this order (linear) in fluctuations, Coulomb gauge and temporal gauge (A0 = 0) are equivalent. This can be seen trivially from Eqn. (2.12), the Gauss' law constraint. In the linear regime, this equation reads ∂j∂jA0 − ∂τ ∂jAj = 0. In Coulomb gauge, assuming k = 0, this constraint reads A0 = 0. In temporal gauge, Gauss's law reads ∂τ ∂jAj = 0, which for k = 0, implies ∂jAj = 0.

In this work we compute the production of magnetic fields in models of axion inflation coupled to the hypercharge sector of the Standard Model through a Chern-Simons interaction term. We make the simplest choice of a quadratic inflationary potential and use lattice simulations to calculate the magnetic field strength, helicity and correlation length at the end of inflation. For small values of the axion-gauge field coupling strength the results agree with no-backreaction calculations and estimates found in the literature. For larger couplings the helicity of the magnetic field differs from the no-backreaction estimate and depends strongly on the comoving wavenumber. We estimate the post-inflationary evolution of the magnetic field based on known results for the evolution of helical and non-helical magnetic fields. The magnetic fields produced by axion inflation with large couplings to U (1) Y can reach B eff 10 −16 G, exhibiting a field strength B phys ≈ 10 −13 G and a correlation length λ phys ≈ 10 pc. This result is insensitive to the exact value of the coupling, as long as the coupling is large enough to allow for instantaneous preheating. Depending on the assumptions for the physical processes that determine blazar properties, these fields can be found consistent with blazar observations based on the value of B eff . Finally, the intensity of the magnetic field for large coupling can be enough to satisfy the requirements for a recently proposed baryogenesis mechanism, which utilizes the chiral anomaly of the Standard Model.

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 ðfÞ < 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-toscalar ratio of r ¼ 0.11. However, the combination of all the above experiments limits n t < 0.36. Future * paul.lasky@monash.eduPublished by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.PHYSICAL REVIEW X 6, 011035 (2016) 2160-3308=16=6(1)=011035 (11) 011035-1 Published by the American Physical Society 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.

We study gravitational wave production during Abelian gauge-field preheating following inflation. We consider both scalar and pseudoscalar inflaton models coupled directly to Abelian gauge fields via either a dilatonic coupling to the gauge-field kinetic term or an axial coupling to a Chern-Simons term. In both cases gravitational waves are produced efficiently during the preheating phase, with a signature louder than most cosmological signals. These gravitational waves can contribute to the radiation energy budget of Universe at a level which will be probed by upcoming cosmic microwave background experiments through N eff . For axially coupled fields the resulting gravitational wave spectrum is helically polarized-a unique feature that can be used to differentiate it from other stochastic gravitational wave backgrounds. We compute the gravitational topological charge and demonstrate that gauge preheating following axion inflation may be responsible for the matter-antimatter asymmetry of the Universe via gravitational leptogenesis.

We study gravitational wave production from gauge preheating in a variety of inflationary models, detailing its dependence on both the energy scale and the shape of the potential. We show that gauge preheating generically leads to a large gravitational wave background that contributes significantly to the effective number of relativistic degrees of freedom in the early Universe, N eff . We demonstrate that the efficiency of gravitational wave production is correlated with the tensor-to-scalar ratio, r.In particular, we show that efficient gauge preheating in models whose tensor-to-scalar ratio would be detected by next-generation cosmic microwave background experiments (r 10 −3 ) will either be detected through its contribution to N eff or ruled out. Furthermore, we show that bounds on N eff provide the most sensitive probe of the possible axial coupling of the inflaton to gauge fields regardless of the potential.

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.

A population of very light primordial black holes which evaporate before nucleosynthesis begins is unconstrained unless the decaying black holes leave stable relics. We show that gravitons Hawking radiated from these black holes would source a substantial stochastic background of high frequency gravititational waves (10 12 Hz or more) in the present universe. These black holes may lead to a transient period of matter dominated expansion. In this case the primordial universe could be temporarily dominated by large clusters of "Hawking stars" and the resulting gravitational wave spectrum is independent of the initial number density of primordial black holes.