We present a toy model of an axion gauge field inflation scenario that yields viable density and gravitational wave spectra. The scenario consists of an axionic inflaton in a steep potential that is effectively flattened by a coupling to a collection of non-Abelian gauge fields. The model predicts a blue-tilted gravitational wave spectrum that is dominated by one circular polarization, resulting in unique observational targets for cosmic microwave background and gravitational wave experiments. The handedness of the gravitational wave spectrum is incorporated in a model of leptogenesis through the axial-gravitational anomaly; assuming electroweak sphaeleron processes convert the lepton asymmetry into baryons, we predict an approximate lower bound on the tensorto-scalar ratio r ∼ 3 − 4 × 10 −2 for models that also explain the matter-antimatter asymmetry of the Universe.

Gravitational waves propagating through a stationary gauge field transform into gauge field waves and back again. When multiple families of flavor-space locked gauge fields are present, the gravitational and gauge field waves exhibit novel dynamics. At high frequencies, the system behaves like coupled oscillators in which the gravitational wave is the central pacemaker. Due to energy conservation and exchange among the oscillators, the wave amplitudes lie on a multidimensional sphere, reminiscent of neutrino flavor oscillations. This phenomenon has implications for cosmological scenarios based on flavor-space locked gauge fields.In a remarkable series of papers starting with the work of Gertsenshteyn [1], the authors showed that a gravitational wave propagating through a stationary magnetic field converts into an electromagnetic wave and back again [2][3][4]. Now that gravitational waves have been directly detected [5], no doubt there will be searches for this effect [6].Here we consider the more general phenomenon of the conversion of a gravitational wave into a stationary gauge field, as may be present in the early stages of the Universe [7][8][9]. In particular, we show that gravitational waves transform into tensor waves of a gauge field, disappearing and reappearing much like neutrino flavor oscillations. More complicated oscillation patterns are possible for multiple families of gauge fields. Quantization of these gravitational and gauge field tensor modes reveals a novel relationship between the energy and flavor eigenstates that may leave an imprint on a spectrum of primordial gravitational waves, or even suggest a new mechanism for the origin of a primordial spectrum.We consider a gauge field under general relativity,with metric signature − + ++, M P is the reduced Planck mass, and L m represents any other fields that may be present. We take an SU(2) fieldwhere g Y is the Yang-Mills coupling and the vector notation indicates direction in the three-dimensional flavor space. It is essential for this effect that the gauge field have a vacuum expectation value (vev), the analog of a stationary electric or magnetic field. To match the symmetries of our cosmological spacetime, we build a homogeneous and isotropic configuration as recently considered in the context of cosmic acceleration for inflation [7][8][9] or dark energy [10][11][12]. We work in the timelike gauge, so that A t = 0, and require that the remaining components, one per each group generator, be spatially independent in order to ensure homogeneity. Isotropy is then achieved by identifying the global symmetry of SU(2) with the rotational O(3) symmetry of Euclidean space. Hence, we write A µ = φ(τ ) e µ where e µ is a set of three mutually orthogonal, spacelike basis vectors. That is, the vector fields for flavors 1, 2, 3 point along the x, y, z directions, and we call this configuration flavorspace locked. The equation of motion in an expanding spacetime with line element ds, which may be solved exactly in terms of elliptic Jacobi functions. The...

We show that astrophysical gravitational waves can undergo an anomalous modulation when propagating through cosmic gauge field dark energy. A sufficiently strong effect, dependent on the gauge field energy density, would appear as a redshift-dependent opacity, thereby impacting the use of gravitational wave standard sirens to constrain the expansion history of the Universe. We investigate a particular model of cosmic gauge field dark energy and show that at early times it behaves like dark radiation, whereas a novel interaction causes it to drive cosmic acceleration at late times. Joint constraints on the cosmological scenario due to type 1a supernovae, baryon acoustic oscillations, and cosmic microwave background data are presented. In view of these constraints, we show that standard siren luminosity distances in the redshift range 0.5 z 1.5 would systematically dim by up to 1%, which may be distinguishable by third-generation gravitational wave detectors. I. INTRODUCTIONThe recent detection of gravitational waves has led to the emergence of gravitational wave astronomy, opening a new vista to astrophysical phenomena. The tantalizing prospect of combining gravitational wave (GW) sources with an electromagnetic (EM) counterpart is expected to lead to the development of a new method to constrain the expansion history of the Universe [1,2]. The GW profile of binary inspirals, for example, is so distinctive that the luminosity distance of the source can be inferred within 1 − 10% uncertainty [3]. Observatories such as advanced LIGO [4,5], the proposed Einstein Telescope [6,7], and the future space-based detector LISA [8] are expected to achieve the sensitivity required to make the detection of such "standard sirens" commonplace, extending the reach of GW astronomy to high redshift.The luminosity distance inferred from GW standard sirens is susceptible to novel effects that could be within reach of future GW detectors. In particular, we focus on the phenomenon of gravitational wave -gauge field (GWGF) oscillations, in which the amplitude of a GW modulates as it propagates through a cosmic gauge field [9]. In a dark energy model based on a homogeneous non-Abelian gauge field, this effect would result in a distinct imprint on astrophysical GWs. Specifically, GWs couple to wave-like excitations in a background gauge field. At high frequencies relevant for astrophysical sources, the system is akin to a pair of coupled oscillators: as energy exchange occurs between the two oscillators, the GW amplitude weakens and grows continuously, leading to temporal blind spots. An otherwise strong GW would thus arrive at our detectors with a much lower amplitude. To study this effect in a cosmological setting, we begin this article by considering a model of dark energy based on a SU(2) gauge field. While originally introduced in the context of primordial inflation [10], a similar model can also be used to address the present-day cosmic acceleration [11]. We show that the net effect on astrophysical GWs is a redshift-dependent reducti...

The dynamics of a gravitational wave propagating through a cosmic gauge field are dramatically different than in vacuum. We show that a gravitational wave acquires an effective mass, is birefringent, and its normal modes are a linear combination of gravitational waves and gauge field excitations, leading to the phenomenon of gravitational wave -gauge field oscillations. These surprising results provide insight into gravitational phenomena and may suggest new approaches to a theory of quantum gravity.