John T. Giblin Jr, James B. Mertens, Glenn D. Starkman

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 observer's 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.

Paul H. Frampton

The putative black holes which may constitute all the dark matter are described by a Kerr metric with only two parameters, mass M and angular momentum J. There has been little discussion of J since it plays no role in the upcoming attempt at detection by microlensing. Nevertheless J does play a central role in understanding the previous lack of detection, especially of CMB distortion. We explain why bounds previously derived from lack of CMB distortion are too strong for primordial black holes with J non-vanishing. Almost none of the dark matter black holes can be from stellar collapse, and nearly all are primordial, to avoid excessive CMB distortion.

Emory F. Bunn, Qingyang Xue, Haoxuan Zheng

We examine the degree to which observations of large-scale cosmic microwave background (CMB) polarization can shed light on the puzzling large-scale power modulation in maps of CMB anisotropy. We consider a phenomenological model in which the observed anomaly is caused by modulation of large-scale primordial curvature perturbations, and calculate Fisher information and error forecasts for future polarization data, constrained by the existing CMB anisotropy data. Because a significant fraction of the available information is contained in correlations with the anomalous temperature data, it is essential to account for these constraints. We also present a systematic approach to finding a set of normal modes that maximize the available information, generalizing the well-known Karhunen-Loeve transformation to take account of the constraints from the temperature data. A polarization map covering at least $\sim 60\%$ of the sky should be able to provide a $3\sigma$ detection of modulation at the level favored by the temperature data. A significant fraction of the information in such a data set is contained in the single mode that optimally encapsulates the signal due to temperature-polarization correlation.

Katy Clough, Eugene A. Lim, Brandon S. DiNunno, Willy Fischler, Raphael Flauger, Sonia Paban

We consider the effects of inhomogeneous initial conditions in both the scalar field profile and the extrinsic curvature on different inflationary models. In particular, we compare the robustness of small field inflation to that of large field inflation, using numerical simulations with Einstein gravity in 3+1 dimensions. We find that small field inflation can fail in the presence of subdominant gradient energies, suggesting that it is much less robust to inhomogeneities than large field inflation, which withstands dominant gradient energies. However, we also show that small field inflation can be successful even if some regions of spacetime start out in the region of the potential that does not support inflation. In the large field case, we confirm the results of [1-3] that inflation is robust if the inflaton occupies the inflationary part of the potential. Furthermore, we show that increasing initial scalar gradients will not form sufficiently massive inflation-ending black holes if the initial hypersurface is approximately flat. Finally, we consider the large field case with a varying extrinsic curvature K, such that some regions are initially collapsing. We find that this may again lead to local black holes, but overall the spacetime remains inflationary if the spacetime is open, which confirms previous theoretical studies.

Kurt Hinterbichler, Austin Joyce

In four dimensions, partially massless fields of all spins and depths possess a duality invariance akin to electric-magnetic duality. We construct metric-like gauge invariant curvature tensors for partially massless fields of all integer spins and depths, and show how the partially massless equations of motion can be recovered from first order field equations and Bianchi identities for these curvatures. This formulation displays duality in its manifestly local and covariant form, in which it acts to interchange the field equations and Bianchi identities.

Minxi He, Junyu Liu, Shiyun Lu, Siyi Zhou, Yi-Fu Cai, Yi Wang, Robert Brandenberger

A characteristic signature of String Gas Cosmology is primordial power spectra for scalar and tensor modes which are almost scale-invariant but with a red tilt for scalar modes but a blue tilt for tensor modes. This feature, however, can also be realized in the so-called G-inflation model, in which Horndeski operators are introduced which leads to a blue tensor tilt by softly breaking the Null Energy Condition. In this article we search for potential observational differences between these two cosmologies by performing detailed perturbation analyses based on the Effective Field Theory approach. Our results show that, although both two models produce blue tilted tensor perturbations, they behave differently in three aspects. Firstly, String Gas Cosmology predicts a specific consistency relation between the index of the scalar modes $n_s$ and that of tensor ones $n_t$, which is hard to be reproduced by G-inflation. Secondly, String Gas Cosmology typically predicts non-Gaussianities which are highly suppressed on observable scales, while G-inflation gives rise to observationally large non-Gaussianities because the kinetic terms in the action become important during inflation. However, after finely tuning the model parameters of G-inflation, there could remain a degeneracy between the two models. This degeneracy can be broken by a third observable, namely the scale dependence of the nonlinearity parameter, which vanishes for G-inflation but has a blue tilt in the case of String Gas Cosmology. Therefore, we conclude that String Gas Cosmology is in principle observationally distinguishable from the single field inflationary cosmology, even allowing for modifications such as G-inflation.

Robert W. Brown, Stephen G. Naculich

We introduce a new set of symmetries obeyed by tree-level gauge-theory amplitudes involving at least one gluon. The symmetry acts as a momentum-dependent shift on the color factors of the amplitude. Using the radiation vertex expansion, we prove the invariance under this color-factor shift of the $n$-gluon amplitude, as well as amplitudes involving massless or massive particles in an arbitrary representation of the gauge group with spin zero, one-half, or one. The Bern-Carrasco-Johansson relations are a direct consequence of this symmetry. We also introduce the cubic vertex expansion of an amplitude, and use it to derive a gauge-invariant constraint on the kinematic numerators of the amplitude. We show that the amplitudes of the bi-adjoint scalar theory are invariant under the color-factor symmetry, and use this to derive the null eigenvectors of the propagator matrix. We generalize the color-factor shift to loop level, and prove the invariance under this shift of one-loop $n$-gluon amplitudes in any theory that admits a color-kinematic-dual representation of numerators. We show that the one-loop color-factor symmetry implies known relations among the integrands of one-loop color-ordered amplitudes.