The key to the phenomenological success of inflation models with axion and SU(2) gauge fields is the isotropic background of the SU(2) field. Previous studies showed that this isotropic background is an attractor solution during inflation starting from anisotropic (Bianchi type I) spacetime; however, not all possible initial anisotropic parameter space was explored. In this paper, we explore more generic initial conditions without assuming the initial slow-roll dynamics. We find some initial anisotropic parameter space which does not lead to the isotropic background, but to violation of slow-roll conditions, terminating inflation prematurely. The basin of attraction increases when we introduce another scalar field acting as inflaton and make the axion-SU(2) system a spectator sector. Therefore, the spectator axion-SU(2) model is phenomenologically more attractive.

At the linear level, the gravitational wave (GW) spectrum predicted by inflation, and many of its alternatives, can have arbitrarily small amplitude and consequently an unconstrained tilt. However, at second order, tensor fluctuations are sourced by scalar fluctuations that have been measured in the cosmic microwave background (CMB). These second order fluctuations generically produce a minimum amount of tensor perturbations corresponding to a tensor-to-scalar ratio of r ∼ 10 −6 . Inverting this relationship yields a bound on the tensor tilt sourced by scalar fluctuations. Since this induced GW spectrum depends on the scalar spectrum, we derive a new indirect bound that involves all scales of the scalar spectrum based on CMB observations. This bound comes from the constraint on the number of effective relativistic degrees of freedom, N ef f . We estimate the bound using current data, and the improvements expected by future CMB experiment. The bound forces the running and running of running to conform to standard slow-roll predictions of α, β (n s − 1) 2 where α ≡ dns d ln k and β ≡ d 2 ns s ln k 2 , improving on current CMB measurements by an order of magnitude. This bound has further implications for the possibility of primordial black holes as dark matter candidates. Performing a likelihood analysis, including this new constraint, we find that positive α and/or β are disfavored at least at 1σ. Even using conservative analysis β + 0.074 α > 8.6 × 10 −4 are ruled out at 3σ. Finally, using bounds on the fractional energy density of gravitational waves today obtained by LIGO and the Pulsar Timing Array, we obtain a bound on the primordial scalar spectrum on these scales and give forecast for future measurements.

We study scale dependence of the cosmic microwave background (CMB) power spectrum in a class of small, single-field models of inflation which lead to a high value of the tensor to scalar ratio. The inflaton potentials that we consider are degree 5 polynomials, for which we precisely calculate the power spectrum, and extract the cosmological parameters: the scalar index ns, the running of the scalar index nrun and the tensor to scalar ratio r. We find that for non-vanishing nrun and for r as small as r = 0.001, the precisely calculated values of ns and nrun deviate significantly from what the standard analytic treatment predicts. We study in detail, and discuss the probable reasons for such deviations. As such, all previously considered models (of this kind) are based upon inaccurate assumptions. We scan the possible values of potential parameters for which the cosmological parameters are within the allowed range by observations. The 5 parameter class is able to reproduce all of the allowed values of ns and nrun for values of r that are as high as 0.001. Subsequently this study at once refutes previous such models built using the analytical Stewart-Lyth term, and revives the small field brand, by building models that do yield an appreciable r while conforming to known CMB observables.

SU(2) gauge fields coupled to an axion field can acquire an isotropic background solution during inflation. We study homogeneous but anisotropic inflationary solutions in the presence of such (massless) gauge fields. A gauge field in the cosmological background may pose a threat to spatial isotropy. We show, however, that such models generally isotropize in Bianchi type-I geometry, and the isotropic solution is the attractor. Restricting the setup by adding an axial symmetry, we revisited the numerical analysis presented in [1]. We find that the reported numerical breakdown in the previous analysis is an artifact of parametrization singularity. We use a new parametrization that is well-defined all over the phase space. We show that the system respects the cosmic no-hair conjecture and the anisotropies always dilute away within a few e-folds.

The cycloid is one of the most intriguing objects in the classical physics world, at once solving the brachistochrone and isochronous curve problems. Historically, the cycloid shape has been employed to great success in many physical contexts. We discuss one such case, presenting the longitude problem as a pathway into an in-depth discussion of the analytical solution of a point mass motion along a cycloid. The classical solution is presented, and the modifications needed for a rolling ball along a cycloid rail are made. A comparison is then made between the two cases, and we show that the difference in most physical cases between the point mass and the rolling ball is at most~7%. Next, an experiment is presented in which the isochronous nature of the cycloid path is tested, to different degrees of success. The results are discussed and several possible origins of the discrepancy between the theory and the experimental results are identified. We conclude with a discussion of skidding and slipless rolling.