Finding the chiral gravitational wave background of an axion- SU(2) inflationary model using CMB observations and laser interferometers

Abstract

A detection of B-mode polarization of the Cosmic Microwave Background (CMB) anisotropies would confirm the presence of a primordial gravitational wave background (GWB). In the inflation paradigm this would be an unprecedented probe of the energy scale of inflation as it is directly proportional to the power spectrum of the GWB. However, similar tensor perturbations can be produced by the matter fields present during inflation, breaking the simple relationship between energy scale and the tensor-to-scalar ratio r. It is therefore important to find ways of distinguishing between the generation mechanisms of the GWB. Without doing a full model selection, we analyse the detectability of a new axion-SU(2) gauge field model by calculating the signal-to-noise of future CMB and interferometer observations sensitive to the chirality of the tensor spectrum. We forecast the detectability of the resulting CMB temperature and B-mode (TB) or E-mode and B-mode (EB) cross-correlation by the LiteBIRD satellite, considering the effects of residual foregrounds, gravitational lensing, and assess the ability of such an experiment to jointly detect primordial TB and EB spectra and self-calibrate its polarimeter. We find that LiteBIRD will be able to detect the chiral signal for r * > 0.03 with r * denoting the tensor-to-scalar ratio at the peak scale, and that the maximum signal-to-noise for r * < 0.07 is ∼ 2. We go on to consider an advanced stage of a LISA-like mission, which is designed to be sensitive to the intensity and polarization of the GWB. We find that such experiments would complement CMB observations as they would be able to detect the chirality of the GWB with high significance on scales inaccessible to the CMB. We conclude that CMB two-point statistics are limited in their ability to distinguish this model from a conventional vacuum fluctuation model of GWB generation, due to the fundamental limits on their sensitivity to parity-violation. In order to test the predictions of such a model as compared to vacuum fluctuations it will be necessary to test deviations from the self-consistency relation, or use higher order statistics to leverage the non-Gaussianity of the model. On the other hand, in the case of a spectrum peaked at very small scales inaccessible to the CMB, a highly significant detection could be made using space-based laser interferometers.

Tensor spectra templates for axion-gauge fields dynamics during inflation

“…The prototypical cosine potential first associated with natural inflation [13,14] falls under this category for p = 2. This is also the most studied axion potential in Chromo-Natural inflation [15][16][17] along with its Higgsed [29] and spectator variants [30][31][32][33][34][35]. Finally Type III describes an axion monodromy potential, in which the axion probes multiple periods of the modulated potential during inflation.…”

“…Ref. [33] addressed this issue for p = 2 and m * = 4, and found that the agreement between numerical and analytic results is excellent for ∆N = 10, while the relative error becomes more than a few percent for ∆N = 5. We expect the slow-roll approximation to break down for ∆N 1, signaling a very sharply peaked gaussian power spectrum.…”

“…A difference of the sourced GW's in this model to the usual vacuum modes is the amount of Non-Gaussianity [32]. Whereas vacuum GW's are very gaussian and respect the parity symmetry, sourced GW's are predicted to exhibit a level of non-Gaussianity and chirality that could be in principle measured by future experiments, such as LiteBIRD [33][34][35].…”

Squeezed tensor non-Gaussianity in non-attractor inflation

“…Tensor non-Gaussianity can also be an important observable for characterizing the primordial stochastic gravitational wave background at CMB scales, and have been explored in other contexts, see e.g [20,23,107]…”

Interferometer constraints on the inflationary field content

“…The information of interest to the present discussion is that the coupling in such theories is typically implemented through a Chern-Simons (CS) term. As a result of the CS coupling, the GW spectrum can be blue or exhibit bump-like features that peak at small scales [45][46][47][48][49][50][51][52][53].…”