Non-Gaussian signatures of Tachyacoustic Cosmology Dennis Bessada 1,2* 1 UNIFESP - Universidade Federal de S˜ao Paulo - Laborat´ orio de F´ısica Te´orica e Computa¸c˜ ao Cient´ıfica, Rua S˜ ao Nicolau, 210, 09913-030, Diadema, SP, Brazil 2 INPE - Instituto Nacional de Pesquisas Espaciais - Divis˜ ao de Astrof´ısica, Av. dos Astronautas, 1758, 12227-010, S˜ ao Jos´e dos Campos, SP, Brazil I investigate non-Gaussian signatures in the context of tachyacoustic cosmology, that is, a nonin- flationary model with superluminal speed of sound. I calculate the full non-Gaussian amplitude A, its size fNL, and corresponding shapes for a red-tilted spectrum of primordial scalar perturbations. Specifically, for cuscuton-like models I show that fNL ∼O(1), and the shape of its non-Gaussian amplitude peaks for both equilateral and local configurations, the latter being dominant. These results, albeit similar, are quantitatively distinct from the corresponding ones obtained by Magueijo et. al in the context of superluminal bimetric models. PACS numbers: 98.80.Cq I. INTRODUCTION The physics of the very early universe is a rich investigation field, for there is a plethora of potential models that solve, at least partially, the well-known problems of the standard cosmological paradigm. Inflationary cosmology [1] is surely the most successful model, but alternatives to it have been proposed in the recent past: pre-big bang cosmology [2], ekpyrotic and cyclic models [3], nonsingular quantum cosmological models [4], noncanonical models [5, 6], among others. All of them lead to a near-scale invariant spectrum, so that a very important question emerges: how can we falsify such distinct cosmologies? An answer can be provided by the investigation of their non-Gaussian signatures; single-field inflation, for example, predicts a nearly-Gaussian CMB anisotropy field, whereas some noncanonical mod- els, for example, can predict large deviations from Gaussianity, as in DBI inflation (see, for example, references [7] for large-field polynomial models, and [8]). Therefore, the study of non-Gaussian signatures can be a very important tool to rule out many models proposed to cope with the problems of the very early universe. In particular, noncanonical Lagrangians lead to models with varying speed of sound, a feature which substantially enhances or diminishes their non-Gaussian amplitudes, since they are usually related to terms with a c -2 s dependence [9–11]; hence, for c s < 1, such terms dominate, enhancing non-Gaussianities as in the case of DBI inflation. For superluminal models, c s  1, such terms become subdominant, so that the size of the non-Gaussian amplitude becomes f NL ∼ 1 [12, 13], which distinguishes this class of superluminal models from inflation (for which f NL ∼O(0.01)) [14, 15]. In [12], the authors take into account a minimal and a nonminimal bimetric model, that is, models in which a disformal transformation between matter and gravity metric is evocated, and has the form ˆ g μν = g μν - B∂ μ φ∂ ν φ, where the coupling B is regarded as a constant in the former, whereas in the latter it can run with φ. They then calculate non-Gaussian amplitudes for the nonminimal bimetric model in the superluminal limit, showing that it only mildly depends on the tilt n s - 1 of the power spectrum. In [13], the authors take a step further and consider non-Gaussianity for a wider class of models without slow-roll and exact scale invariance assumptions, including DBI and bimetric models, and study the superluminal limit of the latter. However, despite the generality of their analysis, there was still room for another class of superluminal models, which we presented in [6] and dubbed tachyacoustic. Tachyacoustic cosmology is a noncanonical, noninflationary model with superluminal speed of sound, in which a nearly scale-invariant spectrum is generated by quantum perturbations redshifted outside of a shrinking acoustic horizon. Since this model is noninflationary, and the scale factor is a power law of time, a(t) ∝ t 1/ , where  = const is the flow parameter associated with the ratio - ˙ H/H, we can take a radiative equation of state for the model, discarding the need of a reheating period to make the scalar field decay into radiation. Also, as shown recently in [16], DBI and cuscuton-like cosmological solutions also exhibit attractor behavior. Having this model a nearly scale invariant spectrum of perturbations, as mentioned, the next step to take is exactly the analysis of its non-Gaussian features, which is the subject of this paper. As we shall see, the distinguishing feature of the tachyacoustic model with its cuscuton-like Lagrangian 1 with regard * Electronic address: dennis.bessada@unifesp.br 1 A cuscuton is a causal field with infinite speed of sound, originally proposed in [17]. From the flow hierarchy devised for arbitrary arXiv:1206.0728v2 [gr-qc] 22 Sep 2012