Rapidly-Varying Speed of Sound, Scale Invariance and Non-Gaussian Signatures

By J. Khoury, F. Piazza. 2008

173 citations recorded by the source corpus.

We show that curvature perturbations acquire a scale invariant spectrum for any constant equation of state, provided the fluid has a suitably time-dependent sound speed. In order for modes to exit the physical horizon, and in order to solve the usual problems of standard big bang cosmology, we argue that the only allowed possibilities are inflationary (albeit not necessarily slow-roll) expansion or ekpyrotic contraction. Non-Gaussianities offer many distinguish features. As usual with a small sound speed, non-Gaussianity can be relatively large, around current sensitivity levels. For DBI-like lagrangians, the amplitude is negative in the inflationary branch, and can be either negative or positive in the ekpyrotic branch. Unlike the power spectrum, the three-point amplitude displays a large tilt that, in the expanding case, peaks on smallest scales. While the shape is predominantly of the equilateral type in the inflationary branch, as in DBI inflation, it is of the local form in the ekpyrotic branch. The tensor spectrum is also generically far from scale invariant. In the contracting case, for instance, tensors are strongly blue tilted, resulting in an unmeasurably small gravity wave amplitude on cosmic microwave background scales.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fc7f3add057984e4f25d8470f0440c4a9befe6cc

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Citations in the corpus

Review of local non-Gaussianity from multi-field inflation (2010, background): “The scale dependence of an equilateral form of fNL has also been considered from both a theoretical and observational perspective, see for example [144–147].”
An infinite set of Ward identities for adiabatic modes in cosmology (2013, background): “Conversely, to observe a significant 3-point function in this limit requires violating one of the assumptions above, for instance through additional scalar fields [23–28] or an unstable background [29, 30, 33, 34]2.”
The DESI Experiment Part I: Science,Targeting, and Survey Design (2016, background): “Recently, a number of inflationary models have been proposed which predict a potentially observable level of non-Gaussianity, these include those from fast-roll inflation [130, 131, 132, 133, 134], quasi-single field inflation [135, 136], warm inflation [137, 138], and non-Bunch-Davies or excited in”
The (not so) squeezed limit of the primordial 3-point function (2011, background): “After defining a modified conformal time dy = (cs/a)dt, this action reads [8] M(2) Pl ∫”
Signatures of Initial State Modifications on Bispectrum Statistics (2009, background): “Models of new ekpyrosis [11] and the recently proposed contracting models with an increasing speed of sound [17] , in which a bouncing universe is replacing inflation, also yield large non-Gaussianities of the local type.”
Conformal consistency relations for single-field inflation (2012, result): “Even if we phrased the paper using inflation as the key example, our results are more general and can be extended to other single-field models like [26, 27, 28, 29].”
Planck 2018 results. IX. Constraints on primordial non-Gaussianity (2019, background): “Further possibilities for strong scale dependence exist (see e.g., Khoury & Piazza 2009; Riotto & Sloth 2011), but we will not consider these in our study.”
Primordial Non-Gaussianities from Inflation Models (2010, background): “Local form is also found in different contexts, such as models with special types of massive gauge fields that acquire super-horizon evolution [160–162], some non-local theories of inflation [163,164], and certain cyclic universe scenario as alternatives to inflation [165–169].”