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Paper IPM / Physic / 15251  


Abstract:  
I investigate the "General" case that arise in the Extended Effective Field Theory of Inflation (GEEFToI), in which the coefficients of the the sextic polynomial dispersion relation are timedependent. The general solution to the mode equation in this case can be expressed as a combination of angular and radial Confluent Heun (CH) functions. Depending on the values of the GEEFToI parameters in the unitary gauge action, two scenarios can arise: in one scenario, the coefficients of the sextic polynomial become singular and flip signs at some physical wave length and then approach zero in the infinite UV limit. I show that in this case, starting from the vacuum, the twopoint function evolves outside the horizon and becomes singular in the infinite IR limit. In the other case, the coefficients of the dispersion relation evolve monotically from zero to their value in IR. In this case the power spectrum becomes constant in the infinite IR limit up to a normalization. Requiring the mode function to be finite at infinite UV, the mode function has to be an eigensolution of the CH equation, which leads to a confined parameter space for GEEFToI with finite twopoint functions. At the end, I look at a solution of the CH equation, expressed as an expansion in terms of regular confluent hypergeometric functions, which is regular in the infinite IR limit and yields a finite power spectrum for both scenarios. I show that this solution is as a combination of positive and negative frequency WKB modes in the infinite UV limit, namely it is an excited state. This is interpreted noting that the Goldstone mode, although can be arranged to be decoupled at horizon crossing, gets coupled to gravity at subPlanckian wavelengths. This demonstrates that the inflationary predictions in this setup can be extremely sensitive to the way perturbations interact with gravity at very small wavelengths.
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