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Register a new userStrongly Coupled Perturbations in Two-Field Inflationary Models
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Added by
Krzysztof Turzynski
Publication date
2010
fields
Physics
and research's language is
English
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We study models of inflation with two scalar fields and non-canonical kinetic terms, focusing on the case in which the curvature and isocurvature perturbations are strongly coupled to each other. In the regime where a heavy mode can be identified and integrated out, we clarify the passage from the full two-field model to an effectively single-field description. However, the strong coupling sets a new scale in the system, and affects the evolution of the perturbations as well as the beginning of the regime of validity of the effective field theory. In particular, the predictions of the model are sensitive to the relative hierarchy between the coupling and the mass of the heavy mode. As a result, observables are not given unambiguously in terms of the parameters of an effectively single field model with non-trivial sound speed. Finally, the requirement that the sound horizon crossing occurs within the regime of validity of the effective theory leads to a lower bound on the sound speed. Our analysis is done in an extremely simple toy model of slow-roll inflation, which is chosen for its tractability, but is non-trivial enough to illustrate the richness of the dynamics in non-canonical multi-field models.
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We study the quantum mechanical evolution of the tensor perturbations during inflation with non-linear tensor interactions. We first obtain the Lindblad terms generated by non-linear interactions by tracing out unobservable sub-horizon modes. Then we calculate explicitly the reduced density matrix for the super-horizon modes, and show that the probability of maintaining the unitarity of the squeezed state decreases in time. The decreased probability is transferred to other elements of the reduced density matrix including off-diagonal ones, so the evolution of the reduced density matrix describes the quantum-to-classical transition of the tensor perturbations. This is different from the classicality accomplished by the squeezed state, the suppression of the non-commutative effect, which is originated from the quadratic, linear interaction, and also maintains the unitarity. The quantum-to-classical transition occurs within 5 - 10 e-folds, faster than the curvature perturbation.
We construct the gauge invariant free action for cosmological perturbations for the nonminimally coupled inflaton field in the Jordan frame. For this the phase space formalism is used, which keeps track of all the dynamical and constraint fields. We perform explicit conformal transformations to demonstrate the physical equivalence between the Jordan and Einstein frames at the level of quadratic perturbations. We show how to generalize the formalism to the case of a more complicated scalar sector with an internal symmetry, such as Higgs inflation. This work represents a first step in developing gauge invariant perturbation theory for nonminimally coupled inflationary models.
We study the Wigner function for the inflationary tensor perturbation defined in the real phase space. We compute explicitly the Wigner function including the contributions from the cubic self-interaction Hamiltonian of tensor perturbations. Then we argue that it is no longer an appropriate description for the probability distribution in the sense that quantum nature allows negativity around vanishing phase variables. This comes from the non-Gaussian wavefunction in the mixed state as a result of the non-linear interaction between super- and sub-horizon modes. We also show that this is related to the explicit infrared divergence in the Wigner function, in contrast to the trace of the density matrix.
We derive a closed-form, analytical expression for the spectrum of long-wavelength density perturbations in inflationary models with two (or more) inflaton degrees of freedom that is valid in the slow-roll approximation. We illustrate several classes of potentials for which this expression reduces to a simple, algebraic expression.
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