Gauge-invariant perturbation theory for trans-Planckian inflation

Abstract

The possibility that the scale-invariant inflationary spectrum may be modified due to the hidden assumptions about the Planck scale physics -dubbed as trans-Planckian inflation -has received considerable attention. To mimic the possible trans-Planckian effects, among various models, modified dispersion relations have been popular in the literature. In almost all the earlier analyzes, unlike the canonical scalar field driven inflation, the trans-Planckian effects are introduced to the scalar/tensor perturbation equations in an ad hoc manner -without calculating the stress-tensor of the cosmological perturbations from the covariant Lagrangian. In this work, we perform the gaugeinvariant cosmological perturbations for the single-scalar field inflation with the Jacobson-Corley dispersion relation by computing the fluctuations of all the fields including the unit time-like vector field which defines a preferred rest frame. We show that: (i) The non-linear effects introduce corrections only to the perturbed energy density. The corrections to the energy density vanish in the super-Hubble scales. (ii) The scalar perturbations, in general, are not purely adiabatic. (iii) The equation of motion of the Mukhanov-Sasaki variable corresponding to the inflaton field is different than those presumed in the earlier analyzes. (iv) The tensor perturbation equation remains unchanged. We perform the classical analysis for the resultant system of equations and also compute the power-spectrum of the scalar perturbations in a particular limit. We discuss the implications of our results and compare with the earlier results.

Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity

“…Thus, perturbations generated during a single scalar field epoch are no longer purely adiabatic -perturbations contain a small entropic contribution. Although such an effect has been seen earlier in a class of Lorentz violating models [46], our example here is the first to show that the primordial perturbations from inflation are not purely adiabatic and always contain a small entropic perturbation. (Note that anomaly-freedom of our equations [2] ensures that there are no violations of Lorentz symmetry, although the specific form of symmetries can be quantum corrected.…”

“…which is (46). The last equation implies that diffeomorphism invariant canonical variables do have commuting time derivative and gauge transformation.…”

Critical Evaluation of Common Claims in Loop Quantum Cosmology

“…Violating such an important consistency condition is not an approximation that may be improved by including further corrections. Models that violate essential symmetries rather produce spurious solutions which invalidate any analysis; see for instance [91] in a different context. In loop quantum cosmology, this outcome is shown by the possibility of signature change at high density in non-classical space-time structures compatible with holonomy modifications [92,93,94].…”

Trans-Planckian problem in the healthy extension of Horava-Lifshitz gravity

“…as a special case and that it is defined as a path integral in the complex plane [40,41]. For example, the integral:…”