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 gauge-invariant 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.

19 Pages, Revtex4; V2 Final version, To appear in Phys. Rev. D., 1 figure and references added

References in corpus (13)

• Modern tests of Lorentz invariance
• Lorentz-Violating Vector Fields Slow the Universe Down
• Can We See Lorentz-Violating Vector Fields in the CMB?
• Adiabatic and entropy perturbations with interacting fluids and fields
• Back-Reaction and the Trans-Planckian Problem of Inflation Revisited
• Decoupling in an expanding universe: backreaction barely constrains short distance effects in the CMB
• Initial state of matter fields and trans-Planckian physics: Can CMB observations disentangle the two?
• Running of the Spectral Index and Violation of the Consistency Relation Between Tensor and Scalar Spectra from trans-Planckian Physics
• Spontaneous Lorentz Violation and the Long-Range Gravitational Preferred-Frame Effect
• On the Tensor/Scalar Ratio in Inflation with UV Cutoff
• Boundary Effective Field Theory and Trans-Planckian Perturbations: Astrophysical Implications
• Noncommutative models in patch cosmology
• Observing Trans-Planckian Signatures in the Cosmic Microwave Background

Cited by in corpus (13)

• Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity
• Critical evaluation of common claims in loop quantum cosmology
• Quantum Cosmology: Effective Theory
• Cosmological perturbations in a healthy extension of Horava gravity
• High energy modifications of blackbody radiation and dimensional reduction
• Non-covariance of the dressed-metric approach in loop quantum cosmology
• The Trans-Planckian Problem in the Healthy Extension of Horava-Lifshitz Gravity
• Signatures of trans-Planckian dispersion in inflationary spectra
• Path integral duality and Planck scale corrections to the primordial spectrum in exponential inflation
• Confronting the trans-Planckian question of inflationary cosmology with dissipative effects
• Expansion-contraction duality breaking in a Planck-scale sensitive cosmological quantum simulator
• Effective field theory of magnetogenesis identify necessary and sufficient conditions
• Signatures of Planck-scale interactions in the cosmic microwave background?