Gauge-invariant perturbation theory for trans-Planckian inflation

Journal Article · Wed Dec 14 23:00:00 EST 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.72.123513· OSTI ID:20774511

Shankaranarayanan, S; Lubo, Musongela ^[1]

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1. HEP Group, International Centre for Theoretical Physics, Strada costiera 11, 34100 Trieste (Italy)

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 analyses, 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-timelike vector field which defines a preferred rest frame. We show that: (i) The nonlinear 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 from those presumed in the earlier analyses. (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.

• OSTI ID: 20774511
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 12 Vol. 72; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPARATIVE EVALUATIONS
CORRECTIONS
DISPERSION RELATIONS
DISTURBANCES
ENERGY DENSITY
EQUATIONS OF MOTION
FLUCTUATIONS
GAUGE INVARIANCE
INFLATIONARY UNIVERSE
LAGRANGIAN FUNCTION
NONLINEAR PROBLEMS
PERTURBATION THEORY
SCALAR FIELDS
SCALARS
STRESSES
TENSORS
VECTOR FIELDS