Anomaly free cosmological perturbations with generalised holonomy correction in loop quantum cosmology

Abstract

In the spatially flat case of loop quantum cosmology, the connection $\bar{k}$ is usually replaced by the holonomy $\frac{\sin (\bar{\mu }k)}{\bar{\mu }}$ in the effective theory. In this paper, instead of the $\bar{\mu }$ scheme, we use a generalised, undertermined function $g(\bar{k},\bar{p})$ to represent the holonomy and by using the approach of anomaly free constraint algebra we fix all the counter terms in the constraints and find the restriction on the form of $g(\bar{k},\bar{p})$, then we derive the gauge invariant equations of motion of the scalar, tensor and vector perturbations and study the inflationary power spectra with generalised holonomy correction.

26 pages,presentation improved and references added

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Cited by in corpus (10)

• Non-singular black holes and the Limiting Curvature Mechanism: A Hamiltonian perspective
• Anomaly-free deformations of spherical general relativity coupled to matter
• Covariance in self dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems
• Holonomy and inverse-triad corrections in spherical models coupled to matter
• Alleviation of anomalies from the non-oscillatory vacuum in loop quantum cosmology
• Cosmological implications of generalized holonomy corrections
• Impact of generalized holonomy corrections on the cosmological primordial power spectra
• Gravitational waves with generalized holonomy corrections
• Cosmological perturbations with inverse-volume corrections in loop quantum cosmology
• Nonclassical cosmological dynamics in the low-energy limit of loop quantum scalar-tensor theory