Scalar field inflation driven by a modification of the Heisenberg algebra
arXiv:2309.16107 · doi:10.1142/S0218271824500378
Abstract
We study the modifications induced on scalar field inflation produced by considering a general modification of the Heisenberg algebra. We proceed by modifying the Poisson brackets on the classical theory whenever the corresponding quantum commutator is modified. We do not restrict ourselves to a specific form for such modification, instead we constrain the functions involved by the cosmological behaviour of interest. We present whenever possible the way in which inflation can be realized approximately via three slow roll Hubble parameters that depend on the standard slow roll parameters in a very different form than in the usual case and that can be less restrictive. Furthermore we find a general analytical solution describing an expanding universe with constant Hubble parameter that generalizes the standard cosmological constant case by restricting the form of the modification of the Heisenberg algebra. It is found that even if such modification can be neglected in some limit and the cosmological constant is set to zero in that limit, the exponential expansion is present when the modification is important. Thus an appropriate modification of the Heisenberg algebra is sufficient to produce an exponentially expanding universe without the need of any other source.
36 pages, 1 figure. All sections were improved. References added
References in corpus (15)
- Discreteness of Space from the Generalized Uncertainty Principle
- The Generalized Uncertainty Principle in (A)dS Space and the Modification of Hawking Temperature from the Minimal Length
- Influence of Generalized and Extended Uncertainty Principle on Thermodynamics of FRW universe
- Minimum Length Cutoff in Inflation and Uniqueness of the Action
- Generalized uncertainty principle in Bianchi type I quantum cosmology
- On the Tensor/Scalar Ratio in Inflation with UV Cutoff
- Deformation of the Wheeler-DeWitt Equation
- Comparison of the Semiclassical and Quantum Dynamics of the Bianchi I Cosmology in the Polymer and GUP Extended Paradigms
- Noncommutativity, generalized uncertainty principle and FRW cosmology
- Cosmology with minimal length uncertainty relations
- Emergent Universe Model from Modified Heisenberg Algebra
- Deformation of Second and Third Quantization
- Dynamics of Quintessence in Generalized Uncertainty Principle
- Quantum Cosmology with Dynamical Vacuum in a Minimal-Length Scenario
- Generalized Uncertainty Principle effects in the Hořava-Lifshitz quantum theory of gravity