https://doi.org/10.1140/epjc/s10052-022-10779-y
Regular Article - Theoretical Physics
Fermionic wave functions and Grassmann fields as possible sources of dark energy
1
Departamento de Física, Instituto de Ciências Naturais, Universidade Federal de Lavras (UFLA), Caixa Postal 3037, 37200-900, Lavras, MG, Brazil
2
Departamento de Física, Faculdade de Engenharia e Ciências de Guaratinguetá, Universidade Estadual Paulista (UNESP), Av. Dr. Ariberto Pereira da Cunha 333, 12516-410, Guaratinguetá, SP, Brazil
3
Departamento de Física, Instituto de Ciências Naturais, Universidade Federal de Lavras (UFLA), Caixa Postal 3037, 37200-900, Lavras, MG, Brazil
4
Instituto de Física, Universidade Federal Fluminense, Avenida General Milton Tavares de Souza s/n, RJ 24210-346, Gragoatá, Niterói, Brazil
5
Instituto de Engenharia, Ciência e Tecnologia, Universidade Federal dos Vales do Jequitinhonha e Mucuri (UFVJM), Avenida Um, 4050, Cidade Universitária, 39447-790, Janaúba, MG, Brazil
6
Instituto de Ciências e Engenharia, Universidade Estadual Paulista (UNESP), R. Geraldo Alckmin, 519, 18409-010, Itapeva, SP, Brazil
Received:
11
May
2022
Accepted:
2
September
2022
Published online:
16
September
2022
We study a cosmological model with a fermionic field which can be interpreted as a source of dark energy in the universe. Two different approaches were considered, the first one with a massless fermionic field represented by a standard wave-function and the second one where a massive field is a Grassmann variable. The first case naturally reduces to a XCDM model with a constant equation of state parameter, while the last case reproduces a w(z)CDM model for a massive field, and in the massless limit, the intrinsic Grassmannian property of the field leads always to a vacuum equation of state parameter, irrespective the specific form of the potential. Both cases leads to a dark energy contribution of the fermionic sector. The models are totally compatible with recent cosmological data from Supernovae, BAO and Hubble parameter measurements. A brief study of linear evolution of density perturbations shows that some of the small scale problems related to standard model can be at least alleviated.
© The Author(s) 2022
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