https://doi.org/10.1140/epjc/s10052-019-7544-3
Regular Article - Theoretical Physics
Viable non-singular cosmic bounce in holonomy improved F(R) gravity endowed with a Lagrange multiplier
1
Institut de Ciències de l’Espai (ICE-CSIC/IEEC), Campus UAB, c. Can Magrans s/n, 08193, Barcelona, Spain
2
ICREA, Passeig Luis Companys, 23, 08010, Barcelona, Spain
3
Institute of Space Sciences (IEEC-CSIC), C. Can Magrans s/n, 08193, Barcelona, Spain
4
Department of Physics, Chandernagore College, Hooghly, 712 136, India
5
Department of Theoretical Physics, Indian Association for the Cultivation of Science, 2A & 2B Raja S.C. Mullick Road, Kolkata, 700 032, India
6
International Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050, Tomsk, Russia
* e-mail: pul.tnmy9@gmail.com
Received:
9
October
2019
Accepted:
9
December
2019
Published online:
6
January
2020
Matter and quasi-matter bounce scenarios are studied for an F(R) gravity model with holonomy corrections and a Lagrange multiplier, with a scale factor 
, where the Hubble parameter squared has a linear and a quadratic dependence on the effective energy density. Provided 
, it is shown that the primordial curvature perturbations are generated deeply into the contracting era, at large negative time, which makes the low-curvature limit a good approximation for calculating the perturbation power spectrum. Moreover, it is shown that, for n within this range, the obtained cosmological quantities are fully compatible with the Planck constraints, and that the “low curvature limit” comes as a viable approximation to calculate the power spectra of both scalar and tensor perturbations. Using reconstruction techniques for F(R) gravity with the Lagrange multiplier, the precise form of the effective F(R) gravity is found, from which one determines the power spectra of scalar and tensor perturbations in such bouncing scenario. Correspondingly, the spectral index for curvature perturbations and the tensor to scalar ratio are obtained, and these values are successfully confronted with the latest Planck observations. Further, it is shown that both the weak and the null energy conditions are satisfied, thanks to the holonomy corrections performed in the theory–which are then proven to be necessary for achieving this goal. In fact, when approaching the bouncing era, the holonomy corrections become significant and play a crucial role in order to restore the energy conditions. Summing up, a cosmological bouncing scenario with the scale factor above and fulfilling the energy conditions can be adequately described by the F(R) model with a Lagrange multiplier and holonomy corrections, which prove to be very important.
© The Author(s), 2020
