Abstract
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 a(t) = left( a_0t^2 + 1 right) ^n, where the Hubble parameter squared has a linear and a quadratic dependence on the effective energy density. Provided n < 1/2, 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.
Highlights
There seems to be no doubt that, at present, our universe expansion is accelerating
When we go back in time, there are namely two possibilities: (i) the scale factor started from a value zero, what leads to the divergence of the Kretschmann scalar, which in turn ensures the singularity in the spacetime curvature, known as the Big Bang singularity
We have discussed a bouncing scenario which incorporates holonomy corrections in an F(R) gravity model with a Lagrange multiplier and where the Hubble parameter squared is proportional to a linear as well as to a quadratic power of the effective energy density; this differs from the usual Friedmann case, where H 2 is proportional to the linear power of energy density, only
Summary
There seems to be no doubt that, at present, our universe expansion is accelerating. Its expansion rate is quantified by the Hubble parameter, defined as H = a/a, where a(t) is a scale factor of the universe at cosmic time t. (ii) In the absence of a fully accepted quantum gravity theory, there is at present another possibility to deal with this issue within the domain of classical gravity This is known as the bouncing scenario [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45], in which the spacetime curvature singularity is absent.
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