Cosmology in the mimetic higher-curvature f(R,R_{mu nu }R^{mu nu }) gravity

Adam Z. Kaczmarek,Dominik Szczȩśniak

doi:10.1038/s41598-021-97907-y

Adam Z. Kaczmarek, Dominik Szczȩśniak

Open Access

https://doi.org/10.1038/s41598-021-97907-y

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Abstract

In the framework of the mimetic approach, we study the f(R,R_{mu nu }R^{mu nu }) gravity with the Lagrange multiplier constraint and the scalar potential. We introduce field equations for the discussed theory and overview their properties. By using the general reconstruction scheme we obtain the power law cosmology model for the f(R,R_{mu nu }R^{mu nu })=R+d(R_{mu nu }R^{mu nu })^p case as well as the model that describes symmetric bounce. Moreover, we reconstruct model, unifying both matter dominated and accelerated phases, where ordinary matter is neglected. Using inverted reconstruction scheme we recover specific f(R,R_{mu nu }R^{mu nu }) function which give rise to the de-Sitter evolution. Finally, by employing the perfect fluid approach, we demonstrate that this model can realize inflation consistent with the bounds coming from the BICEP2/Keck array and the Planck data. We also discuss the holographic dark energy density in terms of the presented f(R,R_{mu nu }R^{mu nu }) theory. Thus, it is suggested that the introduced extension of the mimetic regime may describe any given cosmological model.

Highlights

We presented mimetic extension of the f (R, Rμν Rμν ) gravity using the Lagrange multiplier formalism with the mimetic scalar potential added to the Lagrangian, where mimetic field isolates conformal degree of freedom
Our work is closed with discussion of the inflationary cosmology in a given regime
The reconstructed inflationary model is phenomenologically viable for the wide range of the parameters when confronted with BICEP2/Keck data[50,63]

Summary

Theoretical model

The main idea behind the mimetic gravity is that the gμν metric (the fundamental variable in gravity) may be expressed by the new degrees of freedom[19]. We note that the equations obtained from the variation with respect to the physical metric gμν with imposed mimetic constraint are fully equivalent to the equations that one can derive by using action written in terms of the auxiliary metric gμν. By using the FLRW metric (6), the corresponding (t, t) component of the mimetic f (R, Rμν Rμν ) gravity equations (4) is:. Given the Hubble parameter H(t) for the specified f(R, Y) function, one can find corresponding multiplier and mimetic potential V (φ). Given the form of the mimetic potential and the Lagrange multiplier , one can solve above equations to find proper f (R, Rμν Rμν ) gravity model that realizes cosmological scenario of interest

Reconstruction of the FLRW cosmologies

Ricci scalar and

Summary

Methods

Additional information