Observational Constraints and Some Toy Models in f(Q) Gravity with Bulk Viscous Fluid

Round 1

Reviewer 1 Report

In this work, modified f(Q) telepallalel gravity models are considered in presence of a generic fluid with bulk viscosity, for a homogeneous cosmology. The nonmetricity Q is chosen as the symmetric teleparallel equivalent of GR, for a FLRW metric, following reference 6. The model is written in terms of the Hubble parameter, with a viscosity pressure term added, following reference 15. Further, a detailed fit is done for a known proposal of the Hubble parameter, from reference 22, in terms of the redshift, from two Hubble collections of observational data. This fitted Hubble parameter is substituted into the model, and from there the fluid density, pressure, and the equation of state parameter, are plotted for three choices of f(Q) and the viscosity constant, to evaluate the energy conditions, and verify the right behavior. The f(Q) functions considered are lineal, power, and logarithmic.

I have the following observations:

1. Section 4 is misleading. It is stated "In this section, we adopted the parametrization technique, which will be used to reconstruct the cosmological models". However, what is done is a fit for a general form of the Hubble parameter (ref. 22) in terms of the redshift, and has no relation to the model f(Q) under consideration. At this point, also Saini et. al., Phys. Rev. Lett. 85 (2000) 1162, should be quoted.
2. The evaluation of the energy conditions is straightforwardly done for three specific choices of f(Q) and the viscosity parameter. There are no analyses of the consequences of viscosity for the energy conditions, nor observational constraints on the model.
3. The substitution of the fitted Hubble parameter into the equations of motion of the f(Q) model does not amount to a reconstruction, and could even lead to inconsistencies as it is being a priori assumed, that this model is consistent with observations. For a reconstruction in these terms, see e.g. Capozziello et. al., Phys. Rev. D71 (2005) 043503.

Actually, the paper does not correspond to the topics mentioned in the title and abstract; it refers to observational constraints for f(Q) gravity, and to the construction of three bulk viscous fluid models, and none of these points is really attended.

Therefore, I do not recommend the publication of this paper in Universe.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

In this paper the authors examine a class of cosmological models where viscous fluids are analyzed in the framework of symmetric teleparallel f(Q)-gravity. In f(Q)-gravity the gravitational interaction is driven by non-metricity Q. Despite to the fact that the theory is quite involved and several new ingredients are introduced respect to GR, the authors present a detailed analysis of the models in view of recent observations, making the results acceptable and of physical interest. It may be interesting if the authors  also present a small comparison between standard teleparallel gravity and symmetric teleparallel gravity. For example, modified teleparallel gravity preserve second order field equations as in GR, there are some issues related to the breaking of Lorentz invariance (see the non flat FRW case etc...): are this feature the same in f(Q)-gravity, we have some advantages in this theory etc? 

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

In the manuscript the authors investigate in detail some f(Q) type modified gravity models in the presence of bulk viscosity, by comparing the theoretical predictions with the observational data. The manuscript may be publishable in Universe if the authors would fully consider the following points:

1. The authors introduce in the matter energy-momentum tensor a bulk viscous pressure term. What is the physical motivation for considering the effect of viscosity? If for the high density matter in the early Universe the presence of bulk viscosity term may be physically motivated, for the present day Universe describing ordinary matter as having bulk viscosity is at least problematic.
2. The Raychaudhury equations (17) and (18) are valid only in Riemannian geometry. In a Weyl geometry with non-metricity they take a different form, which must be at least discussed by the authors.
3. It seems that the numerical values of the parameter $\lambda$ in the expression of the bulk viscous pressure are fixed in an arbitrary way ($\lambda =0.002$ or $\lambda =2$, for example). Would it be possible to obtain some observational constraints on its acceptable physical range?   
4. The authors use for the description of the bulk viscous effects the non-causal Eckart theory. They should at least mention that a causal theory, the Israel-Stewart theory does exist, and briefly discuss its possible relevance in the present context.
5.  All the plots must be done and presented in physical units. For example, what is the unit of energy in the plots displaying the energy conditions? 
6. The Introduction and the Discussions Sections must be extended to include more discussions on the general cosmological context to which the manuscript does belong, and on the relevance of the obtained results. 

Author Response

Attached

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have responded satisfactorily to the observations.

Reviewer 3 Report

The authors have improved their manuscript, and hence I think the present version is suitable for publication in Universe.