Linear Stability of Einstein and de Sitter Universes in the Quadratic Theory of Modified Gravity

Dear Editor, Thank you very much for your valuable comments and remarks. I tried hard to make the paper up to the level of your satisfaction. List of the changes are explained below: 1. The typos mentioned are corrected plus others, 2. The change has been made from "non-isotroposity" to "anisotropy" as suggested. 3. The term "arrive at" is used instead of "yield to" as suggested thankfully. 4. The word "redeuced" to "reduced". 5. Equation mentioned (eq 28) has been removed to clear our to confusion that it may cause. 6. Equation 43 is corrected. We have done a thorough revision of equations as follows: a. Equations in the previous versions were too long and somewhat boring. The equations (starting from Equation 6) are written in a shorter format and the repeated terms are written separately (equation 9, 17, 21, 27-29 in the updated version). b. In Section 6 in equation 27 (in the previous version, equation 24 in the updated version), there was a typo of h as mentioned by the referees. This also has been corrected. This leads to formulating the subsequent equations again accordingly (equations 25-38). 7. The parameters A_1, A_2, C_1, C_2, E_1, E_2 are rewritten again (as explained in point 6b above). The constant A,B,C A_1, A_2, C_1, C_2, E_1, E_2 are replaced by Greek letters instead to avoid the confusion with the earlier notations used for the scale factors. An example of our claim is given in a subsection. The above mentioned parameters are rewritten again because of the reason mentioned in 6b. 8. I rechecked equation 5-8. They seem to be OK. We think that, after substituting the perturbation terms and because we are omitting the higher order perturbation terms, somewhat the mentioned symmetry in the equation has been lost specially we can see that the Lagrangian (eq 5) is not highly symmetric. 9. The conclusion is modified and few sentences are added as future works. The updated version of the file is attached. Thank you, again, for your fruitful comments which led, undoubtfully, to the improvement of the search. Mudhahir Al-Ajmi

1. The typos mentioned are corrected plus others,
2. The change has been made from "non-isotroposity" to "anisotropy" as suggested.
3. The term "arrive at" is used instead of "yield to" as suggested thankfully.
4. The word "redeuced" to "reduced".
5. Equation mentioned (eq 28) has been removed to clear our to confusion that it may cause.
6. Equation 43 is corrected. We have done a thorough revision of equations as follows: a. Equations in the previous versions were too long and somewhat boring. The equations (starting from Equation 6) are written in a shorter format and the repeated terms are written separately (equation 9, 17, 21, 27-29 in the updated version). b. In Section 6 in equation 27 (in the previous version, equation 24 in the updated version), there was a typo of h as mentioned by the referees. This also has been corrected. This leads to formulating the subsequent equations again accordingly (equations 25-38).
7. The parameters A_1, A_2, C_1, C_2, E_1, E_2 are rewritten again (as explained in point 6b above). The constant A,B,C A_1, A_2, C_1, C_2, E_1, E_2 are replaced by Greek letters instead to avoid the confusion with the earlier notations used for the scale factors. An example of our claim is given in a subsection. The above mentioned parameters are rewritten again because of the reason mentioned in 6b.
8. I rechecked equation 5-8. They seem to be OK. We think that, after substituting the perturbation terms and because we are omitting the higher order perturbation terms, somewhat the mentioned symmetry in the equation has been lost specially we can see that the Lagrangian (eq 5) is not highly symmetric.
9. The conclusion is modified and few sentences are added as future works. The updated version of the file is attached. Thank you, again, for your fruitful comments which led, undoubtfully, to the improvement of the search.