Cosmological solutions and growth index of matter perturbations in f(Q) gravity

The present work studies one of Einstein's alternative formulations based on the nonmetricity scalar Q generalized as f(Q) theory. More specifically, we consider the power-law form of f(Q) gravity, i.e., f(Q) = Q + alpha Q(n). Here, we analyze the behavior of the cosmological model at the background and perturbation level. Using the dynamical system analysis, at the background level, we find the effective evolution of the model is the same as that of the.CDM for vertical bar n vertical bar < 1. Interestingly, the geometric component of the theory solely determined the late-time acceleration of the Universe. We also examine the integrability of the model by employing the method of singularity analysis. In particular, we find the conditions under which field equations pass the Painleve test and hence possess the Painleve property. While the equations pass the Painleve test in the presence of dust for any value of n, the test is valid after the addition of radiation fluid only for n < 1. Finally, at the perturbation level, the behavior of matter growth index signifies a deviation of the model from the.CDM even for vertical bar n vertical bar < 1.

Automated summary

The study investigates one of Einstein's alternative formulations based on nonmetricity scalar Q generalized as f(Q) theory, focusing on the power-law form of f(Q) gravity. The analysis reveals that the geometric component of the theory determines the late-time acceleration of the Universe, and the model deviates from ΛCDM even for |n| < 1 at the perturbation level. The integrability of the model is examined using singularity analysis, finding conditions under which field equations pass the Painleve test and possess the Painleve property.