A characteristic signature of fourth order gravity

Instabilities in modified theories of gravity

“…In cosmology this problem has been consider for different forms F(R) in Refs. [44,45,46,47,48,49,50,51]. A analysis of the Jeans instability for the stellar-like objects in modified gravity was performed in works [52,53,54].…”

Complete density perturbations in the Jordan-Fierz-Brans-Dicke theory

“…We obtain them by combining equations ( 23) and ( 25) in such a way that Φ ′ cancels. Then we differentiate the obtained equation and substitute the variables we already know from ( 32) and (32). Thus, from this combination we get:…”

“…Modifications to the linear order Einstein equations are thus introduced in terms of general functions of scale and time. In general all these investigations proved that the perturbations growth depend on the scale (while in GR the evolution of dust matter is scale-independent [32] and that models claimed as viable are in fact almost ruled-out due to the matter power spectrum [33,34]. Perturbations in scalar-tensor theories have been considered from different approaches, for example: the reconstruction problem was addressed in [18], the density contrast evolution was studied in [35][36][37] where in general, some intermediate approximations were performed, the integrated Sachs-Wolfe effect was determined in [38] and finally second order perturbations were presented in [39].…”

Unifying the study of background dynamics and perturbations in $f(R)$-gravity

“…In particular, in a number of recent papers [23][24][25] we derived the evolution equations for scalar and tensor perturbations of a subclass of fourth order theories of gravity characterized by an action which is a general analytic function of the Ricci scalar. The results obtained in [23][24][25] clearly demonstrated that the evolution of scalar perturbations is determined by a fourth order differential equation rather than a second order one. This implies that the evolution of the density fluctuations contains, in general, four modes rather than two and can give rise to a more complex evolution than what is obtained in General Relativity.…”

“…This implies that the evolution of the density fluctuations contains, in general, four modes rather than two and can give rise to a more complex evolution than what is obtained in General Relativity. It was also found that the perturbations depend on the scale for any value of the equation of state parameter of standard matter (while in GR the evolution of the dust perturbations are not scale dependent) and that there is a characteristic scale-dependent signature in the matter power spectrum [25]. This means that in FOG the evolution of super-horizon and sub-horizon perturbations are different.…”