“…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].…”
Section: Gravitational Instability In Quickly Oscillating Backgroundmentioning
“…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].…”
Section: Gravitational Instability In Quickly Oscillating Backgroundmentioning
“…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:…”
Section: Evolution Of Density Perturbations In Jfbd Theoriesmentioning
confidence: 99%
“…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].…”
In the context of scalar-tensor theories we study the evolution of the density contrast for JordanFierz-Brans-Dicke theories in a Friedmann-Lemaître-Robertson-Walker Universe. Calculations are performed in the Einstein Frame with the cosmological background described as Λ-Cold Dark Matter (ΛCDM) and supplemented by a Jordan-Fierz-Brans-Dicke field. By using a completely general procedure valid for all scalar-tensor theories, we obtain the exact fourth-order differential equation for the density contrast evolution in modes of arbitrary size. In the case of sub-Hubble modes, the expression reduces to a simpler but still fourth-order equation that is then compared with the standard (quasistatic) approximation. Differences with respect to the evolution as predicted by the standard Concordance ΛCDM model are observed depending on the value of the coupling.
“…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.…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
In this paper we show how the covariant gauge invariant equations for the evolution of scalar, vector and tensor perturbations for a generic f (R)-gravity theory can be recast in order to exploit the power of dynamical system methodology. In this way, recent results describing the dynamics of the background FRW model can be easily combined with these equations to reveal important details pertaining to the evolution of cosmological models in fourth order gravity.
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