Standard Perturbation Theory in Scale-Dependent Modified Gravity

The late-time accelerated expansion of the universe remains one of the central problems in modern cosmology. Modified gravity theories offer an alternative to invoking the elusive dark energy to account for this expansion. These mod- ifications introduce an additional degree of freedom that alters the dynamics of gravitational instability on cosmological scales while reproducing a ΛCDM back- ground expansion. In this thesis, we analyse a perturbative framework for study- ing structure growth within such theories, with a focus on chameleon-screened f (R) gravity. We begin by deriving the fluid equations for cold dark matter within standard perturbation theory. The non-linear mode couplings are encoded in the kernels Fn and Gn, which enter higher-order statistics, like one-loop cor- rections to the matter power spectrum in the quasi-non-linear regime. We then introduce modified gravity and set up screening mechanisms that suppress EP violations in local high-density environments....Show moreThe late-time accelerated expansion of the universe remains one of the central problems in modern cosmology. Modified gravity theories offer an alternative to invoking the elusive dark energy to account for this expansion. These mod- ifications introduce an additional degree of freedom that alters the dynamics of gravitational instability on cosmological scales while reproducing a ΛCDM back- ground expansion. In this thesis, we analyse a perturbative framework for study- ing structure growth within such theories, with a focus on chameleon-screened f (R) gravity. We begin by deriving the fluid equations for cold dark matter within standard perturbation theory. The non-linear mode couplings are encoded in the kernels Fn and Gn, which enter higher-order statistics, like one-loop cor- rections to the matter power spectrum in the quasi-non-linear regime. We then introduce modified gravity and set up screening mechanisms that suppress EP violations in local high-density environments. Specialising to f (R) gravity, we derive the modified Poisson equation that contains a scale-dependent linear mod- ification and non-linear source terms that are characterised by the interaction co- efficients M1, M2, and M3. For the Hu-Sawicki model, we compute the Poisson equation vertices assuming a ΛCDM background and implement a numerical analysis to study their scale and time-dependence. Our results show that GR is recovered at early times, while deviations emerge below the Compton scale. We find that the non-linear vertices dominate close to the Compton crossing and the location and width of this transition depend sensitively on the model parame- ter fR0. These findings highlight the importance of non-linear corrections and screening effects when modelling structure formation for Stage IV surveys like Euclid.Show less

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Standard Perturbation Theory in Scale-Dependent Modified Gravity