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The current accelerated expansion of our universe could be due to an unknown energy component (dark energy) or a modification to general relativity (modified gravity). In the literature, it has been proposed that combining the probes of the cosmic expansion history and growth history can distinguish between dark energy and modified gravity. In this work, without invoking non-trivial dark energy clustering, we show that the possible interaction between dark energy and dark matter could make the interacting dark energy model and the modified gravity model indistinguishable. An explicit example is also given. Therefore, it is required to seek some complementary probes beyond the ones of cosmic expansion history and growth history.
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In this paper, we make a comparison for the impacts of smooth dynamical dark energy, modified gravity, and interacting dark energy on the cosmological constraints on the total mass of active neutrinos. For definiteness, we consider the $Lambda$CDM model, the $w$CDM model, the $f(R)$ model, and two typical interacting vacuum energy models, i.e., the I$Lambda$CDM1 model with $Q=beta Hrho_{rm c}$ and the I$Lambda$CDM2 model with $Q=beta Hrho_{Lambda}$. In the cosmological fits, we use the Planck 2015 temperature and polarization data, in combination with other low-redshift observations including the baryon acoustic oscillations, the type Ia supernovae, the Hubble constant measurement, and the large-scale structure observations, such as the weak lensing as well as the redshift-space distortion. Besides, the Planck lensing measurement is also employed in this work. We find that, the $w$CDM model favors a higher upper limit on the neutrino mass compared to the $Lambda$CDM model, while the upper limit in the $f(R)$ model is similar with that of $Lambda$CDM model. For the interacting vacuum energy models, the I$Lambda$CDM1 model favors a higher upper limit on neutrino mass, while the I$Lambda$CDM2 model favors an identical neutrino mass with the case of $Lambda$CDM.
The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades there has been a huge theoretical and observational effort into improving our understanding of the Universe. The cosmological equations describing the dynamics of a homogeneous and isotropic Universe are systems of ordinary differential equations, and one of the most elegant ways these can be investigated is by casting them into the form of dynamical systems. This allows the use of powerful analytical and numerical methods to gain a quantitative understanding of the cosmological dynamics derived by the models under study. In this review we apply these techniques to cosmology. We begin with a brief introduction to dynamical systems, fixed points, linear stability theory, Lyapunov stability, centre manifold theory and more advanced topics relating to the global structure of the solutions. Using this machinery we then analyse a large number of cosmological models and show how the stability conditions allow them to be tightly constrained and even ruled out on purely theoretical grounds. We are also able to identify those models which deserve further in depth investigation through comparison with observational data. This review is a comprehensive and detailed study of dynamical systems applications to cosmological models focusing on the late-time behaviour of our Universe, and in particular on its accelerated expansion. In self contained sections we present a large number of models ranging from canonical and non-canonical scalar fields, interacting models and non-scalar field models through to modified gravity scenarios. Selected models are discussed in detail and interpreted in the context of late-time cosmology.
The next generation of galaxy surveys will allow us to test one of the most fundamental assumptions of the standard cosmology, i.e., that gravity is governed by the general theory of relativity (GR). In this paper we investigate the ability of the Javalambre Physics of the Accelerating Universe Astrophysical Survey (J-PAS) to constrain GR and its extensions. Based on the J-PAS information on clustering and gravitational lensing, we perform a Fisher matrix forecast on the effective Newton constant, $mu$, and the gravitational slip parameter, $eta$, whose deviations from unity would indicate a breakdown of GR. Similar analysis is also performed for the DESI and Euclid surveys and compared to J-PAS with two configurations providing different areas, namely an initial expectation with 4000 $mathrm{deg}^2$ and the future best case scenario with 8500 $mathrm{deg}^2$. We show that J-PAS will be able to measure the parameters $mu$ and $eta$ at a sensitivity of $2% - 7%$, and will provide the best constraints in the interval $z = 0.3 - 0.6$, thanks to the large number of ELGs detectable in that redshift range. We also discuss the constraining power of J-PAS for dark energy models with a time-dependent equation-of-state parameter of the type $w(a)=w_0+w_a(1-a)$, obtaining $Delta w_0=0.058$ and $Delta w_a=0.24$ for the absolute errors of the dark energy parameters.
We propose a new cosmological framework in which the strength of the gravitational force acted on dark matter at late time can be weaker than that on the standard matter fields without introducing extra gravitational degrees of freedom. The framework integrates dark matter into a type-II minimally modified gravity that was recently proposed as a dark energy mimicker. The idea that makes such a framework possible consists of coupling a dark matter Lagrangian and a cosmological constant to the metric in a canonically transformed frame of general relativity (GR). On imposing a gauge fixing constraint, which explicitly breaks the temporal diffeomorphism invariance, we keep the number of gravitational degrees of freedom to be two, as in GR. We then make the inverse canonical transformation to bring the theory back to the original frame, where one can add the standard matter fields. This framework contains two free functions of time which specify the generating functional of the above mentioned canonical transformation and which are then used in order to realize desired time evolutions of both the Hubble expansion rate $H(z)$ and the effective gravitational constant for dark matter $G_{rm eff}(z)$. The aim of this paper is therefore to provide a new framework to address the two puzzles present in todays cosmology, i.e. the $H_0$ tension and the $S_8$ tension, simultaneously. When the dark matter is cold in this framework, we dub the corresponding cosmological model the V Canonical Cold Dark Matter (VCCDM), as the cosmological constant $Lambda$ in the standard $Lambda$CDM is replaced by a function $V(phi)$ of an auxiliary field $phi$ and the CDM is minimally coupled to the metric in a canonically transformed frame.
We develop an approach to compute observables beyond the linear regime of dark matter perturbations for general dark energy and modified gravity models. We do so by combining the Effective Field Theory of Dark Energy and Effective Field Theory of Large-Scale Structure approaches. In particular, we parametrize the linear and nonlinear effects of dark energy on dark matter clustering in terms of the Lagrangian terms introduced in a companion paper, focusing on Horndeski theories and assuming the quasi-static approximation. The Euler equation for dark matter is sourced, via the Newtonian potential, by new nonlinear vertices due to modified gravity and, as in the pure dark matter case, by the effects of short-scale physics in the form of the divergence of an effective stress tensor. The effective fluid introduces a counterterm in the solution to the matter continuity and Euler equations, which allows a controlled expansion of clustering statistics on mildly nonlinear scales. We use this setup to compute the one-loop dark-matter power spectrum.
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