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Despite two decades of tremendous experimental and theoretical progress, the riddle of the accelerated expansion of the Universe remains to be solved. On the experimental side, our understanding of the possibilities and limitations of the major dark energy probes has evolved; here we summarize the major probes and their crucial challenges. On the theoretical side, the taxonomy of explanations for the accelerated expansion rate is better understood, providing clear guidance to the relevant observables. We argue that: i) improving statistical precision and systematic control by taking more data, supporting research efforts to address crucial challenges for each probe, using complementary methods, and relying on cross-correlations is well motivated; ii) blinding of analyses is difficult but ever more important; iii) studies of dark energy and modified gravity are related; and iv) it is crucial that R&D for a vibrant dark energy program in the 2030s be started now by supporting studies and technical R&D that will allow embryonic proposals to mature. Understanding dark energy, arguably the biggest unsolved mystery in both fundamental particle physics and cosmology, will remain one of the focal points of cosmology in the forthcoming decade.
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We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG), beyond the cosmological constant scenario. We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state, principal component analysis and parameterizations related to the potential of a minimally coupled DE scalar field. When estimating the density of DE at early times, we significantly improve present constraints. We then move to general parameterizations of the DE or MG perturbations that encompass both effective field theories and the phenomenology of gravitational potentials in MG models. Lastly, we test a range of specific models, such as k-essence, f(R) theories and coupled DE. In addition to the latest Planck data, for our main analyses we use baryonic acoustic oscillations, type-Ia supernovae and local measurements of the Hubble constant. We further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. These additional probes are important tools for testing MG models and for breaking degeneracies that are still present in the combination of Planck and background data sets. All results that include only background parameterizations are in agreement with LCDM. When testing models that also change perturbations (even when the background is fixed to LCDM), some tensions appear in a few scenarios: the maximum one found is sim 2 sigma for Planck TT+lowP when parameterizing observables related to the gravitational potentials with a chosen time dependence; the tension increases to at most 3 sigma when external data sets are included. It however disappears when including CMB lensing.
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.
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.
Employing a nonparametric approach of the principal component analysis (PCA), we forecast the future constraint on the equation of state $w(z)$ of dark energy, and on the effective Newton constant $mu(k,z)$, which parameterise the effect of modified gravity, using the planned SKA HI galaxy survey. Combining with the simulated data of Planck and Dark Energy Survey (DES), we find that SKA Phase 1 (SKA1) and SKA Phase 2 (SKA2) can well constrain $3$ and $5$ eigenmodes of $w(z)$ respectively. The errors of the best measured modes can be reduced to 0.04 and 0.023 for SKA1 and SKA2 respectively, making it possible to probe dark energy dynamics. On the other hand, SKA1 and SKA2 can constrain $7$ and $20$ eigenmodes of $mu(k,z)$ respectively within 10% sensitivity level. Furthermore, 2 and 7 modes can be constrained within sub percent level using SKA1 and SKA2 respectively. This is a significant improvement compared to the combined datasets without SKA.
We study the properties of dark matter haloes in a wide range of modified gravity models, namely, $f(R)$, DGP, and interacting dark energy models. We study the effects of modified gravity and dark energy on the internal properties of haloes, such as the spin and the structural parameters. We find that $f(R)$ gravity enhance the median value of the Bullock spin parameter, but could not detect such effects for DGP and coupled dark energy. $f(R)$ also yields a lower median sphericity and oblateness, while coupled dark energy has the opposite effect. However, these effects are very small. We then study the interaction rate of haloes in different gravity, and find that only strongly coupled dark energy models enhance the interaction rate. We then quantify the enhancement of the alignment of the spins of interacting halo pairs by modified gravity. Finally, we study the alignment of the major axes of haloes with the large-scale structures. The alignment of the spins of interacting pairs of haloes in DGP and coupled dark energy models show no discrepancy with GR, while $f(R)$ shows a weaker alignment. Strongly coupled dark energy shows a stronger alignment of the halo shape with the large-scale structures.
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