We implement the effective field theory (EFT) approach to dark energy and modified gravity in the public Einstein-Boltzmann solver CAMB. The resulting code, which we dub EFTCAMB, is a powerful and versatile tool that can be used for several objectives. It can be employed to evolve the full dynamics of linear scalar perturbations of a broad range of single field dark energy and modified gravity model, once the model of interest is mapped into the EFT formalism. It offers a numerical implementation of EFT as a model-independent framework to test gravity on cosmological scales. EFTCAMB has a built-in check for the fulfillment of general stability conditions such as the absence of ghost and superluminal propagation of perturbations. It handles phantom-divide crossing models and does not contain any quasistatic approximation, but rather evolves the full dynamics of perturbations on linear scales. As we will show, the latter is an important feature in view of the accuracy and scale range of upcoming surveys. We show the reliability and applicability of our code by evolving the dynamics of linear perturbations and extracting predictions for power spectra in several models. In particular we perform a thorough analysis of $f(R)$ theories, comparing our outputs with those of an existing code for $\mathrm{$\Lambda${}}\mathrm{CDM}$ backgrounds, and finding an agreement that can reach 0.1% for models with a Compton wavelength consistent with current cosmological data. We then showcase the flexibility of our code studying two different scenarios. First we produce new results for designer $f(R)$ models with a time-varying dark energy equation of state. Second, we extract predictions for linear observables in some parametrized EFT models with a phantom-divide crossing equation of state for dark energy.

We introduce EFTCAMB/EFTCosmoMC as publicly available patches to the commonly used camb/CosmoMC codes. We briefly describe the structure of the codes, their applicability and main features. To illustrate the use of these patches, we obtain constraints on parametrized pure effective field theory and designer $f(R)$ models, both on $\mathrm{\Lambda }\mathrm{CDM}$ and $w\mathrm{CDM}$ background expansion histories, using data from Planck temperature and lensing potential spectra, WMAP low-$\ell$ polarization spectra (WP), and baryon acoustic oscillations (BAO). Upon inspecting the theoretical stability of the models on the given background, we find nontrivial parameter spaces that we translate into viability priors. We use different combinations of data sets to show their individual effects on cosmological and model parameters. Our data analysis results show that, depending on the adopted data sets, in the $w\mathrm{CDM}$ background case these viability priors could dominate the marginalized posterior distributions. Interestingly, with $\mathrm{Planck}+\mathrm{WP}+\mathrm{BAO}+\mathrm{lensing}$ data, in $f(R)$ gravity models, we get very strong constraints on the constant dark energy equation of state, $w_0\in (-1,-0.9997)$ (95% C.L.).

The cosmic microwave background (CMB) and baryon acoustic oscillations (BAO) are two of the most robust observations in cosmology. The recent BAO measurements from the DESI collaboration have presented, for the first time, inconsistency between BAO and CMB within the standard cosmological model ΛCDM, indicating a preference for dynamical dark energy over a cosmological constant. We analyze the theoretical implication of the DESI BAO observation for dark energy and gravity employing a nonparametric reconstruction approach for both the dark energy equation of state w_{DE}(a) and the effective field theory coefficients. We find that the DESI data can rule out quintessence dark energy by indicating a crossing of the phantom divide at z≲1. Furthermore, when analyzed within the broad context of Horndeski gravity which includes general relativity and many known modified gravity theories such as generalized Galileons, f(R), and Brans-Dicke, our result implies that gravity should be nonminimally coupled to explain the observations, establishing the DESI result as the first hint of modified gravity. Based on these insights, we propose the thawing gravity model to explain the nonminimal coupling and phantom crossing indicated by observation, which also fits better to DESI BAO, CMB, and type Ia Supernovae data than ΛCDM.

We compute the large scalar four-point correlation functions in general single field inflation models, where the inflaton Lagrangian is an arbitrary function of the inflaton and its first derivative. We find that the leading order trispectra have four different shapes determined by three parameters. We study features in these shapes that can be used to distinguish among themselves, and between them and the trispectra of the local form. For the purpose of data analyses, we give two simple representative forms for these ``equilateral trispectra''. We also study the effects on the trispectra if the initial state of inflation deviates from the standard Bunch-Davies vacuum.

We investigate the linear cosmological perturbations of Hořava-Lifshitz gravity in a Friedmann-Robertson-Walker universe without any matter. Our results show that a new gauge-invariant dynamical scalar mode emerges, due to the gauge transformation under the “foliation-preserving” diffeomorphism and “projectability condition,” and it can produce a scale invariant power spectrum. In the infrared regime with $\lambda =1$, the dynamical scalar degree of freedom turns to be a nondynamical one at the linear order level.