Reconstructing Gravity on Cosmological Scales

TL;DR

This work performs a data-driven reconstruction of late-time gravity theories and Dark Energy models within the Effective Field Theory framework, constraining a finite set of time-dependent functions that capture DE/MG phenomenology. By representing EFT functions on a smooth time grid and applying stability- and priors-informed reconstructions, the authors compare Quintessence, KGB, GBD, Scalar Horndeski, and Full Horndeski models against LCDM using a combined data set of Planck CMB, CMB lensing, weak lensing, BAO, and SN observations, plus a local $H_0$ measurement. They quantify the constraining power via $N_{\rm eff}$ and Bayes factors, finding that SH and FH yield the strongest data-driven improvements and can alleviate the $H_0$ tension, while simpler models offer limited gains. The analysis emphasizes that the EFT approach ties observed deviations to physically viable models, and it highlights degeneracies and prior-volume effects that influence model comparison. The study also discusses limitations (e.g., partial tension resolutions) and outlines future extensions to explore recombination-era physics and higher-order operators to further test gravity and dark energy on cosmological scales.

Abstract

We present the data-driven reconstruction of gravitational theories and Dark Energy models on cosmological scales. We showcase the power of present cosmological probes at constraining these models and quantify the knowledge of their properties that can be acquired through state of the art data. This reconstruction exploits the power of the Effective Field Theory approach to Dark Energy and Modified Gravity phenomenology, which compresses the freedom in defining such models into a finite set of functions that can be reconstructed across cosmic times using cosmological data. We consider several model classes described within this framework and thoroughly discuss their phenomenology and data implications. We find that some models can alleviate the present discrepancy in the determination of the Hubble constant as inferred from the cosmic microwave background and as directly measured. This results in a statistically significant preference for the reconstructed theories over the standard cosmological model.

Figures (18)

• Figure 1: The effective window function, $W_{\rm eff}$, for the different data sets that we consider, normalized to unity at maximum, over the time range of the EFT reconstruction. Different colors represent different probes, as shown in legend. Notice that this is not representative of the overall constraining power of a single data set but only of the times at which a data set is contributing its constraints.
• Figure 2: The joint marginalized posterior distribution of the Hubble constant $H_0$, matter density $\Omega_m$ and the scale of the sound horizon at the time of radiation drag $r_s$. Different colors correspond to different models, as shown in legend. The darker and lighter shades correspond to the $68\%$ C.L. and $95\%$ C.L. regions respectively.
• Figure 3: The joint marginalized posterior distribution of the Hubble constant $H_0$, matter density $\Omega_m$ and the scale of the sound horizon at radiation drag $r_s$. Different colors correspond to different models, as shown in legend. The darker and lighter shades correspond to the $68\%$ C.L. and $95\%$ C.L. regions respectively.
• Figure 4: Reconstruction of Quintessence models.Panel (a) the marginalized posterior distribution of the EFT function $\Delta \Lambda/\Lambda$, describing all Quintessence models, as a function of scale factor and redshift. The white line shows the mean of the distribution while the other contours represent the $68\%$, $95\%$ and $99.7\%$ C.L. regions respectively. The shade represents the posterior probability distribution. The two dashed lines show the redshift of equality between DM and DE, $z_{\rm eq}$, and the redshift of the beginning of cosmic acceleration $z_{\rm acc}$ in the best fitting $\Lambda$CDM model. Panel (b) the KL decomposition of the best fitting Quintessence cosmological model. The continuous black line represent the best fit model. Different lines correspond to different KL modes, as shown in legend. The black dashed line shows the model obtained as the sum of the KL modes that are shown.
• Figure 5: Reconstruction of Quintessence models. The marginalized distribution of the best fitting subspace for the reconstruction of Quintessence models. All quantities follow the same conventions of Fig. \ref{['fig:LambdaReconstruction']}. KL modes have been filtered by requiring that $\sigma_{\rm KL}<3 \sigma_{\Pi}$.