Although General Relativity (GR) is the well-established theory for the description of the gravitational interaction, there are two main motivations that justify the large amount of research devoted to its modification and extension. The first arises from cosmological grounds, since modified gravity is very efficient in describing the universe’s two phases of accelerated expansion, and moreover it can alleviate the two possible tensions of ΛCDM cosmology, namely the H0 and the σ8 ones. The second, and chronologically older, motivation is purely theoretical, and aims towards the improvement of the renormalizability of General Relativity with the further goal to finally reach to a quantum gravitational theory. Hence, the goal is to construct gravitational theories that possess General Relativity as a particular limit, but which in general include extra degree(s) of freedom that are able to fulfill the above requirements.

Now, Anagnostopoulos and colleagues proposed a specific model in the framework of the recently constructed f(Q) modified gravity, which they showed is very efficient in fitting the cosmological data. In this class of modification, one starts from the so-called symmetric teleparallel theories, which is an equivalent description of gravity using the non-metricity scalar Q, and extends it to an arbitrary function f(Q). f(Q) gravity leads to interesting applications, and trivially passes the constraints arising from gravitational wave observations. By confronting their new model with data from Supernovae type Ia (SNIa), Baryonic Acoustic Oscillations (BAO), Hubble parameter cosmic chronometers (CC) and Redshift Space Distortions (RSD) fσ8 observations, they deduced that the scenario at hand is, in some cases, statistically better than ΛCDM, although it does not include it as a particular limit.

“Nevertheless, confrontation with observations at both background and perturbation levels, namely with Supernovae type Ia (SNIa), Baryonic Acoustic Oscillations (BAO), cosmic chronometers (CC), and Redshift Space Distortion (RSD) data, reveals that the scenario, according to Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and the Deviance Information Criterion (DIC), is at some cases statistically preferred comparing to ΛCDM cosmology.”

For SNIa + CC datasets, they found that the two models are statistically compatible. However, for SNIa + BAOs + CC datasets, their f(Q) model is slightly more preferred (by the data) compared to ΛCDM one. In contrast, for SNIa + BAOs + RSD datasets, the f(Q) model is deemed inferior by the data, however still statistically indistinguishable from ΛCDM.

They also showed that, in the large redshift limit (i.e at large E²(z) ≡ H²(z)/H²0) the proposed f(Q) tends to Q and thus the scenario at hand tends to GR, hence it trivially passes the early universe constraints and in particular the Big Bang Nucleosynthesis (BBN) ones. Additionally, knowing the observational bounds of E²(z) throughout the evolution, and using parameter ‘λ’, they got the effective Newton’s constant,

from which they deduced that throughout the evolution | (Geff/G) − 1| remains smaller than 0.1 and therefore it satisfies the observational constraints.

“In simple terms, the model doesnt exhibit early dark energy features and thus it immediately passes Big Bang Nucleosynthesis constraints, while the variation of the effective Newtons constant lies well inside the observational bounds”

Finally, they concluded that, this result could be used as motivation for further study of the present model, as well as f(Q) gravity in general, as it constitutes one of the first alternatives to the concordance model that apart from being preferred by the data (at least by some datasets), it additionally possesses a Lagrangian description. Further studies on this model, using the full CMB and LSS spectra, weak lensing data and other datasets, could enlighten their findings and verify whether the present f(Q) model outperforms the concordance one or not.

**Featured image: ***The 1σ and 2σ iso-likelihood contours for the f(Q) model, as well as for the ΛCDM scenario, for the 2D subsets of the parameter space (Ωm0, h,M, rd), using graphic package getdist. We have used the joint analysis of SNIa+CC+BAOs datasets. © Anagnostopoulos et al. *

**Reference***: Fotios K. Anagnostopoulos, Spyros Basilakos, Emmanuel N. Saridakis, “First evidence that non-metricity f(Q) gravity can challenge ΛCDM”, Arxiv, pp. 1-4, 2021. **https://arxiv.org/abs/2104.15123*

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