Alternatively, an exponential form for the f ( Q ) function has been recently proposed, explicitly f ( Q ) = Q e λ Q 0 Q, for which a statistical preference over ΛCDM has been found when the combination of cosmic chronometers, SNIa and BAO data sets is considered . A similar investigation has been performed using a power-law term for f ( Q ), namely f ( Q ) = Q + β Q n , for which cosmological solutions and the evolution of the growth index of matter perturbations have been investigated as well . Constraints at background level have been provided using the expansion rate data from early type galaxies, Supernovae type Ia (SNIa), quasars, gamma ray bursts, Baryonic Acoustic Oscillations (BAO) data, and Cosmic Microwave Background (CMB) distance priors, for different parametrizations of f ( Q ) as an explicit function of redshift z . These motivated further exploration of their impact on the cosmological observables.
As such, the main linear perturbation equations for scalar, tensor and vector modes were derived, showing specific modifications with respect to the ΛCDM model . The theory does not show strong coupling problems when considering perturbations around a Friedmann Lemaître Robertson Walker (FLRW) background . It belongs to the Symmetric Teleparallel Gravity ,, in which gravity is attributed to the non-metricity and where f ( Q ) is a general function of the non-metricity scalar, Q. Alternatives beyond ΛCDM, among which those modifying the long range gravitational interaction known as Modified Gravity (MG) theories ,, ,, ,, ,, ,, ,, ,, ,, ,, have been deeply scrutinized, with some of them proving able to alleviate the tensions within 1 − 2 σ ,, ,, ,, ,, , see also for a review.į ( Q ) gravity ,, ,, is a MG theory which recently attracted a lot of attention. In fact, besides the well known theoretical problems ,, ,, , the ΛCDM model suffers from some mild observational tensions as well, namely on the measurements of the value of the Hubble constant H 0 ,, ,, ,, and the present-time amplitude of the matter power spectrum σ 8 0 ,. The resulting cosmological model, known as Λ Cold Dark Matter ( ΛCDM), is recently facing some relevant challenges. The observed late-time accelerated expansion of the Universe ,, ,, ,, , is modelled by the cosmological constant Λ within the Einstein’s theory of General Relativity (GR).
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