The symmetric teleparallel framework brings about the possibility of alleviating cosmological tensions. The current burning issue in cosmological studies is the increase in discrepancies in measurements from several surveys. Here, we have focused on and tensions, which are important factors in describing the evolution of the Universe from primordial perturbation to late-time acceleration. Additionally, the consistency of the sound horizon is verified against the Planck results. The gravity model is constrained using recently obtained data. Implementing gravitational wave data to study late-time acceleration is one of the key features of our study. Since standard sirens show promising results, the implementation of gravitational waves to probe dark energy is an interesting study. Through our work, we introduce this possibility by performing statistical MCMC analysis for late-time cosmological evolution. Also, the and tensions are explored utilizing gravitational wave data alongside other prominent datasets, such as the latest DESI BAO, redshift space distortion, cosmic chronometers, Pantheon+SH0ES, and cosmic microwave background data. With the results obtained, we analyzed the profile of cosmological parameters. Finally, the study presents the tension of the model with observations, which is found to have a much lower magnitude compared to the current trend. Thus, the considered f(Q) model alleviates tension, making it the best candidate for further investigation.
Cosmology is facing a significant challenge as the era of precision cosmology and high-resolution imaging unveils discrepancies with the standard models of galactic and cosmic evolution. These inconsistencies question the fundamental principles of the dynamics of the Universe, leading to intense debates within the astrophysical community. The discussions focus on scrutinizing observational techniques and reevaluating the basic assumptions of the current cosmological models. Addressing these challenges could solidify the foundations of cosmology and potentially uncover new physical laws or exotic particles influencing the Universe. To understand the issue more deeply, we must first focus on what tension means. Any two independent surveys are expected to yield consistent values for cosmological parameters within an acceptable margin of error. When discrepancies arise between observed results of well-set surveys, this phenomenon is referred to as tension. If the system is free from systematic uncertainties, the primary focus shifts to examining the underlying theoretical assumptions or exploring the potential for new physics. In cosmology, the Hubble parameter is crucial for understanding the expansion of the Universe, relating galaxy velocities to distances. It forms the basis of the cosmic distance ladder, which is essential for observational cosmology. The Hubble constant, , represents its current value and is key to determining the age of the Universe. Observational techniques provide measurements, which can be derived from early-universe models or direct local observations. However, with improved measurements in the corresponding surveys, the discrepancy between the empirical values has been increasing significantly. The observed trend of obtaining precise measurements from early-Universe surveys over the past couple of decades is discussed in references. These surveys are observational studies and experiments that investigate the conditions and properties of the earliest stages, typically within the first few hundred thousand years after the Big Bang, to estimate cosmological parameters. The primary methodology for computing the result relies on a foundational theoretical model, with the standard model serving as the basis. Currently, alongside these methods, several other techniques are employed within the local Universe to determine the value of using the distance-redshift relation. These approaches generally involve building a "local distance ladder," with the most common method being the use of geometric techniques to calibrate the luminosity of specific types of stars, thus estimating the parameter without relying on any particular gravity model. Cepheid variables are commonly utilized to measure distances between 10 and 40 Mpc. In a recent study,, the value of the Hubble constant is reported to be estimated using distance ladder. What is drawing global attention is the fact that this value is in tension with the results from CMB measurements, which give . Averaging different combinations of late-Universe estimates yields values that show tension with those from Planck, with discrepancies ranging from to (The values of tension are usually interpreted as probabilities derived from a one-dimensional normal distribution). In fact, a significant level of tension is observed when the CDM cosmology is constrained against the datasets from different measurements (see Fig. 4 of).
To overcome this issue, in our work, we aim to consider the underlying gravitational framework by modifying geometry and exploring extensions beyond the standard model of cosmology. This modification can be approached in several ways. Here, we focus specifically on modifying General Relativity (GR) by altering the affine connection. The concept of working with modified geometry is not new; shortly after the GR was proposed, researchers began exploring its modifications. Initially motivated by the idea of Weyl, in 1930, Einstein himself explored modifications to his theory, focusing on teleparallelism and tetrad formalism. He identified ten tetrad components with the metric tensor and speculated that the remaining six might represent electromagnetic potentials. Extensions of this work are detailed in advanced discussions. Also, prior to this, in 1922, Cartan introduced a framework incorporating torsion into GR, proposing its connection to quantum angular momentum and noting that torsion vanishes in a vacuum. In the 1960s, Kibble and Sciama revisited this idea, reformulating it within gauge theory for the Poincaré group and extending it to the affine group, leading to metric-affine gauge gravity. Furthermore, this general affine connection can be viewed from a differential geometric perspective where it can be decomposed into three distinct components: the Levi-Civita connection , which is torsion-free, the contortion tensor , which captures the effects of torsion, and the disformation tensor , which represents the influence of nonmetricity. The decomposition is expressed as
with the individual components being
where is the torsion tensor, is the nonmetricity tensor.
In this work, we intend to set our gravity background as the symmetric teleparallel framework in which torsion and curvature are zero, and only nonmetricity is the primary geometric feature. This leads to significant interest and outcomes. This framework has demonstrated its potential to address a wide range of astrophysical and cosmological phenomena. Keeping in mind the success of this theory, our current work aims to provide novel insights and contribute to resolving the persistent tensions in contemporary cosmology.
The manuscript is structured as follows: In section 2, we explain the geometrical background of f(Q) gravity and perform the perturbation analysis within this framework. In section 3, a viable f(Q) model is considered and subsequently confronted with recent observations, as detailed in section 4. The results obtained, along with their implications for addressing cosmological tensions, are discussed in section 5. Finally, we conclude our findings and summarize the study in section 7.