[Paper Review] Cosmological observational constraints on the power law $f(Q)$ type modified gravity theory

Sanjay Mandal, Sneha Pradhan+2 more|arXiv (Cornell University)|Sep 29, 2023

Cosmology and Gravitation TheoriesPhysics and Astronomy44 references3 citations

TL;DR

This paper proposes a power-law $f(Q)$ gravity model with $f(Q) = Q + 6\gamma H_0^2 (Q/Q_0)^n$ to explain the accelerated expansion of the Universe, using Markov Chain Monte Carlo (MCMC) analysis on Hubble and Pantheon+SHOES datasets. The model shows consistency with current cosmological observations and provides a viable geometric alternative to $\Lambda$CDM, with distinct cosmographic and dark energy behavior.

ABSTRACT

In modern cosmology, the curiosity of ultimately understanding the nature of the dark energy controlling the recent acceleration of the Universe motivates us to explore its properties by using some novel approaches. In this work, to explore the properties of dark energy we adopt the modified $f(Q)$ gravity theory, where the non-metricity scalar $Q$, emerging from Weyl geometry, plays the dynamical role. For the function $f(Q)$ we adopt the functional form $f(Q)=Q+ 6γ\,H_0^2(Q/Q_0)^n$, where $n,\, γ,\, H_0$ and $Q_0$ are constants. Then, we test our constructed model against the various observational datasets, such as the Hubble, and the Pantheon+SHOES samples, and their combined sample, through the Markov Chain Monte Carlo (MCMC) statistical analysis. We also employ the parameter estimation technique to constrain the free parameters of the model. In addition, we use the constrained values of the model parameters to explore a few implications of the cosmological model. A detailed comparison of the predictions of our model with the $Λ$CDM model is also performed. In particular, we discuss in detail some cosmographic parameters, like the deceleration, the jerk, and the snap parameters, as well as the behavior of the dark energy and matter energy densities to see the evolution of various energy/matter profiles. The $Om$ diagnostics is also presented to test the dark energy nature of our model, as compared to the standard $Λ$CDM paradigm. Our findings show that the considered version of the non-metric $f(Q)$ type modified gravity theory, despite some differences with respect to the $Λ$CDM paradigm, can still explain the current observational results on the cosmological parameters, and provide a convincing and consistent account for the accelerating expansion of the Universe.

Motivation & Objective

• To investigate whether a power-law $f(Q)$ gravity model can explain the observed accelerating expansion of the Universe without invoking a cosmological constant.
• To constrain the model's free parameters ($n$, $\gamma$, $H_0$, $Q_0$) using cosmological observational datasets via MCMC statistical analysis.
• To compare the model's predictions with those of the $\Lambda$CDM paradigm using cosmographic parameters, energy density evolution, and the $Om$ diagnostic.
• To explore the dynamical behavior of dark energy, including its equation of state, and assess its consistency with current data.

Proposed method

• The model adopts a power-law functional form $f(Q) = Q + 6\gamma H_0^2 (Q/Q_0)^n$, where $Q$ is the non-metricity scalar from Weyl geometry.
• Generalized Friedmann equations are derived from the $f(Q)$ gravity action to describe the background evolution of the Universe.
• The Hubble parameter and cosmographic parameters (deceleration, jerk, snap) are computed in redshift space to analyze the expansion history.
• Parameter estimation is performed using MCMC techniques on three datasets: Cosmic Chronometers (CC), Pantheon+SHOES Type Ia supernovae, and their combined sample.
• The $Om$ diagnostic is employed to test the nature of dark energy and compare the model with $\Lambda$CDM.
• The energy density evolution of dark energy and matter is analyzed to assess the model’s consistency with observed cosmic structure formation.

Figure 1: The marginalized constraints on the parameters $H_{0},\Omega_{m0},\,\omega_{0},\omega_{a},n,\gamma$ of our model using the Hubble sample. The dark orange shaded regions presents the $1-\sigma$ confidence level (CL), and the light orange shaded regions present the $2-\sigma$ confidence leve

Experimental results

Research questions

• RQ1 Can the power-law $f(Q)$ gravity model reproduce the observed late-time acceleration of the Universe without a cosmological constant?
• RQ2 How do the cosmographic parameters (deceleration, jerk, snap) evolve in the $f(Q)$ model compared to $\Lambda$CDM?
• RQ3 What are the constrained values of the model parameters $n$, $\gamma$, $H_0$, and $Q_0$ when fitted to Hubble and SNIa data?
• RQ4 How does the dark energy equation of state $\omega_{de}$ behave in this $f(Q)$ model, and does it deviate from $-1$?
• RQ5 Is the $Om$ diagnostic consistent with the $f(Q)$ model being a dark energy candidate, and how does it compare to $\Lambda$CDM?

Key findings

• The power-law $f(Q)$ model provides a consistent fit to the combined Hubble and Pantheon+SHOES datasets, with parameter constraints obtained via MCMC analysis.
• The model exhibits a non-trivial evolution of the deceleration parameter, indicating a transition from decelerated to accelerated expansion, consistent with observations.
• The jerk and snap parameters in the $f(Q)$ model deviate from their $\Lambda$CDM values, suggesting distinct expansion dynamics.
• The dark energy equation of state $\omega_{de}$ evolves with redshift and does not remain constant at $-1$, indicating a dynamical dark energy component.
• The $Om$ diagnostic shows behavior distinct from $\Lambda$CDM, supporting the model as a viable alternative to the cosmological constant.
• The model's predictions for energy density evolution of dark energy and matter are consistent with current cosmological constraints, indicating no immediate conflict with observations.

Figure 2: The red line represents the Hubble parameter profile of the power-law model $f(Q)$ model with the constraint values of $H_{0},\Omega_{m0},\,\omega_{0},\omega_{a},n,\gamma$ . The blue dots with the green bars represent the CC sample, and the black dotted line represents the Hubble parameter